Optimization-based hierarchical cooperative control of traffic rules and mixed traffic in multi-intersection environments

Abstract

The present disclosure provides a system and method for jointly controlling one or more connected autonomous vehicles (CAVs) and one or more human-operated vehicles (HDVs) according to integer constraints for traversing each of a plurality of intersections on a roadway. The method includes collecting digital representations of the states of each CAV, each HDV, and each traffic sign; solving an optimization problem to jointly optimize traffic flow based on a macroscopic traffic flow model in a centralized traffic controller (CTC) according to a convex relaxation of the integer constraints; and solving a multivariable mixed integer programming (MIP) problem in each of a plurality of intersection traffic controllers (ITCs), the multivariable MIP problem optimizing a cost function to minimize tracking error in traffic flow values ​​of the microscopic traffic flow model relative to the relaxed traffic flow values ​​from the CTC; and transmitting the optimized values ​​of control commands to the corresponding CAVs and the corresponding traffic signs.

Description

[Technical Field]

[0001] The present disclosure relates generally to optimization-based control, and more particularly to a method and apparatus for optimization-based hierarchical cooperative control of dynamic traffic rules and mixed traffic in a transportation network of multiple interconnected traffic intersections. [Background technology]

[0002] The automation of transportation systems, even partial automation, leads to fewer road accidents and more efficient use of road networks. Connected and automated vehicles (CAVs) therefore hold great promise for improving safety and traffic flow, resulting in reduced congestion, journey times, emissions, and energy consumption. While this has been known for decades, much of the successful development has been achieved in recent years through technological advances in sensing, computing, control, and connectivity. While road conditions are often highly dynamic—vehicle participants and their behaviors change rapidly and significantly—vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) communications (also known as vehicle-to-everything (V2X) communications for short) enable efficient planning and decision-making by providing access to real-time information about all vehicles within a specific planning area.

[0003] Significant progress has been made in planning and control for autonomous driving, which typically requires a multi-layered guidance and control architecture implemented onboard the vehicle. At the highest level, an intelligent navigation system finds a route through the transportation network from the vehicle's current location to the requested destination. Decision makers select the appropriate driving behavior at any given time, taking into account the route plan, current environmental conditions, and the behavior of other traffic participants, using, for example, set reachability or automata combined with formal languages ​​and optimization. Given target behaviors, including lane following, lane changing, or stopping, motion planning algorithms calculate dynamically feasible and safe trajectories that low-level feedback controllers can track in real time. A common approach uses a sampling-based motion planner combined with model predictive control (MPC) for reference tracking. While the guidance and control architecture for CAVs may appear similar to that for standard autonomous driving, some modules may be implemented within the infrastructure, such as a mobile edge computer (MEC), to provide decisions for multiple vehicles in an area, while other modules may still be implemented individually onboard each vehicle.

[0004] Coordinating cooperative agents makes it possible to reach a socially optimal behavior for a transportation network. As an example, we describe a first-come, first-serve (FCFS) policy for autonomous traffic management at intersections. Recently, coordination strategies for intersection control using nonlinear optimization or mixed-integer linear programming (MILP) have been proposed. The latter has been extended to a distributed MILP algorithm for scheduling grids of interconnected intersections. Also, a MILP-based approach for on-ramp merging of CAVs has been proposed. Alternative techniques for coordinating CAVs can be found in the following references, but it should also be noted that the intersection and merging control problems are very similar in nature.

[0005] In certain areas, such as parking lots and shipping yards, certain urban networks, automated roads, or industrial parks, the operation of CAVs can be coordinated from a centralized infrastructure computer, such as an edge computer or a cloud computer, to achieve optimization of the entire transportation network, such as minimizing average or worst-case travel time, overall idling time, etc. Such a centralized coordination system will hereinafter be referred to as a Central Traffic Coordinator (CTC). In some cases, only autonomous vehicles may be on the road, which means that the CTC directly controls all vehicles in the transportation network.

[0006] However, in most situations, it is reasonable to expect that autonomous vehicles will share the road with conventional vehicles, i.e., human-driven vehicles (HDVs), for many years, possibly forever. Therefore, ensuring proper interaction between automated and manual vehicles is paramount to optimizing traffic behavior across the transportation network. In these cases, CTC only needs to directly control CAVs while assuming a specific behavior for HDVs. In some approaches, HDVs are always prioritized since there is nothing to change their behavior, and CAVs will always adjust their behavior to the expected behavior of HDVs. However, this solution is inherently suboptimal because only partial control of the vehicles is possible in this situation.

[0007] In other HDV-only situations, HDV traffic flow is controlled through controllable roadway infrastructure elements, such as traffic lights. HDV flow is influenced by the timing and sequencing of traffic lights, such that the overall operation of the transportation network is positively affected. However, in such models, because vehicles are driven by human drivers, the only control effect over the vehicles is to stop them at specific locations at specific times. Therefore, the ability to control only traffic lights limits control over the transportation network. To address this issue, centralized coordination systems and methods are used to coordinate the operation of CAVs and to achieve overall optimization of transportation networks that include multiple connected traffic intersections as well as a mix of CAVs and HDVs, using controllable infrastructure elements, such as traffic lights, that can affect HDV traffic. However, the resulting centralized optimization problem is a large-scale mixed-integer programming (MIP) problem that is computationally challenging to solve in real time.

[0008] Therefore, there is a need to consider a computationally traceable, optimization-based hierarchical system and method that coordinates the real-time operation of CAVs and controllable infrastructure elements, such as traffic lights, that can affect HDV traffic by solving one or more decoupled optimization problems to achieve overall optimization of a transportation network that includes multiple connected traffic intersections and has a mix of CAVs and HDVs. Summary of the Invention

[0009] Some embodiments are based on the recognition that there is a need for a solution for the global optimization of transportation networks with mixed traffic that is computationally tractable and has higher computational performance than the previous solutions mentioned above.

[0010] An objective of some embodiments is to provide an optimization-based hierarchical system and method for dynamic traffic rules and collaborative coordination and control of mixed traffic including connected autonomous vehicles (CAVs) and human-driven vehicles (HDVs) in a transportation network of multiple connected traffic intersections. In some embodiments of the present disclosure, the hierarchical system calculates dynamic traffic rules that affect HDVs over a forecast horizon via controllable infrastructure elements, referred to herein as traffic signs. Examples of traffic signs include traffic light signals, lane enabling electronic displays, and variable speed limits. In some embodiments of the present disclosure, the hierarchical system calculates a sequence of speed targets over a forecast horizon for each CAV in the transportation network, and these target trajectories can be executed by each CAV's on-board planning and control architecture.

[0011] Some embodiments are based on the recognition that by decomposing the problem into a high-level global centralized traffic controller (CTC) using a simplified macroscopic traffic model and into a set of lower-level locally decoupled intersection traffic controllers (ITCs) based on a more accurate microscopic traffic model, both computational traceability and high control performance are achieved in an optimization-based hierarchical system and method. Some embodiments of the present disclosure are based on the recognition that the global CTC optimization problem is computationally tractable due to the simplified macroscopic traffic model, and that each of the local ITC optimization problems is computationally tractable due to restricting decision variables to vehicles in a local neighborhood around one particular traffic intersection in the transportation network. At each control time step, the global CTC controller calculates a high-level target for traffic flow in the multi-intersection network. Based on the global CTC target, at each control time step, the local ITCs independently calculate one or more dynamic traffic rules and safe, optimal control trajectories for one or more CAVs in the neighborhood around each traffic intersection in the transportation network.

[0012] In one embodiment, the hierarchical system is based on a multi-layer guidance and control architecture, in which some modules are implemented onboard each CAV and other modules operate centralized or decentralized within the transportation network infrastructure, e.g., in mobile edge computers, to take advantage of V2X connectivity. Specifically, in each CAV, given a target behavior representing an action such as lane following, lane changing, or stopping, a motion planning algorithm calculates a dynamically feasible and safe trajectory that the corresponding CAV's vehicle controller can track in real time. Some embodiments are based on a probabilistic sampling-based motion planner and an MPC algorithm for reference tracking in each CAV.

[0013] Some embodiments recognize that, depending on the infrastructure of a transportation network, obtaining accurate predictions for HDVs may be difficult. Therefore, in some embodiments, a hierarchical vehicle coordination and scheduling module is implemented in a retreating horizon manner based on up-to-date information. Some embodiments recognize that a CTC controller may calculate high-level targets over a medium- or long-term forecast horizon relatively infrequently, while an ITC controller may calculate control trajectories over a short- or medium-term forecast horizon relatively frequently, e.g., an update period of 0.5 to 1 second for each ITC controller, while an update period of 1 to 2 seconds is used for the global CTC controller. Any discrepancies in the predictions can be accommodated by the inherent feedback mechanism of the retreating horizon strategy of the coordination system.

[0014] Some embodiments recognize that the presence of other traffic participants, including, for example, bicycles and pedestrians, can be managed as obstacles by onboard modules, such as motion planning and / or vehicle control algorithms, within each CAV's multi-layer guidance and control architecture. Due to their relatively low computational cost compared to hierarchical vehicle coordination systems, motion planning and vehicle control algorithms can run at relatively fast sampling rates in order to have fast reaction times to unexpected changes in the behavior of other traffic participants, including, for example, bicycles, pedestrians, and other vehicles within a transportation network. For example, vehicle control algorithms often run with update periods of 50-100 milliseconds.

[0015] In some embodiments, the global CTC controller solves a medium- or long-term horizon optimization problem that calculates high-level targets for traffic flow in a multi-intersection network based on a simplified macroscopic traffic model for a transportation network of connected intersections. In some embodiments, the high-level target for each traffic intersection corresponds to the percentage of the intersection's capacity that should be allocated to each traffic direction in which vehicles may pass through the traffic intersection. In this case, the high-level target can be either a time-varying sequence of percentage values ​​or a constant set of average percentage values ​​over a forecast horizon. These high-level targets can be used to prioritize traffic flow in specific directions through one or more connected traffic intersections to reduce overall congestion, travel times, emissions, and energy consumption of vehicles in the transportation network.

[0016] In some embodiments, the simplified macroscopic traffic model may be based on representing the transportation network, for example, as a directed graph, where each road segment is represented as a node and each traffic direction is represented as an edge. The state of the macroscopic traffic model may include the number of vehicles planning to go straight, turn left, or turn right at each road segment, represented as a node in the directed graph. Inputs to the macroscopic traffic model may include the number of vehicles transitioning from one road segment to the next, taking into account the directed graph and the maximum capacity of each traffic intersection and time delay constraints that enforce the expected travel time of vehicles within each road segment. In other embodiments, the simplified macroscopic traffic model may be based on a Cell Transmission Model (CTM).

[0017] In some embodiments, the optimization problem of the global CTC controller is a convex optimization problem for which a globally optimal solution can be calculated at each time step of the global CTC controller. For example, the CTC controller may use a linear traffic flow model, linear inequality constraints, and a linear objective function, resulting in a convex linear programming (LP) problem that can be solved using an LP optimization algorithm, such as the simplex method, the active constraint method, or the interior point method. In some embodiments, the optimization problem of the global CTC controller is a nonconvex smooth nonlinear programming (NLP) or mixed integer programming (MIP) optimization problem for which a locally optimal or suboptimal solution can be calculated at each time step of the global CTC controller.

[0018] In some embodiments, each ITC controller solves a short- or medium-term horizon optimization problem that calculates a sequence of speed targets and lane-change commands for each CAV, as well as a sequence of commands for one or more dynamic traffic rules, e.g., traffic light signals, in the vicinity of a traffic intersection. The resulting optimization problem is an MIP, e.g., a mixed-integer linear programming (MILP) or mixed-integer quadratic programming (MIQP) problem. Some embodiments of the present disclosure are based on the recognition that each ITC controller solves the MIP based on a microscopic traffic model that includes prediction and control for each of the vehicles and dynamic traffic rules in the transportation network.

[0019] In one example, a microscopic traffic model involves predicting the motion of each CAV based on a controlled, discrete-time system subject to constraints. The constraints include the CAV's physical limitations in terms of acceleration, speed, lane changes, and steering, obstacle avoidance constraints, and traffic rules that the CAV must satisfy. Traffic rules may be expressed in MIP as mixed logical inequality constraints. For example, these traffic rules may enforce that a CAV can enter a traffic intersection in a particular direction only if the corresponding traffic light signal is green at that time step. MIP objectives include maximizing traffic throughput while minimizing a combination of waiting time and fuel consumption.

[0020] In some embodiments, the microscopic traffic model includes predicting HDV behavior using a switched dynamic system to represent HDV responses to potentially changing traffic rules. In one example, the state-dependent switched dynamics may include: (1) if a traffic light for the HDV's desired traffic direction is red and the HDV is within a predetermined distance from a stopping zone at a particular intersection, the HDV stops at the traffic light at this intersection; (2) otherwise, if a leading vehicle is within a certain predetermined distance ahead of the HDV in the transportation network, the HDV follows the leading vehicle to maintain a safe following distance; and (3) otherwise, the HDV travels at a desired target speed through the transportation network.

[0021] In some embodiments, HDV modeling can be used to model both HDVs and CAVs controlled by different ITCs. To that end, each CAV can be assigned to a specific ITC dedicated to control or prediction. This technique is used to improve the safety of traffic controllers, especially when vehicles transition from one ITC to the next. In some embodiments, the assignment of vehicles to each ITC controller can be performed in the following given steps, but is not limited to: (1) Each HDV is assigned to the predictive ITC of the next traffic intersection if it is within a predetermined distance.

[0022] (2) Each CAV is assigned to the ITC for control of the next traffic intersection if it is within a predetermined distance.

[0023] (3) Each CAV is assigned to the predictive ITC of the preceding traffic intersection if it is within a predetermined distance, i.e., it will be considered an HDV by the ITC controller.

[0024] In some embodiments of the present disclosure, each ITC calculates CAV speeds and lane change trajectories, as well as traffic light phase switching trajectories for its particular traffic intersection, and these calculations for each ITC may be performed in parallel on separate computing units.

[0025] Some embodiments recognize that optimization problems for CTC and ITC controllers can be solved exactly or inexactly. An exact solution is feasible and locally or globally optimal, while an inexact solution can be approximately feasible or suboptimal. Examples of exact optimization algorithms include, but are not limited to, interior point methods, active constraint methods, gradient methods, operator decomposition, sequential quadratic programming, sequential convex programming, branch and bound, branch and cut, and branch and price methods. Examples of inexact optimization algorithms include, but are not limited to, heuristic rules, early termination of exact optimization algorithms, rounding methods, machine learning-based approximations of optimal solutions, or approximate dynamic programming.

[0026] In some embodiments, one or both of the CTC and ITC control policies may be approximated by a deep neural network architecture. In one, but not limited to, example, reinforcement learning may be used to directly maximize a reward function for reducing congestion, travel time, emissions, and energy consumption in a transportation network. In other embodiments, one or both of the CTC and ITC control policies may be implemented using a deep neural network architecture based on imitation learning, which aims to approximate an expert solution of the corresponding optimization problem using an exact optimization algorithm.

[0027] Accordingly, some embodiments disclose a traffic control system for jointly controlling one or more connected and autonomous vehicles (CAVs) and one or more human-operated vehicles (HDVs) traversing a plurality of intersections of a road according to integer constraints for traversing each of the intersections. The traffic control system includes at least one processor and a memory having stored thereon instructions that, when executed by the at least one processor, cause the traffic control system to collect digital representations of the states of each of the CAVs, each of the HDVs, and each traffic sign regulating traffic on the road. The at least one processor further causes the traffic control system to solve an optimization problem to jointly optimize traffic flow based on a macroscopic traffic flow model in a centralized traffic controller (CTC) for the plurality of intersections using convex optimization subject to convex relaxation of the integer constraints for traversing each of the plurality of intersections. The at least one processor further causes the traffic control system to solve a multivariable mixed integer programming (MIP) problem in each of a plurality of intersection traffic controllers (ITCs), individually for each of the plurality of intersections, to generate control command values ​​for changing the state of each of the CAVs associated with an intersection among the plurality of intersections and control command values ​​for changing the state of each of the traffic signs associated with the intersection, the multivariable MIP problem optimizing a cost function according to the integer constraints to minimize a tracking error in traffic flow values ​​of a microscopic traffic flow model relative to relaxed traffic flow values ​​from the ITC, the cost function being optimized according to a motion model of the CAV described by differential equations relating control commands for the CAVs associated with the intersections to changes in the state of the CAVs, and according to a motion model of the HDV described by switching functions relating dynamic traffic rules for HDVs to the state of the HDV and the states of corresponding traffic signs. The at least one processor further causes the traffic control system to transmit the optimized values ​​of the control commands to the corresponding CAVs and corresponding traffic signs.

[0028] According to another embodiment, a method is disclosed for jointly controlling one or more connected autonomous vehicles (CAVs) and one or more human-operated vehicles (HDVs) traversing a plurality of intersections of a road according to integer constraints for traversing each of the intersections. The method includes collecting digital representations of the states of each of the CAVs, each of the HDVs, and each traffic sign regulating traffic on the road. The method further includes solving an optimization problem to jointly optimize traffic flow based on a macroscopic traffic flow model in a centralized traffic controller (CTC) for the plurality of intersections using convex optimization subject to convex relaxation of the integer constraints for traversing each of the plurality of intersections. The method further includes solving a multivariable mixed integer programming (MIP) problem in each of a plurality of intersection traffic controllers (ITCs), individually for each of the plurality of intersections, to generate control command values ​​for changing the state of each of the CAVs associated with an intersection among the plurality of intersections and control command values ​​for changing the state of each of the traffic signs associated with the intersection, the multivariable MIP problem optimizing a cost function according to the integer constraints to minimize a tracking error in traffic flow values ​​of a microscopic traffic flow model relative to relaxed traffic flow values ​​from the ITC, the cost function being optimized according to a motion model of the CAV described by differential equations relating control commands for the CAVs associated with the intersections to changes in the state of the CAVs, and according to a motion model of the HDV described by switching functions relating dynamic traffic rules for the HDVs to the state of the HDVs and the states of the corresponding traffic signs, and transmitting the optimized values ​​of the control commands to the corresponding CAVs and the corresponding traffic signs.

[0029] Accordingly, yet another embodiment discloses a non-transitory computer-readable storage medium having embodied thereon a program executable by a processor for performing a method for jointly controlling one or more connected and automated vehicles (CAVs) and one or more human-operated vehicles (HDVs) traversing a plurality of intersections of a road according to integer constraints for traversing each of the intersections. The method includes collecting digital representations of the states of each of the CAVs, each of the HDVs, and each traffic sign regulating traffic on the road. The method further includes solving an optimization problem to jointly optimize traffic flow based on a macroscopic traffic flow model in a centralized traffic controller (CTC) for the plurality of intersections using convex optimization subject to convex relaxation of the integer constraints for traversing each of the plurality of intersections. The method further includes solving a multivariable mixed integer programming (MIP) problem in each of a plurality of intersection traffic controllers (ITCs), individually for each of the plurality of intersections, to generate control command values ​​for changing the state of each of the CAVs associated with an intersection among the plurality of intersections and control command values ​​for changing the state of each of the traffic signs associated with the intersection, the multivariable MIP problem optimizing a cost function according to the integer constraints to minimize a tracking error in traffic flow values ​​of a microscopic traffic flow model relative to relaxed traffic flow values ​​from the ITC, the cost function being optimized according to a motion model of the CAV described by differential equations relating control commands for the CAVs associated with the intersections to changes in the state of the CAVs, and according to a motion model of the HDV described by switching functions relating dynamic traffic rules for the HDVs to the state of the HDVs and the states of the corresponding traffic signs, and transmitting the optimized values ​​of the control commands to the corresponding CAVs and the corresponding traffic signs. The presently disclosed embodiments are further described with reference to the accompanying drawings, in which: The drawings shown are not necessarily to scale, emphasis instead generally being placed upon illustrating the principles of the presently disclosed embodiments. [Brief explanation of the drawings]

[0030] [Figure 1] FIG. 1 is a block diagram illustrating an example network environment for optimization-based hierarchical traffic control of controlled and non-controlled vehicles, according to some embodiments of the present disclosure. [Figure 2] 1 is a flowchart illustrating an exemplary method for optimization-based hierarchical traffic control of controlled and uncontrolled vehicles in accordance with one embodiment of the present disclosure. [Figure 3] FIG. 1 illustrates an example of traffic conditions in a local area of ​​multiple interconnected traffic intersections for optimization-based hierarchical traffic control of controlled and uncontrolled vehicles, according to some embodiments of the present disclosure. [Figure 4A] FIG. 1 illustrates an example of controlling traffic in a local area of ​​multiple interconnected traffic intersections using dynamic traffic rules and optimization-based hierarchical cooperative control of mixed traffic, according to some embodiments of the present disclosure. [Figure 4B] FIG. 1 illustrates an example of traffic conditions and routing information for multiple connected autonomous vehicles in a local area of ​​interconnected intersections, according to some embodiments of the present disclosure. [Figure 5] FIG. 1 is a schematic diagram of possible interactions between a hierarchical traffic control system, a mapping and navigation system, one or more control vehicles and human-operated vehicles, roadside units, a traffic light controller, and a mobile edge computer, according to some embodiments of the present disclosure. [Figure 6A] FIG. 1 is a schematic diagram of a feedback loop for a hierarchical traffic control system in a transportation network, according to some embodiments of the present disclosure. [Figure 6B] FIG. 1 is a schematic diagram of a feedback loop for one Intersection Traffic Controller (ITC) of a hierarchical traffic control system in a transportation network, according to some embodiments of the present disclosure. [Figure 6C] FIG. 1 is a schematic diagram of a feedback loop for a hierarchical traffic control system in a transportation network, according to some embodiments of the present disclosure. [Figure 7] FIG. 1 illustrates an example operation for optimization-based hierarchical traffic control of controlled and non-controlled vehicles according to one embodiment of the present disclosure. [Figure 8A] FIG. 1 is an exemplary situation diagram of a four-way traffic intersection in a transportation network controlled by a hierarchical traffic control system, according to some embodiments of the present disclosure. [Figure 8B] FIG. 1 illustrates an example of a mapping between multiple conflict-free states and traffic light signal values ​​for each cross direction of a traffic intersection in a transportation network controlled by a hierarchical traffic control system, according to some embodiments of the present disclosure. [Figure 8C] FIG. 1 illustrates an example of a traffic flow plan calculated by a centralized traffic coordinator (CTC) using a table of traffic flow values ​​for each cross direction of a traffic intersection in a transportation network controlled by a hierarchical traffic control system, according to some embodiments of the present disclosure. [Figure 9] FIG. 1 illustrates an example cost function adaptation method for a hierarchical traffic control system, according to some embodiments of the present disclosure. [Figure 10A] FIG. 1 illustrates an example of a multi-lane road segment in a transportation network, according to some embodiments of the present disclosure. [Figure 10B] FIG. 1 illustrates an example of vehicle density values ​​over a forecast time horizon for a multi-lane road section in a transportation network used in a macroscopic traffic flow model of a hierarchical traffic control system, according to some embodiments of the present disclosure. [Figure 10C] FIG. 1 illustrates an example of multiple traverse directions over a forecast time range for a three-way traffic intersection in a transportation network, according to some embodiments of the present disclosure. [Figure 10D] FIG. 1 illustrates an example of traffic flow values ​​in multiple cross directions over a forecast time horizon for a three-way traffic intersection in a transportation network used in a macroscopic traffic flow model of a hierarchical traffic control system, according to some embodiments of the present disclosure. [Figure 10E] FIG. 1 illustrates an example of multiple traverse directions over a forecast time range for a three-way traffic intersection in a transportation network, according to some embodiments of the present disclosure. [Figure 10F] FIG. 1 illustrates an example of vehicle density values ​​in multiple cross directions over a forecast time horizon for a three-way traffic intersection in a transportation network used in a macroscopic traffic flow model of a hierarchical traffic control system, according to some embodiments of the present disclosure. [Figure 11A] FIG. 1 illustrates a method for formulating and solving a constrained optimization problem for computing a macroscopic traffic flow motion plan for one or more traffic lights and connected autonomous vehicles (CAVs) in a transportation network that includes multiple interconnected traffic intersections, according to some embodiments of the present disclosure. [Figure 11B] FIG. 1 illustrates a method for formulating and solving a constrained convex programming (CP) problem for computing an optimal sequence of high-level target values ​​for traffic flows in a transportation network of multiple interconnected traffic intersections, according to some embodiments of the present disclosure. [Figure 11C] FIG. 1 illustrates a method for formulating and solving a constrained convex programming (CP) problem for computing an optimal sequence of high-level target values ​​for traffic flows in a transportation network of multiple interconnected traffic intersections, according to some embodiments of the present disclosure. [Figure 12A] FIG. 1 illustrates a method for formulating and solving a constrained optimization problem for computing a microscopic traffic flow motion plan for one or more traffic lights and connected autonomous vehicles (CAVs) in a local area around one or more interconnected traffic intersections in a transportation network, according to some embodiments of the present disclosure. [Figure 12B] FIG. 1 is a schematic diagram of a MIP problem formulation based on a microscopic traffic model for mixed traffic in a local area controlled by an ITC around one or more traffic intersections in a transportation network, according to some embodiments of the present disclosure. [Figure 12C]FIG. 10 is a flow diagram of a switching function in a predictive motion model of one or more HDVs used in a microscopic model for mixed traffic in a local area controlled by an ITC around one or more traffic intersections in a transportation network controlled by a hierarchical traffic control system, according to some embodiments of the present disclosure. [Figure 12D] FIG. 1 is a schematic diagram of a motion model for HDV according to some embodiments of the present disclosure. [Figure 12E] FIG. 1 illustrates a method for constructing and solving a MIP problem based on mixed-integer equality and inequality constraints for a predictive motion model of one or more CAVs, HDVs, TLCs, and non-convex traffic rules in a transportation network controlled by a hierarchical traffic control system, according to some embodiments of the present disclosure. [Figure 13] FIG. 1 illustrates an example of a traffic situation in a transportation network of multiple interconnected traffic intersections including mixed traffic of CAVs and HDVs controlled by one CTC in combination with multiple ITCs in a hierarchical traffic control system, according to some embodiments of the present disclosure. [Figure 14A] FIG. 2 is a schematic diagram of an example integer optimization variable search tree representing a nested tree of search spaces for integer feasible optimal solutions for hierarchical traffic control, according to some embodiments of the present disclosure. [Figure 14B] FIG. 1 is a block diagram of a branch-and-bound mixed integer optimization algorithm for searching for integer-feasible optimal decision solutions based on a nested tree of search regions and corresponding lower / upper bounds, according to some embodiments of the present disclosure. [Figure 14C] FIG. 1 is a block diagram of a branch-and-bound mixed integer optimization algorithm for searching for integer-feasible optimal decision solutions based on a nested tree of search regions and corresponding lower / upper bounds, according to some embodiments of the present disclosure. [Figure 15] FIG. 1 illustrates a block diagram of a hierarchical traffic control system for calculating motion plans for one or more controlled vehicles in a transportation network of one or more interconnected conflict zones, according to some embodiments of the present disclosure. [Figure 16A] FIG. 1 is a schematic diagram of a vehicle including a multi-layer guidance and control architecture according to some embodiments of the present disclosure. [Figure 16B] FIG. 1 is a schematic diagram of the interaction between the multi-layer guidance and control architecture and other controllers of the vehicle, according to some embodiments of the present disclosure. DETAILED DESCRIPTION OF THE INVENTION

[0031] Some embodiments of the present disclosure provide systems and methods for controlling one or more connected and autonomous vehicles (CAVs) in a transportation network that is made up of one or more interconnected traffic intersections and that includes a dynamic environment, including, but not limited to, one or more human-operated vehicles, traffic participants, or dynamic obstacles.

[0032] As used in this specification and claims, the terms "for example," "for instance," and "such as," as well as the verbs "comprising," "having," "including," and other forms of those verbs, when used in conjunction with a list of one or more components or other items, should each be construed as open-ended, meaning that the list should not be considered to exclude further components or items. The term "based on" means based at least in part on. Furthermore, it should be understood that the phraseology and terminology used herein are for purposes of description and should not be regarded as limiting. Any headings used within this description are for convenience only and do not have any legal or restrictive effect.

[0033] FIG. 1 is a block diagram illustrating an exemplary network environment for optimization-based hierarchical traffic control of controlled and uncontrolled vehicles, according to one embodiment of the present disclosure. Referring to FIG. 1, a network environment 100 is shown. The network environment 100 may include a hierarchical traffic control system 102 and a transportation network 104 communicatively coupled to the hierarchical traffic control system 102. Further shown is a communications network 106 and a database 108 accessible to the hierarchical traffic control system 102 via the communications network 106. While FIG. 1 illustrates the hierarchical traffic control system 102, the communications network 106, and the database 108 as separate devices, in some embodiments, the entire functionality of the hierarchical traffic control system 102, the communications network 106, and the database 108 may be incorporated into the hierarchical traffic control system 102 without departing from the scope of the present disclosure.

[0034] The hierarchical traffic control system 102 may include suitable logic, circuitry, code, and / or interfaces that may be configured to generate control commands that change the state of controlled vehicles and traffic signs or traffic lights associated with multiple intersections in the transportation network 104. The hierarchical traffic control system 102 transmits the generated control commands to the controlled vehicles and traffic signs or traffic lights. Examples of the hierarchical traffic control system 102 may include, but are not limited to, a server, a computer workstation, a mainframe machine, and / or a laptop.

[0035] The transportation network 104 may include a control vehicle 110, human-operated vehicles 112, a traffic controller 114, and sensors 116. While the sensors 116 are shown in FIG. 1 as being separate from the control vehicle 110 and the human-operated vehicles 112, in some embodiments, the entire functionality of the sensors 116 may be individually incorporated into the control vehicle 110 or the human-operated vehicles without departing from the scope of the present disclosure. Examples of the control vehicles 110 may include, but are not limited to, unmanned vehicles, connected autonomous vehicles (CAVs), and / or connected semi-autonomous vehicles. Examples of the human-operated vehicles 112 may include, but are not limited to, manually operated vehicles that are largely governed and controlled by a human. Examples of the traffic controller 114 may include, but are not limited to, traffic lights or traffic signs that control the movement of traffic on roads and across intersections within the transportation network 104. The color of the traffic light or traffic sign defines whether to stop, continue moving, or slow down vehicles traveling on roads or intersections in the transportation network 104. Examples of sensors 116 may include, but are not limited to, rangefinders, radar, lidar, or cameras to accurately detect the state of vehicles and the dynamic environment, including connected and non-connected vehicles, autonomous, semi-autonomous, and manually operated vehicles, and other traffic participants such as bicyclists and pedestrians.

[0036] The communication network 106 may include a communication medium through which the hierarchical traffic control system 102 can communicate with the transportation network 104 and other devices omitted from this disclosure for brevity. The communication network 106 may be one of a wired connection or a wireless connection. Examples of the communication network 106 may include, but are not limited to, the Internet, a cloud network, a wireless fidelity (Wi-Fi) network, a personal area network (PAN), a local area network (LAN), or a metropolitan area network (MAN). The various devices in the network environment 100 may be configured to connect to the communication network 106 according to various wired and wireless communication protocols. Examples of such wired and wireless communication protocols may include, but are not limited to, at least one of Transmission Control Protocol and Internet Protocol (TCP / IP), User Datagram Protocol (UDP), Hypertext Transfer Protocol (HTTP), File Transfer Protocol (FTP), Zig Bee, EDGE, IEEE 802.11, Light Fidelity (Li-Fi), 802.16, IEEE 802.11s, IEEE 802.11g, multi-hop communication, wireless Access Point (AP), end-to-end communication, cellular communication protocols, and Bluetooth (BT) communication protocols.

[0037] The database 108 may include suitable logic, circuitry, and / or interfaces that may be configured to store a traffic model for the transportation network 104. In another embodiment, the database 108 may store program instructions executed by the hierarchical traffic control system 102. The traffic model may include a microscopic traffic model or a macroscopic traffic model. Exemplary implementations of the database 108 may include, but are not limited to, random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), hard disk drive (HDD), solid-state drive (SSD), CPU cache, and / or secure digital (SD) card.

[0038] FIG. 2 is a flowchart illustrating an exemplary method for optimization-based hierarchical traffic control of controlled and uncontrolled vehicles in accordance with one embodiment of the present disclosure. FIG. 2 is described in relation to elements from FIG. 1. With reference to FIG. 2, a flowchart 200 is shown. The method illustrated in flowchart 200 may be performed by any computing system, such as hierarchical traffic control system 102, for collaboratively controlling one or more connected and autonomous vehicles (CAVs) and one or more human-operated vehicles (HDVs) traversing multiple intersections of a road according to integer constraints for traversing each of the intersections. The method begins at 200-1 and proceeds to 200-4.

[0039] In 200-1, digital representations of the status of each CAV, each HDV, and each traffic sign or traffic light regulating traffic on a road are collected. Details of collecting the status of each CAV, each HDV, and each traffic sign are described, for example, with reference to FIG. 3. In one example, the status of the CAV includes, but is not limited to, at least one of the CAV's position, speed, acceleration, and lane. In one example, the status of the traffic sign or traffic light includes, but is not limited to, the color of the traffic sign or traffic light. The color of the traffic sign or traffic light is one of red, yellow, or blue. In one example, the status of the HDV includes, but is not limited to, at least one of the HDV's position, speed, acceleration, and lane.

[0040] In 200-2, an optimization problem for jointly optimizing traffic flow is solved based on a macroscopic traffic flow model in a centralized traffic controller (CTC) for multiple intersections using convex optimization that undergoes convex relaxation of integer constraints for traversing each of the multiple intersections. In one embodiment, optimizing traffic flow includes optimizing traffic flow values ​​through convex relaxation of integer constraints for traversing each of the multiple intersections. Optimizing the traffic flow values ​​results in relaxed traffic flow values. The integer constraints are carefully designed and incorporated into the optimization problem to avoid collisions, for example, while traversing the intersections. The integer constraints restrict some or all of the variables in the optimization problem to take on only integer values. This makes it possible to accurately model optimization problems that involve discrete quantities, such as discrete representations of the states of each CAV, each HDV, and each traffic sign or traffic light regulating traffic on the road. Convex optimization of integer constraints is a problem in which all constraints are convex functions, and the objective is a convex function in the case of minimization or a concave function in the case of maximization. In general, relaxation simply refers to a technique for removing certain constraints from an optimization problem. Specifically, convex relaxation means that the problem becomes convex upon relaxation or removal of certain constraints. In one embodiment, the convex relaxation of integer constraints enforcing multiple traffic rules includes convex relaxation of integer constraints for vehicles crossing each intersection and traffic light switching behavior. To this end, the traffic flow values ​​are relaxed using a convex relaxation that includes removing certain constraints to obtain relaxed traffic flow values, which make the optimization problem convex.

[0041] At 200-3, a multivariable mixed integer programming (MIP) problem is solved in each of the multiple intersection traffic controllers (ITCs) to generate control command values ​​for changing the state of each CAV associated with an intersection among a plurality of intersections and control command values ​​for changing the state of each traffic sign associated with the intersection. To generate control command values ​​for changing the state of each CAV associated with the intersection and control command values ​​for changing the state of each traffic sign associated with the intersection, the multivariable MIP problem optimizes a cost function, subject to integer constraints, to minimize tracking errors in traffic flow values ​​of a microscopic traffic flow model relative to relaxed traffic flow values ​​from the CTC. In one embodiment, the cost function is optimized according to a motion model of the CAV associated with the intersection described by differential equations relating control commands for the CAV to changes in the state of the CAV, and according to a motion model of the HDV described by switching functions relating dynamic traffic rules for the HDV to the state of the HDV and the states of corresponding traffic signs.

[0042] At 200-4, the optimized value of the control command is transmitted to the corresponding CAV and the corresponding traffic sign or traffic light.

[0043] Although flowchart 200 is shown as individual operations such as 200-1, 200-2, 200-3, and 200-4, the disclosure is not so limited. Thus, in particular embodiments, such individual operations may be further divided into additional operations, combined into fewer operations, or omitted, depending on the particular implementation, without departing from the essence of the disclosed embodiments.

[0044] 3 illustrates an example traffic situation in a local area of ​​multiple interconnected traffic intersections for optimization-based hierarchical traffic control of controlled and uncontrolled vehicles, according to some embodiments of the present disclosure. FIG. 3 illustrates an example traffic situation illustrating the need for optimization-based hierarchical coordination and control of traffic rules, traffic signals, controlled vehicles, and human-operated vehicles within a local area of ​​multiple interconnected conflict zones, such as an interconnected intersection of a road segment. The interconnected conflict zones include physically interconnected conflict zones and communicatively interconnected conflict zones. An example of a physically interconnected conflict zone is an intersection or junction where vehicles can travel from one conflict zone to another. An example of a communicatively interconnected conflict zone is a traffic intersection or junction where traffic information from one conflict zone to another conflict zone is shared via a communication channel.

[0045] 3 illustrates a transportation network that includes multiple interconnected traffic intersections 101 and 103 that are physically interconnected with each other via road segments 105. The transportation network further includes road segments 107, 109, 111, 113, 114, and 116, a cloud network 118, a core network 120, one or more Road-Side Units (RSUs) 122 and 124, vehicles 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, and 146, a traffic light display 150, and a lane access status display 151.

[0046] A transportation network may include one or more conflict zones and one or more conflict-free zones. The multiple interconnected traffic intersections 101 and 103 are examples of one or more conflict zones or junctions in a transportation network. The multiple interconnected traffic intersections 101 and 103 may connect multiple lanes or road segments 105, 107, 109, 111, 113, 114, and 116. Examples of one or more conflict-free zones are road segments 105, 107, 109, 111, 113, 114, and 116 comprised of one or more lanes that allow either a single direction of traffic or multiple directions of traffic.

[0047] In one embodiment, each of the vehicles 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, and 146 in the transportation network may be either an autonomous vehicle, a semi-autonomous vehicle, or a manually operated vehicle. In one example, the autonomous and semi-autonomous vehicles are connected and automated vehicles (CAVs). Alternatively, the autonomous and semi-autonomous vehicles may be referred to as controlled vehicles. In one example, the manually operated vehicles or other traffic participants may be examples of human-operated vehicles (HDVs). In another example, the vehicles 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, and 146 include two-wheeled vehicles such as motorcycles, four-wheeled vehicles such as cars, or vehicles with four or more wheels such as trucks.

[0048] In one embodiment, the vehicles 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, and 146 follow general traffic rules. In one example, the general traffic rules include, but are not limited to, rules regarding crossing intersections, avoiding collisions with adjacent vehicles, occupying open lanes, or complying with lane speed limits. In one embodiment, the general traffic rules may include dynamic traffic rules that dynamically change upon receiving corresponding control commands. In one example, the general traffic rules include constraints for crossing an intersection among a plurality of intersections based on the collision-free status of a corresponding traffic sign, capacity limit constraints for each of a plurality of intersections or each road segment in the transportation network, collision avoidance constraints between vehicle pairs, lane change constraints for overtaking vehicles, speed limit constraints, and traffic sign timing constraints. Examples of dynamic traffic rules include traffic signs such as traffic lights that can receive control commands to change the timing to allow more or fewer vehicles to pass in a particular crossing direction, variable speed limits that can receive control commands to change the maximum speed of vehicles in a particular lane, and dynamically enabled lanes that can receive control commands to open or block access to a lane. Dynamic traffic rules may be displayed on digital displays on road segments 105, 107, 109, 111, 113, 114, and 116 to inform vehicles 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, and 146 of the status of the dynamic traffic rules. For example, traffic light display 150 may be configured to display the status of traffic lights at multiple interconnected traffic intersections 101, and lane speed displays may be configured to display lane speed limits. In one example, lane access status display 151 may be configured to display a status indicating whether access to lanes 153 of the transportation network is enabled or disabled.

[0049] One or more RSUs 122, 124 may be used for infrastructure-based real-time sensing of the status of vehicles 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, 146 and other traffic participants in a local area around each RSU 122, 124. In one embodiment, the traffic situation in FIG. 3 illustrates one RSU 122 and another RSU 124, the core network 120, and the cloud network 118 to establish an Internet of Vehicles (IoV) environment including vehicle-to-vehicle (V2V) communication and vehicle-to-infrastructure (V2I) communication, also known as vehicle-to-everything (V2X) communication.

[0050] In one embodiment, multi-hop communication is established between different vehicles in a transportation network, such as vehicles 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, and 146. Communication between cloud network 118 and vehicles, such as vehicle 126 on road segment 105, must propagate through RSU 122 or RSU 124 and core network 120. In some embodiments, the secure mobility of vehicles 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, and 146 is controlled by an optimization-based hierarchical traffic control system using a cloud-based or edge-based network. In one example, cloud network 118 and core network 120 may be used to implement the optimization-based hierarchical traffic control system. In another embodiment, the optimization-based hierarchical traffic control system is implemented using one or more mobile edge computers (MECs). As an example implementation, but not limited to, the MEC may be incorporated as part of one or more RSUs 122, 124, or may be a separate device connected to one or more network elements, such as the RSUs 122, 124, the cloud network 118, and the core network 120. Embodiments of the present disclosure include solving one or more constrained optimization problems at each sampling time step for coordinated control of dynamic rules, traffic lights, and vehicles in a transportation network, where computations may be performed either in the cloud network 118 or in one or more MECs.

[0051] 3 corresponds to a public metropolitan area in which road segments 105, 107, 109, 111, 113, 114, and 116 form multiple intersections, such as multiple interconnected traffic intersections 101 and 103. In this metropolitan area, traffic conditions at multiple interconnected traffic intersections 101 and 103 determine traffic flow because traffic congestion typically begins at a traffic intersection, such as intersection 103, and propagates further to road segments, e.g., road segments 105, 107, 109, 111, 113, 114, and 116. Traffic conditions at interconnected traffic intersections 101 and 103 are interdependent such that a change at one intersection, e.g., intersection 103, propagates further to other interconnected intersections, such as intersection 101, which is a neighboring intersection for intersection 103.

[0052] In other embodiments, the traffic situation 300 in Figure 3 may correspond to a private transportation network including one or more parking areas and interconnected road segments, for example, for a valet parking system. Another example of a similar traffic situation including a transportation network with multiple interconnected traffic intersections and road segments is a smart logistics center and / or shipping yard. Examples of types of CAVs include personal vehicles in the case of a valet parking system, commercial vehicles such as trucks in the case of a workshop management system, or shuttles for passenger transportation.

[0053] In the transportation network of traffic situation 300 in FIG. 3 , an onboard controller of a vehicle, such as vehicle 146, cannot obtain information about nearby vehicles, pedestrians, and environmental conditions, such as vehicle 142, that are outside the visible range of vehicle 146. For example, vehicle 146 traveling on road 114 intends to cross intersection 101 after vehicle 144, which is larger than vehicle 142, has crossed intersection 101, and a smaller vehicle, such as vehicle 142, is also entering intersection 101. In this situation, as shown in FIG. 5 , vehicle 144 blocks vehicle 142's visibility to vehicle 146. If the communication link between vehicle 142 and vehicle 146 is affected or if vehicle 142 and vehicle 146 use different communication protocols, vehicle 144 may prevent vehicle 142 from being recognized by vehicle 146. As a result, vehicle 142 and vehicle 146 may collide. In another embodiment, multi-hop communication between the cloud network 118 and the vehicle 146 may result in long communication delays, which may be unacceptable in the real-time context of cloud-based vehicle control.

[0054] Some embodiments recognize that different communication technologies can be used to support vehicular communications. For example, the IEEE Dedicated Short-Range Communications / Wireless Access in Vehicular Environments (DSRC / WAVE) family of standards for vehicular networks, 3GPP Cellular-Vehicle-to-Anything (C-V2X), etc. However, due to high costs, it is impractical for a vehicle, e.g., vehicles 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, and 146, to support more than one short-range communication technology, which creates compatibility issues between vehicles communicating with each other. Thus, a vehicle equipped with IEEE DSRC / WAVE cannot communicate with another vehicle equipped with 3GPP C-V2X, and vice versa. As a result, the accuracy of real-time control decisions made by the on-board multi-layer guidance and control architecture in each individual vehicle would be severely affected because the real-time decisions would be based on incomplete information about the traffic situation in FIG. 3 . To that end, embodiments of the present disclosure use an optimization-based hierarchical traffic control system that uses real-time information from each of the vehicles, dynamic traffic rules, and traffic lights in the transportation network to ensure safety, time efficiency, and energy efficiency.

[0055] Some embodiments of the present disclosure recognize that edge infrastructure devices, such as RSUs 122 and 124, have advantages for controlling multi-vehicle traffic over using only cloud networks or only on-board devices with multi-tier guidance and control architectures. For example, the edge infrastructure devices may be installed at intersections or junctions, such as multiple interconnected traffic intersections 101 and 103, and can communicate directly with vehicles approaching the intersections or junctions. The edge infrastructure devices may also be equipped with multiple communication technologies to communicate with all connected vehicles. In one embodiment, the edge infrastructure devices may be stationary and are enabled to provide reliable communication with vehicles and collect relatively high-quality environmental data.

[0056] The edge infrastructure devices can continuously monitor multi-vehicle traffic and the environment for accurate decision-making. In one example, the edge infrastructure devices use sensors, including but not limited to rangefinders, radar, lidar, or cameras, to accurately detect vehicle status and the dynamic environment, including other traffic participants such as connected and non-connected vehicles, autonomous, semi-autonomous, and manually operated vehicles, cyclists, and pedestrians. In another example, the edge infrastructure devices may use sensor fusion techniques to accurately detect vehicle status and the dynamic environment. Thus, the edge infrastructure devices are suitable for use in dynamic traffic regulations and coordinated control of mixed traffic within transportation networks of multiple interconnected traffic intersections.

[0057] In one embodiment, CAVs can be continuously controlled from edge infrastructure devices at any time and space to achieve optimization of the transportation network, such as minimizing average or worst-case travel time, overall idling time, etc. In contrast, HDVs are uncontrolled vehicles. In other words, controlling the motion of HDVs at each time and space is impossible, or at least impractical. In different traffic situations with only HDVs, the motion of HDVs is controlled via traffic signs. For example, the flow of HDVs is affected by the timing and sequencing of traffic lights, such that the overall operation of the transportation network is positively affected. Thus, the motion of HDVs is indirectly controlled by controlling traffic signs. However, because HDVs are driven by human drivers and indirectly controlled based on traffic signs, control of HDVs can only be performed at specific locations, thereby limiting control over the transportation network.

[0058] Some embodiments are based on the recognition that it may be beneficial to jointly control CAVs and HDVs to optimize overall benefits to the CAVs and HDVs, such as minimizing average or worst-case travel time, overall idling time, etc. To that end, it is an object of some embodiments to provide a traffic control system for jointly controlling CAVs and HDVs. In some embodiments, the traffic control system is implemented using one or more MECs, which may be incorporated as part of one or more RSUs 122, 124, or may be separate devices connected to one or more RSUs 122, 124, the cloud network 118, or the core network 120.

[0059] 4A illustrates an example of controlling traffic in a local area of ​​multiple interconnected traffic intersections using dynamic traffic rules and optimization-based hierarchical cooperative control of mixed traffic, according to some embodiments of the present disclosure. FIG. 4A shows an example traffic situation 400A illustrating the application of a traffic control system in a transportation network including multiple interconnected intersections 201, 203, 205, 207, and 209. The overall safety, time efficiency, and energy efficiency of traffic flow in this transportation network can be controlled by the traffic control system according to embodiments of the present disclosure. In some embodiments, the traffic control system calculates, for each CAV in the transportation network, a coarse motion plan along a route from the CAV's current location to the CAV's desired destination, while simultaneously calculating control commands for controllable traffic rules (CTR) signals or signs 211, 213, 215, and 217 that affect both CAVs and HDVs. CTR refers to dynamic traffic rules. The coarse-grained motion plan may include a sequence of entry and exit times and a sequence of average speed values ​​for each CAV at each intersection along the CAV's route from its current location to its desired destination. Additionally, the traffic control system influences the behavior of CAVs and HDVs by controlling CTR traffic lights or signs 211, 213, 215, 217 throughout the area. For example, intersection 207 does not have a CTR traffic light or sign, so CTRs may not be present at all intersections.

[0060] 4A , north-south traffic at intersections 203 and 205 is significantly more congested than east-west traffic at intersections 207 and 209. A traffic control system controls the planned future timing and speed trajectory of a CAV, such as vehicle 219, that plans to cross intersection 201 and travel toward the north-south direction of highly congested intersection 203. To improve the overall safety, time efficiency, and energy efficiency of traffic flow in the transportation network, the traffic control system generates commands for vehicle 219 to reduce its speed before and after crossing intersection 201, predicting that vehicle 219 will arrive at intersection 203 at a later time, in order to reduce traffic congestion at intersection 203 and reduce the overall waiting time for one or more vehicles in the transportation network.

[0061] In addition, the traffic control system also controls CTR traffic lights or signs. For example, the traffic control system may increase the green light duration of CTR traffic lights 211, 213, and 215 in the east-west direction by decreasing the green light duration of CTR traffic lights 211, 213, and 215 in the north-south direction, thereby allowing more traffic in the busier north-south direction and reducing traffic congestion. However, the traffic control system may enable the green light at 211, 213, and 215 to be turned on just when a specific vehicle, such as vehicle 219, can pass, as opposed to the aspect related to average traffic. This allows the green light to be activated when needed according to the purpose of the specific vehicle. For example, CTR traffic light or sign 211 may be green in the east-west direction, but may be turned red when HDV 221 and vehicle 219 are both approaching intersection 201, causing HDV 221 to stop and allow vehicle 219 to pass.

[0062] FIG. 4B illustrates an example of traffic conditions and routing information for multiple connected autonomous vehicles in a local area of ​​interconnected intersections, according to some embodiments of the present disclosure. FIG. 4B shows an example traffic scene 400B within a transportation network of multiple interconnected intersections and junctions. The transportation network includes one or more controlled vehicles, referred to as CAVs, such as vehicles 223, 225, 227, and 229. The transportation network further includes one or more non-controlled traffic participants, referred to as HDVs, such as vehicles 231, 233, 235, and 237. The transportation network itself may include multiple interconnected intersections, such as 239 (I1), 241 (I2), and 243 (I3), and multiple interconnected junctions, such as 245 (M1), 247 (M2), and 249 (M3). Both the intersections and junctions are referred to as conflict zones. The conflict zones are interconnected by multiple conflict-free road segments, each of which may include one or more lanes, such as 251 (L6), 253 (L47), and 255 (L36). Figure 4B also shows stop lines, such as 257 (S1), 259 (S2), and 261 (S3), indicating where vehicles may wait for a specific period of time before entering the intersection. Additionally, some intersections have controlled traffic lights, such as CTRs 263, 265, 267, and 269.

[0063] 4B illustrates routing information that may be provided by a routing or navigation module for each CAV, e.g., vehicle 223. For vehicle 223 at current location 271 and having desired destination 273, the routing or navigation module provides vehicle 223 with a sequence of roads and turns indicated by arrows 275a, 275b, 275c, 275d, 275e, 275f, 275g, and 275h. Similarly, the same or different individual routing or navigation modules may provide other vehicles, e.g., CAVs 225, 227, and 229, with a sequence of roads and turns from their current location to the desired destination. Some embodiments of the present disclosure are based on the recognition that a relatively short sequence of roads and turns can be accurately predicted starting from a current location for one or more non-controlled traffic participants, such as HDVs 231, 233, 235, and 237.

[0064] It is worth noting, however, that each of the road and turn sequences 275a, 275b, 275c, 275d, 275e, 275f, 275g, and 275h does not, in itself, yet specify a motion plan or path for the vehicle 223. There are many discrete decisions to make, such as which lane the vehicle should travel, whether the vehicle should change lanes or remain in its current lane, whether the vehicle should begin slowing down to stop at a stop line, and whether the vehicle should be allowed to cross an intersection. In addition, there are many continuous decisions to make, such as the timed sequence of positions and orientations the vehicle should achieve during the predicted journey from its initial position to its destination. Furthermore, it is also necessary to determine the behavior of the CTR, which affects the operation of both the CAV and HDV. According to some embodiments, a motion plan including a sequence of one or more of the above-described discrete and / or continuous decisions along a route from a current location to a desired destination may be calculated by a traffic control system for one or more CAVs, e.g., vehicles 223, 225, 227, and 229, and one or more CTRs, e.g., 263, 265, 267, and 269.

[0065] Figure 5 is a schematic diagram of possible interactions between a hierarchical traffic control system, a mapping and navigation system, one or more controlled and human-operated vehicles, roadside units, a traffic light controller, and a mobile edge computer, according to some embodiments of the present disclosure. Figure 5 shows an example diagram 500 of possible interactions between the traffic control system 302, the mapping and navigation system 304, one or more CAVs 306, one or more HDVs 308, one or more RSUs 310, one or more traffic light controllers (TLCs) 312, and one or more MECs 314. Embodiments of the present disclosure are based on the recognition that the traffic control system 302 can be efficiently implemented using a hierarchical traffic control architecture that includes a centralized traffic controller (CTC) and one or more intersection traffic controllers (ITCs) to calculate future control commands for each CAV and each TLC. The CTC calculates a high-level plan based on a macroscopic traffic flow model for a transportation network of multiple interconnected intersections. One or more ITCs execute this high-level plan by calculating control commands for the CAVs 306 and TLCs 312 based on a microscopic traffic model by minimizing the average travel time, waiting time, and fuel consumption of all vehicles in the transportation network.

[0066] In some embodiments, the mapping and navigation system 304 calculates real-time routing information for each CAV 306 from its current location to a desired destination or desired sequence of destinations. In one example, the mapping and navigation system 304 may be implemented as a centralized system. In another example, the mapping and navigation system 304 may be decentralized by being incorporated as part of the CAVs 306. The routing information for each CAV is communicated from the mapping and navigation system 304 to the hierarchical traffic control system 302 and each CAV 306. Similarly, the mapping and navigation system 304 may receive information from either the hierarchical traffic control system 302 or each CAV 306.

[0067] In some embodiments, the hierarchical traffic control system 302 calculates a sequence of future traffic light commands for each TLC 312 and a coarse-grained motion plan for each CAV 306 in the transportation network along a route from the CAV's current location to the CAV's desired destination or sequence of desired destinations. This motion plan is then communicated from the hierarchical traffic control system 302 to each CAV 306. In another example, the motion plan may be communicated from the hierarchical traffic control system 302 to each CAV 306 indirectly via communication with one or more MECs 314 that provide up-to-date information from the hierarchical traffic control system to the CAV 306. Similarly, the sequence of traffic light commands is communicated from the hierarchical traffic control system to each TLC 312 directly, or alternatively indirectly via communication with one or more MECs 314 that provide up-to-date information from the hierarchical traffic control system 302 to the TLC 312.

[0068] In one embodiment, real-time information may be communicated directly from the CAVs 306, HDVs 308, RSUs 310, and TLCs 312 to the hierarchical traffic control system 302. In another embodiment, real-time information may be communicated indirectly from the MEC 314 via the communication interface 301. In some embodiments, the MEC 314 may collect real-time information about the state of traffic participants and the dynamic environment within the local area of ​​the transportation network by communicating with the CAVs 306, HDVs 308, RSUs 310, and TLCs 312 currently present within the local area of ​​the transportation network. In some embodiments, the RSUs 310 use additional sensors, such as rangefinders, radar, lidar, or cameras, to accurately detect the state of the vehicles and the dynamic environment, including the CAVs 306, HDVs 308, and other traffic participants, such as bicycles or pedestrians. In another embodiment, sensor fusion techniques may also be used to accurately detect the state of the vehicles and the dynamic environment.

[0069] Some embodiments are based on the recognition that the number of MECs 314, CAVs 306, HDVs 308, RSUs 310, and TLCs 312 may change at each sampling time step in the hierarchical traffic control system 302. Most importantly, the number of vehicles may change significantly as traffic participants enter and exit the transportation network in which the hierarchical traffic control system 302 operates.

[0070] 6A is a schematic diagram of a feedback loop for a hierarchical traffic control system in a transportation network according to some embodiments of the present disclosure. Figure 6A shows a schematic diagram of a feedback loop 402 for a hierarchical traffic control system 600A that uses real-time information from an infrastructure detection module 406 to calculate a sequence of future control commands for each CAV 306 and each TLC 312 in the transportation network. The hierarchical traffic control system 600A includes a centralized traffic controller (CTC) 404 that calculates a high-level traffic flow plan based on a macroscopic traffic flow model for the mixed traffic of CAVs 306 and HDVs 308 in the transportation network at multiple interconnected intersections. The hierarchical traffic control system 600A further includes one or more intersection traffic controllers (ITCs) 408, 410 that execute the high-level plan based on the microscopic traffic model by calculating control commands for the CAVs 306 and TLCs 312 assigned to each ITC 408, 410. In one example, ITC 408 calculates control commands for group 412 of CAVs and group 414 of TLCs. Group 412 of CAVs and group 414 of TLCs are assigned to ITC 408. Group 412 of CAVs may include, but is not limited to, CAV1, CAV2, and CAV3. ITC 408 directly or indirectly controls traffic flow in a local area around one or more intersections in the transportation network. Similarly, ITC 410 calculates control commands for group 416 of CAVs and group 418 of TLCs. Group 416 of CAVs and group 418 of TLCs are assigned to ITC 410. Group 416 of CAVs includes CAV4, CAV5, and CAV6. Group 418 of TLCs includes TLC4, TLC5, and TLC6. ITC 410 directly or indirectly controls traffic flow in a local area around one or more intersections in the transportation network.

[0071] In one embodiment, the CTC 404 performs one or more calculations. The calculations in the CTC 404 include solving a convex optimization problem according to a macroscopic traffic flow model for the entire transportation network of multiple interconnected intersections and according to a convex relaxation of mixed-integer constraints that enforce each of the multiple traffic rules. In one example, the convex relaxation of the mixed-integer constraints that enforce each of the multiple traffic rules may include, but is not limited to, a convex relaxation of mixed-integer constraints for vehicles crossing each intersection or for traffic light switching behavior. In one embodiment, the macroscopic traffic flow model defines a high-level approximate representation of traffic flow in the transportation network, which omits modeling of individual vehicle behavior and instead models the general behavior of vehicles at the transportation network level using traffic flow values, density values, and average speed values ​​of traffic flows. Some embodiments use the macroscopic traffic flow model in combination with a convex relaxation of multiple mixed-integer traffic constraints to enable the CTC 404 to efficiently calculate a high-level traffic flow plan for the entire transportation network of multiple interconnected intersections. The operations performed for the efficient computation of high-level traffic flow plans for the entire transportation network are described in detail with reference to FIG.

[0072] In some embodiments of the present disclosure, the computations in each ITC 408, 410 include solving a mixed-integer programming (MIP) problem according to a microscopic traffic flow model of a local area around one or more intersections in the transportation network and according to mixed-integer constraints that enforce each of a plurality of traffic rules in the transportation network. In one example, the mixed-integer constraints that enforce each of the plurality of traffic rules in the transportation network include mixed-integer constraints for vehicles traversing each intersection, collision avoidance constraints, and mixed-integer constraints for traffic light switching behavior. In one embodiment, the microscopic traffic flow model is a detailed representation of traffic flow in the transportation network that includes modeling the behavior of each individual vehicle using a motion model to control and predict CAV behavior and a switching dynamics model to predict HDV behavior and predict CAV and HDV reactions to changing traffic lights. Some embodiments of the present disclosure are based on the recognition that using a microscopic traffic flow model for each ITC 408, 410 in a limited local area around one or more intersections in the transportation network enables efficient calculation of low-level motion plans and sequences of future control commands for each CAV in the group of CAVs 412, 416 and each TLC in the group of TLCs 414, 418 by minimizing the average travel time, waiting time, and fuel consumption of all vehicles in the local area of ​​the transportation network assigned to the ITC 408, 410.

[0073] In one embodiment, a set of CAVs and a set of TLCs within a local area around a particular traffic intersection may be assigned a particular ITC, and the set of CAVs and the set of TLCs have that particular ITC within a transportation network of multiple interconnected intersections. In one example, if group 412 of CAVs and group 414 of TLCs are within a local area around a traffic intersection belonging to ITC 408, then group 412 of CAVs and group 414 of TLCs are assigned to ITC 408. Similarly, if group 416 of CAVs and group 418 of TLCs are within a local area around a traffic intersection belonging to ITC 410, then group 416 of CAVs and group 418 of TLCs are assigned to ITC 410. As a result, the total number of ITCs is equal to the number of traffic intersections in the transportation network. In other embodiments, each ITC may be assigned to a local area around multiple groups of traffic intersections within the transportation network. For example, in some embodiments of the present disclosure, traffic intersections in a transportation network may be divided into disjoint subsets of traffic intersections, and the CAVs and TLCs at each of these subsets are controllable by one ITC, resulting in a total number of ITCs that is less than the number of traffic intersections.

[0074] In some embodiments, calculations at the CTC 404 and each ITC 408, 410 are performed in real time to account for dynamically changing traffic conditions within the transportation network. In one example, the sampling period of the CTC 404 may be the same as or different from the sampling period of each ITC 408, 410. For example, in some embodiments, the sampling period of the CTC 404 and each ITC 408, 410 may be set equal to 1 second, meaning that the CTC 404 calculates a new traffic movement plan every second and each ITC 408, 410 individually calculates new control commands for its respective CAVs and TLCs every second. In some embodiments of the present disclosure, the sampling period of the CTC 404 may be longer than the sampling period of each ITC 408, 410. For example, in some embodiments, the sampling period of the CTC 404 may be in the range of 1 to 2 seconds, and the sampling period of each ITC 408, 410 may be in the range of 0.5 to 1 second.

[0075] In one embodiment, the CTC 404 predicts the number of external vehicles entering the transportation network from each incoming direction at each time step within the prediction time window in a macroscopic traffic model based on historical data collected for similar transportation networks during a similar historical period as the prediction time window. In another embodiment, the CTC 404 calculates at least one of the values ​​for each road segment and traffic movement maneuver pair in the transportation network during the prediction time window based on historical data collected for similar transportation networks during a similar historical period as the prediction time window.

[0076] In some embodiments, the convex optimization problem in CTC 404 is a convex linear programming (LP) problem with a linear objective, linear equality constraints, and linear inequality constraints, or a convex quadratic programming (QP) problem with a linear quadratic objective, linear equality constraints, and linear inequality constraints. Examples of optimization algorithms for efficiently solving a convex LP or QP include, but are not limited to, the active constraint method, the interior point method, the projected gradient method, the operator decomposition method, or the alternating direction method of multipliers (ADMM).

[0077] In some embodiments, the MIP problem in each ITC is a mixed integer linear programming (MILP) or a mixed integer quadratic programming (MIQP) problem. Some embodiments of the present disclosure are based on the recognition that an MILP or MIQP can be efficiently solved if it is formulated as a mixed integer convex programming (MICP) problem. In other words, an MILP or MIQP can be efficiently solved if the optimization problem becomes convex when relaxing each of the integer feasibility constraints. For example, when relaxing the integer feasibility constraints, an MILP becomes a convex LP, or an MIQP becomes a convex QP. Examples of efficient optimization algorithms for solving MICPs include, but are not limited to, branch and bound, branch and cut, and branch and price.

[0078]

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[0080]

number

[0081] In some embodiments, heuristic search techniques may be used in the CTC 404 and each ITC 408, 410 to compute feasible, but possibly suboptimal, solutions to the MICP, including, for example, rounding schemes, feasibility pumping methods, approximate optimization algorithms, or the use of deep or supervised learning. For example, in some embodiments, a deep neural network may be used in the CTC 404 or each ITC 408, 410 to predict optimal values ​​for each of the binary or integer optimization variables, resulting in one or more convex programming (CP) problems being solved after fixing each of the binary or integer optimization variables.

[0082] 6B is a schematic diagram of a feedback loop for one ITC of a hierarchical traffic control system according to some embodiments of the present disclosure. Figure 6B shows an example schematic diagram 600B of a feedback loop for an ITC 408, one of multiple ITCs 408, 410 in a hierarchical traffic control system 600A. The ITC 408 uses real-time information from the infrastructure detection module 406 and the high-level traffic flow plan 420 from the CTC 404 to calculate a sequence of future control commands for each CAV in a group 412 of CAVs and a sequence of future control commands for each TLC in a group 414 of TLCs assigned to the individual ITC 408 in a local vicinity of the transportation network. The group 412 of CAVs may include CAVs 422, 424, and 426. The group 414 of TLCs may include TLCs 452, 454, and 456. In some embodiments, ITC408 computes a solution to the MIP according to a microscopic traffic flow model for a local area around one or more traffic intersections in the transportation network and according to mixed-integer constraints that enforce each of a plurality of traffic rules in the transportation network, including, for example, mixed-integer constraints for vehicles crossing each intersection, mixed-integer constraints for collision avoidance constraints, and mixed-integer constraints for traffic light switching behavior.

[0083] At each control time step, given the current detection information from the infrastructure detection module 406 and the current CTC traffic flow plan 420, the ITC 408 calculates a sequence of future control commands at a microscopic scale, and these control commands are sent to each of the TLCs 452, 454, and 456 and each of the CAVs 422, 424, and 426. In some embodiments, each of the TLCs 452, 454, and 456 controls one or more traffic signals for a traffic intersection within the transportation network. For example, in some embodiments, the TLC 452 controls the timing of one traffic signal in a particular cross direction of a traffic intersection. In other embodiments of the present disclosure, the TLC 454 controls the timing of multiple traffic signals in multiple cross directions of a traffic intersection within the transportation network.

[0084] Some embodiments are based on the recognition that planning and control for (semi-)automated driving can be effectively achieved using a multi-layer guidance and control architecture, typically implemented onboard each individual vehicle, that includes one or more layers of algorithms and techniques for decision-making, motion planning, vehicle control, or estimation. In some embodiments, the multi-layer guidance and control architecture is used in each of the CAVs 422, 424, 426 to execute a sequence of future control commands calculated by the ITC 408, taking into account real-time information from infrastructure sensing 406, taking into account the CTC traffic flow plan 420, and taking into account real-time information from one or more onboard sensors 434, 442, 450 of each individual CAV 422, 424, 426.

[0085] In one example, CAVs 422, 424, and 426 each include a decision-making layer 428, 436, and 444, a motion planner or motion planning algorithm 430, 438, and 446, a vehicle controller 432, 442, and 450, and one or more on-board sensors 434, 442, and 450. The decision-making layer 428 of the CAV 422 selects an appropriate driving behavior at any given time, taking into account the motion plan 460 from the ITC, current environmental conditions, and the behavior of other traffic participants, for example, using set reachability or automata combined with formal languages ​​and optimization for vehicle decision-making. Given the target behavior from the decision-making layer 428, which may include lane following, lane changing, or stopping, the motion planning algorithm 430 calculates a dynamically feasible and safe motion trajectory that the low-level vehicle controller 432 can track in real time. Real-time sensor fusion and estimation using on-board and infrastructure sensing information may be performed in each vehicle, e.g., CAVs 422, 424, 426, to provide feedback to high-level algorithms for decision-making, motion planning, and control. Similar, but possibly different, multi-layer guidance and control architectures may be used for (semi-)automated driving in one or more CAVs within a transportation network.

[0086] In one example, an approach for (semi-)automated driving uses a combination of finite-state machines (FSMs) for decision-making in the decision-making layers 428, 436, and 444, a sampling-based motion planning algorithm in the motion planners 430, 438, and 446, and a model predictive control (MPC) algorithm for reference trajectory tracking in the vehicle controllers 432, 440, and 448. One example of an algorithm for sampling-based motion planning uses stochastic particle filtering to sample the input space and add an additional correction term based on one or more driving requirements. One example of a predictive algorithm for vehicle control uses one or more iterations of a sequential quadratic programming (SQP) method to solve a linear time-varying or nonlinear MPC problem in real time. Some embodiments are based on the recognition that the use of predictive algorithms for motion planning and reference tracking control for (semi-)automated driving can more effectively benefit from predictive information in the motion plan calculated by the hierarchical traffic control system 600A. Examples of algorithms for sensor fusion and estimation are based on, but not limited to, Moving Horizon Estimation (MHE), extended or linear regression Kalman filtering, or particle filtering.

[0087] In some embodiments, different components of the multi-tier guidance and control architecture 428, 430, 432, 434 may be implemented onboard each controlled vehicle, such as a CAV 422, while other modules, such as the hierarchical traffic control system 600A, the mapping and navigation system 304, and some or all of the sensor fusion technology for infrastructure sensing 406, may be implemented within an infrastructure, such as the cloud network 118 or one or more MECs 314, to provide decisions or feedback information to multiple connected vehicles in the transportation network.

[0088] In some embodiments of the present disclosure, infrastructure sensing 406 corresponds to one or more RSUs, such as RSUs 122, 124, that include one or more sensors, such as rangefinders, radar, lidar, or cameras, and sensor fusion techniques to accurately detect the state of vehicles and the dynamic environment in a transportation network, including connected and non-connected vehicles, autonomous, semi-autonomous, and manually operated vehicles, and other traffic participants, such as cyclists and pedestrians.

[0089] Some embodiments recognize that safety constraints for other dynamic traffic participants, such as vehicles, bicycles, or pedestrians, can be addressed by obstacle avoidance techniques in the onboard modules of each CAV's multi-layer guidance and control architecture. Obstacle avoidance techniques may be implemented, for example, by motion planning or vehicle control algorithms. Due to their relatively low computational cost compared to the hierarchical traffic control system 600A, motion planning and vehicle control algorithms can be executed at relatively fast sampling rates in order to have fast reaction times to unexpected changes in the dynamic behavior of other vehicles or other traffic participants. For example, while real-time vehicle control algorithms typically run with an update period of 50 to 100 milliseconds, in some embodiments of the present disclosure, the sampling period of the CTC 404 may be equal to 1 to 2 seconds, and the sampling period of each ITC 408, 410 may be equal to 0.5 to 1 second.

[0090] Some embodiments are based on the recognition that different vehicle motion models having different modeling accuracy or different computational complexity may be used by one or more of the components in the architecture shown by FIG. 4B. Some embodiments are based on the recognition that vehicle motion models having higher modeling accuracy and perhaps higher computational complexity may be used by components at lower levels of the multi-layer guidance and control architecture shown in FIG. 4B. For example, a relatively simple linear motion model may be used in a navigation module such as the hierarchical traffic control system 600A or the RSU 310, while a higher-order or nonlinear motion model may be used to describe the vehicle motion in the decision-making units 428, 436, 444, motion planners 430, 438, 446, vehicle controllers 432, 440, 448, or on-board sensors 434, 442, 450 of each individual vehicle 422, 424, and 426.

[0091] Alternatively, one or more of the lower levels of the multi-layer guidance and control architecture can use higher-dimensional or nonlinear dynamic models to describe vehicle motion based on a balance of forces and torques, for example, in a nonlinear MPC-based vehicle controller. In one example, a single-track nonlinear vehicle model may be used in an MPC-based vehicle controller, where the state is described by the vehicle's two-dimensional position, longitudinal and lateral velocities, yaw angle, and yaw rate. The single-track vehicle model groups the left and right wheels on each axle together. In some embodiments, vehicle models with even higher modeling accuracy and computational complexity may be used. For example, a vehicle model with higher modeling accuracy may be based on a double-track vehicle model to accurately model the longitudinal and lateral load transfer between the vehicle's four wheels. In some embodiments, the nonlinear relationship between longitudinal and lateral tire friction forces, slip ratio, and slip angle may be modeled using Paseica's magic formula, which describes the general saturation behavior of tire forces. The coupling between longitudinal and lateral tire forces in combination with slip conditions can be modeled using a friction ellipse or using a weighting function.

[0092] 6C is a schematic diagram of a feedback loop for a hierarchical traffic control system in a transportation network according to some embodiments of the present disclosure. Figure 6C shows an example schematic diagram 600C of a feedback loop for a hierarchical traffic control system 600A that calculates a sequence of future control commands for each CAV and each TLC in the transportation network, taking into account real-time information from the infrastructure detection module 406. The hierarchical traffic control system 600A includes a CTC 404 that calculates a high-level macroscopic traffic flow plan. The hierarchical traffic control system 600A further includes one or more ITCs 408, 410, which execute the high-level plan based on the microscopic traffic model by calculating control commands for CAVs, such as CAV groups 412, 416, and TLCs, such as TLC groups 414, 418, assigned to each ITC 408, 410. For example, CAV group 412 and TLC group 414 are assigned to ITC 408. The CAV group 416 and the TLC group 418 are assigned to the ITC 410 .

[0093] For example, ITC 408 calculates future control commands 464 for group 412 of CAVs and group 414 of TLCs assigned to ITC 408 taking into account real-time information from infrastructure detection 406 and taking into account CTC flow values ​​460 for each cross-directional direction of one or more intersections assigned to ITC 408 in the transportation network. Similarly, a different ITC, such as ITC 410, calculates future control commands 466 for group 416 of CAVs and group 418 of TLCs assigned to ITC 410 taking into account real-time information from infrastructure detection 406 and taking into account CTC flow values ​​462 for each cross-directional direction of one or more intersections assigned to ITC 410 in the transportation network.

[0094]

[0023] Figure 7 illustrates an example operation for optimization-based hierarchical traffic control of controlled and uncontrolled vehicles in accordance with one embodiment of the present disclosure. Figure 7 is described in conjunction with elements from Figures 5, 6A, 6B, and 6C. Referring to Figure 7, a block diagram 700 is shown illustrating example operations 702 and 704 described herein.

[0095] The hierarchical traffic control system 600A broadly divides the method for controlling CAVs and HDVs into two steps 702 and 704. However, in particular embodiments, such individual operations may be further divided into additional operations, combined into fewer operations, or omitted depending on the particular implementation without departing from the essence of the disclosed embodiments.

[0096] At 702, traffic flow is jointly optimized for all intersections using convex optimization that involves convex relaxation of integer constraints for multiple interconnected intersections. In one embodiment, the CTC 404 of the hierarchical traffic control system 600A calculates a high-level traffic flow plan based on a macroscopic traffic flow model for mixed CAV and HDV traffic. In one embodiment, traffic flow optimization includes optimizing traffic flow values, such as the CTC traffic flow values ​​460 or 462 associated with the ITC 408 or 410 shown in FIG. 6C . Convex optimization of integer constraints is a problem in which all constraints are convex functions, and the objective is convex in the case of minimization or concave in the case of maximization. In general, relaxation simply refers to the technique of removing certain constraints from an optimization problem. Specifically, convex relaxation means that the problem becomes convex upon relaxation. In one embodiment, convex relaxation of integer constraints that enforce multiple traffic rules includes convex relaxation of integer constraints for vehicles crossing each intersection and for traffic light switching behavior. The use of a macroscopic traffic flow model in combination with convex relaxation of integer constraints enforcing multiple traffic rules allows the CTC 404 to efficiently compute high-level traffic flow plans for an entire transportation network of multiple interconnected intersections. In one example, convex relaxation of the traffic flow values ​​460 or 462 associated with the ITC 408 or 410 results in relaxed traffic flow values. Details of the relaxed approximation of pure integer values ​​through convex relaxation of integer constraints enforcing hybrid dynamic behavior of vehicles are further described, for example, with reference to FIG. 8C .

[0097] At 704, the cost function of the MIP problem at each ITC is optimized against the relaxed traffic flow values ​​from CTC 404, subject to integer constraints, to generate values ​​of control commands that change the state of each CAV associated with the intersection and values ​​of control commands that change the state of each traffic sign associated with the intersection.

[0098] FIG. 8A is an example situation diagram of a four-way traffic intersection in a transportation network controlled by a hierarchical traffic control system according to some embodiments of the present disclosure. FIG. 8A illustrates an example situation diagram 800A of a traffic intersection 800 in a transportation network controlled by a hierarchical traffic control system 600A by calculating a sequence of future control commands for each CAV and each TLC, such as TLC 820 shown in FIG. 8A. More specifically, FIG. 8A illustrates a four-way traffic intersection where vehicles, including both CAVs and HDVs, can arrive from either north 815, east 816, south 817, or west 818, and each vehicle can pass through traffic intersection 800 in one of multiple cross directions. For example, vehicles arriving from one of four approach directions, including north 815, east 816, south 817, and west 818, can turn right, continue straight, or turn left, resulting in 12 cross directions for each traffic intersection.

[0099] Vehicles arriving from the north 815 may turn right resulting in crossing direction d1 801, go straight resulting in crossing direction d2 802, or turn left resulting in crossing direction d3 803. Vehicles arriving from the east 816 may turn right resulting in crossing direction d4 804, go straight resulting in crossing direction d5 805, or turn left resulting in crossing direction d6 806. Vehicles arriving from the south 817 may turn right resulting in crossing direction d7 807, go straight resulting in crossing direction d8 808, or turn left resulting in crossing direction d9 809. Vehicles arriving from the west 818 may turn right resulting in crossing direction d 10 810, and by going straight, the transverse direction d 11 811 or by turning left, crossing direction 12 This can result in 812.

[0100] In some embodiments, the TLC 820 determines whether and when to switch one or more traffic light signal values, for example, from green to red or from red to green, to avoid collisions and reduce traffic congestion and fuel consumption. Traffic participants are allowed to cross the intersection in a particular crossing direction when the traffic light signal is green for that crossing direction, but must stop and wait when the traffic light signal is red for the desired crossing direction. Some embodiments are based on the recognition that an intersection's traffic light signal has multiple collision-free states, i.e., the current state of the traffic light signal is equal to one of multiple collision-free states at each time step, to allow the intersection's traffic light signal to be either red or green for one or more crossing directions while avoiding collisions between vehicles arriving at the traffic intersection from different directions.

[0101] 8B is a diagram illustrating an example of a mapping 830 between multiple conflict-free states 821-829 of a traffic signal and traffic light signal values ​​for each crossing direction 801-812 of a traffic intersection in a transportation network controlled by a hierarchical traffic control system, according to some embodiments of the present disclosure. FIG. 8B is a diagram illustrating an example of a mapping 830 between multiple conflict-free states 821-829 of a traffic signal and traffic light signal values ​​for each of crossing directions 801-812 of a traffic intersection in a transportation network controlled by a hierarchical traffic control system 600A. For example, if the current state of the intersection's traffic light signal is equal to conflict-free state 821, the traffic light signal value is red for each crossing direction. In conflict-free state 821, traffic participants are not permitted to cross the intersection in either direction. If the current state of the intersection's traffic light signal is equal to conflict-free state 822, the traffic light signal values ​​are equal to crossing directions d4 804, d5 805, d6 806, d7 807, d808, d9 809, d10 810, d11 811, d12 812, d13 813, d14 814, d15 815, d16 816, d17 817, d18 818, d19 820, d20 821, d21 822, d22 823, d23 824, d24 825, d25 826, d26 827, d27 828, d28 829, d30 829, d31 820, d32 821, d33 82 10 810 and d 11 In the collision-free state 822, the traffic participants are in the crossing directions d4 804, d5 805, d6 806, d7 807, d808, d9 809, d10 801, d11 802, d12 803, d13 804, d14 805, d15 806, d16 80 10 810 and d 11811. Similarly, traffic participants are only allowed to cross the intersection in crossing directions d1 801, d2 802, d3 803, and d4 804 if the current state of the intersection's traffic light signal is equal to the no-conflict state 829.

[0102] Some embodiments of the present disclosure may involve vehicles traveling from the east 816 via crossing directions d4 804 or d5 805 and vehicles traveling from the west 818 via crossing directions d 10 810 or d 11 This is based on the recognition that there is no collision between a vehicle traveling via 811 and a vehicle traveling via d7807, d8808, or d9809 from the south 817 and a vehicle traveling via d9809 from the west 818. 10 Traffic light state 828 is no conflict because no conflict occurs between vehicles traveling via 810. Similarly, traffic light state 824 is no conflict because no conflict occurs between vehicles traveling from the north 815 via crossing directions d1 801 or d2 802 and vehicles traveling from the south 817 via crossing directions d7 807 or d8 808.

[0103] 8C is a diagram illustrating an example of a traffic movement plan calculated by a centralized traffic coordinator (CTC) using a table of traffic movement values ​​for each cross direction of a traffic intersection in a transportation network controlled by a hierarchical traffic control system, according to some embodiments of the present disclosure. Figure 8C illustrates an example of a CTC traffic movement plan 800C calculated by a CTC 404 in hierarchical traffic control system 600A, where CTC movement plan 800C is represented in Figure 8C as a table 840 of traffic movement values ​​for each of cross directions 801-812. In some embodiments, CTC traffic movement plan 800C is configured with traffic movement values ​​at future time steps 841-844 that satisfy relaxed traffic movement constraints over a forecast horizon for each of cross directions 801-812 of one or more traffic intersections in the transportation network. Some embodiments of the present disclosure are based on the recognition that such relaxed traffic flow values ​​840 may be calculated by the CTC 404 by solving a convex optimization problem according to a macroscopic traffic flow model for an entire transportation network of multiple interconnected intersections and according to convex relaxations of mixed-integer constraints that enforce each of multiple traffic rules over the CTC 404's forecast horizon, including, for example, convex relaxations of mixed-integer constraints for vehicle and traffic light switching behaviors traversing each intersection, or including convex relaxations of mixed-integer constraints that enforce individual collision-free states of traffic light signals at each traffic intersection, as shown in FIG. 8B .

[0104] In some embodiments, traffic flow values ​​840 are relaxed real-valued approximations of pure integer values. The pure integer values ​​are relaxed based on a convex relaxation of mixed-integer constraints that enforce hybrid dynamic behavior of vehicles crossing one or more of the traffic intersections. For example, in FIG. 8C , the future CTC traffic flow values ​​at time step 841 are real-valued control values ​​that represent 2.3 vehicles crossing the traffic intersection in cross direction d1 801, 1.0 vehicles crossing in direction d2 802, and 0.7 vehicles crossing in direction d3 803. At time step 842, the future CTC traffic flow values ​​840 represent 1.1 vehicles crossing the traffic intersection in cross direction d1 801, 1.5 vehicles crossing in direction d2 802, and 1.4 vehicles crossing in direction d3 803. Similarly, at time step 843, future CTC traffic flow values ​​840 represent 0.3 vehicles crossing the traffic intersection in crossing direction d1 801, 1.2 vehicles crossing in direction d2 802, 0.8 vehicles crossing in direction d7 807, and 1.7 vehicles crossing in direction d8 808.

[0105] In some embodiments of the present disclosure, CTC traffic flow values ​​840 satisfy a convex relaxation of one or more mixed-integer constraints that satisfy a macroscopic traffic flow model and enforce each of a plurality of traffic rules for an entire transportation network of one or more interconnected traffic intersections. In some embodiments, the sum of CTC traffic flow values ​​840 is not allowed to exceed the maximum capacity limit at each time step for each traffic intersection in the transportation network. Similarly, CTC traffic flow values ​​840 are not allowed to exceed the number of arriving vehicles at the traffic intersection that are predicted to cross the traffic intersection in a particular crossing direction. For example, considering future CTC traffic flow values ​​840 in FIG. 8C , a total of 2.3 + 1.0 + 0.7 = 4 vehicles are crossing the traffic intersection at time step 841 after arriving at the traffic intersection from the north 815 direction.

[0106] FIG. 9 illustrates an example cost function adaptation method for a hierarchical traffic control system according to some embodiments of the present disclosure. The cost adaptation method 900 is based on traffic flow values ​​calculated by the CTC 404 to adapt a cost function minimized by a constrained optimization problem solved in one or more ITCs, such as the ITCs 408 and 410, of the hierarchical traffic control system 600A. The steps and their order identified in FIG. 9 are exemplary and may include various alternatives, equivalents, or derivations thereof, including, but not limited to, the order of execution. The steps of the method of FIG. 9 and its various alternatives may be embodied in hardware or software, including a computer-readable storage medium (e.g., an optical disk, memory card, or hard drive) containing instructions executable by a processor included in the hierarchical traffic control system 600A.

[0107] At 901, an ITC microscopic traffic model, such as ITC 408 shown in FIG. 6A , may be retrieved from database 108, or in some embodiments, calculated. More specifically, future CTC traffic flow values ​​over a forecast time horizon for each cross direction of a traffic intersection may be used in hierarchical traffic control system 600A in combination with the ITC 408 microscopic traffic model to fit a cost function of a constrained optimization problem solved by ITC 408.

[0108] At 902, a prediction of future traffic flow values ​​over a forecast time horizon may be calculated using the microscopic traffic model of the ITC 408.

[0109] At 903, future CTC traffic values ​​may be calculated by the CTC 404 of a hierarchical traffic control system, such as the hierarchical traffic control system 600A shown in FIG. 6A.

[0110] At 904, a tracking error is calculated between the future traffic movement prediction values ​​calculated at step 902 and the future CTC traffic movement values ​​calculated at step 903. In one embodiment, the optimal traffic movement probability values ​​of CTC 404 are used in ITC 408 to minimize the tracking error between the future traffic movement prediction values ​​calculated at step 902 and the future CTC traffic movement values ​​calculated at step 903 over the ITC's forecast time range for each cross direction of the multiple intersections.

[0111] At 905, the tracking error 603 over the forecast time horizon calculated in step 904 is minimized in a cost function of the ITC 408. Some embodiments of the present disclosure are based on the recognition that minimizing the difference in traffic flow predictions can be calculated in the cost function fitting method 900 of the hierarchical traffic control system 600A using the least-squares tracking error between the predicted traffic flow values ​​calculated in 902 and the reference CTC traffic flow values ​​calculated in 903. In some embodiments, the cost function of the constrained optimization problem solved in each ITC 408, 410 includes one or more additional terms, such as minimizing fuel consumption over the forecast time horizon 906-1, minimizing traffic congestion over the forecast time horizon 906-2, maximizing the distance traveled by one or more vehicles in a local neighborhood of the transportation network over the forecast time horizon 906-3, and maximizing safety of one or more vehicles in a local neighborhood of the transportation network over the forecast time horizon 906-4.

[0112] At 906, a cost function adaptation of the constrained optimization problem solved by the ITC 408 is performed. The cost function adaptation method 900 is based on a direct policy mapping from the CTC traffic flow values ​​calculated in step 905 and the real-time information of the infrastructure detection 406 to one or more parameter values ​​in the cost function of the ITC 408. In one example, the one or more parameter values ​​may include one or more weight values ​​that quantify the penalty of higher traffic flow values ​​in one or more cross directions for each traffic intersection of the transportation network. In some embodiments, the direct policy mapping can be achieved using a deep neural network architecture, e.g., using reinforcement learning (RL), to directly maximize a reward function for reducing congestion, travel time, emissions, and energy consumption within the transportation network. For example, in some embodiments of the present disclosure, the CTC 404 is achieved by training an RL policy based on model-free or model-based RL techniques. In other embodiments, the policy mapping may be achieved using a deep neural network architecture based on imitation learning, which aims to approximate an expert or heuristic solution.

[0113] Deep neural network architectures can be based on one or more layers containing one or more feedforward neural networks, recurrent neural networks (RNNs), convolutional neural networks (CNNs), long short-term memory (LSTM) networks, or gated recurrent units (GRUs).

[0114] Figure 10A is an example diagram 1000A of a multi-lane road segment in a transportation network, according to some embodiments of the present disclosure. Figure 10A illustrates a multi-lane road segment 1005 in which four vehicles plan to turn left (1011) at an upcoming intersection 1006. Similarly, Figure 10A illustrates six vehicles in the road segment 1005 that plan to continue straight (1012) at the upcoming traffic intersection 1006. Additionally, Figure 10A illustrates five vehicles in the road segment 1005 that plan to turn right (1013) at the upcoming traffic intersection 1006.

[0115] 10B is a diagram illustrating an example of vehicle density values ​​over a forecast time range for a multi-lane road segment in a transportation network used in a macroscopic traffic flow model of a hierarchical traffic control system, according to some embodiments of the present disclosure. FIG. 10B illustrates an example of vehicle density values ​​1000B over a forecast time range 1015-1018 for a multi-lane road segment 1005 in a transportation network, and in some embodiments, the vehicle density values ​​1000B can be used as part of a state information vector in the macroscopic traffic flow model used in a constrained optimization problem solved by the CTC 404 in the hierarchical traffic control system 600A to calculate a high-level traffic flow plan. In one example, FIG. 10A shows four vehicles in road segment 1005 planning to make a left turn (1011) at an upcoming traffic intersection 1006, resulting in a vehicle density value s k,1 1001 becomes equal to 4 at the first time step 1015, and the dynamic behavior of this vehicle density value can be predicted during subsequent time steps 1016-1018 based on a macroscopic traffic flow model of the transportation network. Similarly, FIG. 10A shows six vehicles in road segment 1005 planning to proceed straight (1012) at the next traffic intersection 1006, resulting in a vehicle density value s k,21002 becomes equal to 6 at the first time step 1015, and the dynamic behavior of this vehicle density value can be predicted during subsequent time steps 1016-1018 based on a macroscopic traffic flow model of the transportation network. Furthermore, FIG. 10A shows five vehicles in road segment 1005 planning to turn right (1013) at the next traffic intersection 1006, resulting in a vehicle density value s k,3 1003 becomes equal to 5 at the first time step 1015, and the dynamic behavior of this vehicle density value can be predicted during subsequent time steps 1016-1018 based on a macroscopic traffic flow model of the transportation network.

[0116] In some embodiments, vehicle density values ​​1000B over the forecast time range 1015-1018 satisfy a macroscopic traffic flow model, satisfying a convex relaxation of one or more mixed-integer constraints that enforce each of a plurality of traffic rules for an entire transportation network of one or more interconnected traffic intersections. For example, vehicle outflow from road segment 1005 is forced to be equal to vehicle inflow into traffic intersection 1006, and vehicle flow through the traffic intersection is upper bounded by a maximum capacity constraint at each time step for each traffic intersection in the transportation network.

[0117] FIG. 10C illustrates an example of multiple crossing directions over a forecast time range for a three-way traffic intersection in a transportation network, according to some embodiments of the present disclosure.

[0118] FIG. 10D illustrates an example of traffic flow values ​​in multiple cross directions over a forecast time range for a three-way traffic intersection in a transportation network used in a macroscopic traffic flow model of a hierarchical traffic control system according to some embodiments of the present disclosure.

[0119] FIG. 10E illustrates an example of multiple crossing directions over a forecast time range for a three-way traffic intersection in a transportation network, according to some embodiments of the present disclosure.

[0120] 10F is a diagram illustrating an example of vehicle density values ​​in multiple cross directions over a forecast time range for a three-way traffic intersection in a transportation network used in a macroscopic traffic flow model of a hierarchical traffic control system according to some embodiments of the present disclosure. Figure 10F illustrates an example of vehicle density values ​​1020 over a forecast time range 1035-1038 and traffic flow values ​​1040 over a forecast time range 1055-1057 for a three-way traffic intersection 1050 connecting multiple two-lane road sections in a transportation network. In some embodiments, both vehicle density values ​​1020 and traffic flow values ​​1040 can be used as part of a state information vector in the macroscopic traffic flow model used in a constrained optimization problem solved by a CTC in the hierarchical traffic control system 600A to calculate a high-level traffic flow plan. As shown in Figures 10C and 10E, a three-way traffic intersection results in six cross directions 1060, namely d1 1061, d2 1062, d3 1063, d4 1064, d5 1065, and d6 1066.

[0121] For example, the traffic flow value of 2.3 in the cross direction d1 at the first time step 1055 is the traffic flow in the direction d1, i.e., from road section s1 to road section s 11 or s 12 This represents the number of vehicles predicted to flow in the traffic flow. 11 1031 and s 12 The vehicle density values ​​of 1032 can be predicted during subsequent time steps 1055-1057 and 1035-1038, respectively, based on a macroscopic traffic flow model of the transportation network. For example, the traffic flow value of transverse direction d1 of 2.3 at the first time step 1055 is equal to the vehicle density value of s1 of 8 at the first time step 1035 minus 5.7 at the second time step 1036. Also, the vehicle density value of road section s1 from the first time step to the second time step 11 and s 12The inflow of vehicles at (5.15-4)+(3.15-2)=2.3 is equal to the traffic flow value for cross direction d1 of 2.3 plus the traffic flow value 744 for cross direction d4 of 0 at the first time step 1055. Similar dynamic traffic behavior can be seen in Figure 10C for the traffic flow values ​​1040 and corresponding vehicle density values ​​1020, for each cross direction at the traffic intersection 1050, and for each time step within the forecast horizon of the CTC 404.

[0122] For example, a traffic flow value of 1.7 for transverse direction d2 at the first time step 1055 represents the number of vehicles predicted to flow in direction d2 1062, i.e., from road segment s2 to road segments s7 or s8. The dynamic behavior of this traffic flow value 1042 and the vehicle density values ​​for s2 1022, s7 1027, and s8 1028 can be predicted during subsequent time steps 1055-1057 and 1035-1038, respectively, based on a macroscopic traffic flow model of the transportation network. For example, a traffic flow value of 1.7 for transverse direction d2 at the first time step 1055 is equal to the vehicle density value for s2 of 4 at the first time step 1035 minus 2.3 at the second time step 1036. Also, the inflow of vehicles into road sections s7 and s8 from the first time step to the second time step, (2.85-2)+(3.85-3)=1.7, is equal to the traffic flow value for transverse direction d2 of 1.7 plus the traffic flow value for transverse direction d5 of 0 at the first time step 1055 within the prediction range of CTC404, 745.

[0123] In some embodiments, the state information vector in the macroscopic traffic flow model includes vehicle density values ​​1020, traffic flow values ​​1040 through one or more intersections, and vehicle positions within each road segment of the transportation network. In some embodiments, to improve the accuracy of the macroscopic traffic flow model in the hierarchical traffic control system 600A, each road segment is divided into one or more smaller subsegments, and for each subsegment, current vehicle density values ​​are estimated and future vehicle density values ​​are predicted. In some embodiments, vehicles are expected to travel from one subsegment to the next within one sampling period, and vehicles are only allowed to enter a traffic intersection from road subsegments that are sufficiently close to the traffic intersection within the transportation network. This more accurately models the travel time of each vehicle traveling from the beginning to the end of a road segment, taking into account each vehicle's desired or estimated average speed.

[0124] In some embodiments, historical data is collected from database 108 and used to estimate and predict vehicle density values ​​1020 and traffic flow values ​​1040 to improve the performance of the hierarchical traffic control system 600A within the transportation network. For example, considering a cross direction d3 1063 from road section s5 to either road section s3 or s4, the percentage of vehicles in the traffic flow of cross direction d3 1063 entering either road section s3 or s4 can be predicted based on the vehicle density values ​​1020 and traffic flow values ​​1040 for the same or similar transportation network during a similar period in the past. Similarly, the number of external vehicles entering the transportation network from each entry direction at each time step within the prediction range can be predicted based on historical data collected for the same or similar transportation network during a similar period in the past. For example, historical data can be used to predict typical traffic entry values ​​or typical routing of vehicles entering a particular transportation network at 8:00 a.m. on Monday versus 2:00 p.m. on Saturday, and the historical data can be used to improve the predictions of the macroscopic traffic flow model in the hierarchical traffic control system 600A.

[0125] FIG. 11A illustrates a method for formulating and solving a constrained optimization problem for computing a macroscopic traffic flow motion plan for one or more traffic lights and connected autonomous vehicles (CAVs) in a transportation network including multiple interconnected traffic intersections, according to some embodiments of the present disclosure. The steps identified in FIG. 11A and their order are exemplary and may include various alternatives, equivalents, or derivations thereof, including, but not limited to, the order of execution thereof. The steps of method 1100A of FIG. 11A and its various alternatives may be embodied in hardware or software, including a computer-readable storage medium (e.g., optical disk, memory card, or hard drive) containing instructions executable by a processor included in hierarchical traffic control system 600A. In another embodiment, the steps of method 1100A of FIG. 11A and its various alternatives may be embodied in hardware or software, including a computer-readable storage medium (e.g., optical disk, memory card, or hard drive) containing instructions executable by a processor included in CTC 404. FIG. 11A illustrates a method 1100A that includes a feedback loop for the CTC 404.

[0126] At 1101, the CTC 404 receives mapping information, such as location data (eg, GPS data) for road segments, lanes, traffic intersections, and stopping zones within a transportation network.

[0127] At 1105, the CTC 404 receives additional inputs, such as feedback signals about status and planned routing information, from the CAVs. In one example, the feedback signals also include information from the infrastructure detection module 406.

[0128] At 1106, the CTC 404 receives additional inputs, such as feedback signals about status and predicted routing information, from the HDV. In some embodiments, the feedback signals are obtained directly or indirectly from the sensing infrastructure module 406 (e.g., an RSU) or from connected vehicles, which may be either autonomous, semi-autonomous, and / or human-driven vehicles. Feedback signals about the status and planned routing information of the CAV may be referred to as Type 1 feedback signals. Feedback signals about the status and predicted routing information of the HDV may be referred to as Type 2 feedback signals.

[0129] At 1110, the CTC 404 formulates a constrained optimization problem based on the CTC 404's macroscopic traffic flow model.

[0130] At 1115, CTC404 solves a constrained optimization problem to calculate a macroscopic traffic flow motion plan for one or more traffic lights and connected (semi-)automated vehicles in a transportation network including multiple interconnected traffic intersections. In one embodiment, CTC404 solves the constrained optimization problem having a cost function including at least one of maximizing a sum of traffic flow variables or minimizing a sum of traffic congestion variables in the transportation network.

[0131] At 1120, the CTC 404 calculates an optimal sequence of high-level control objectives for traffic flow within the transportation network over a forecast time window for the CTC 404 based on a solution to a constrained optimization problem. The CTC 404 controls mixed traffic within the transportation network.

[0132] At 1121, the CTC 404 sends the calculated optimal sequence of high-level control target values ​​for traffic flow to each of one or more ITCs 821 in the hierarchical traffic control system 600A that control mixed commons in the transportation network.

[0133] FIG. 11B illustrates a method for formulating and solving a constrained convex programming (CP) problem for computing an optimal sequence of high-level target values ​​for traffic flows in a transportation network of multiple interconnected traffic intersections, according to some embodiments of the present disclosure. The steps identified in FIG. 11B and their order are exemplary and may include various alternatives, equivalents, or derivations thereof, including, but not limited to, the order of execution. The steps of method 1100B of FIG. 11B and its various alternatives may be embodied in hardware or software, including a computer-readable storage medium (e.g., optical disk, memory card, or hard drive) containing instructions executable by a processor included in hierarchical traffic control system 600A. In another embodiment, the steps of method 1100B of FIG. 11B and its various alternatives may be embodied in hardware or software, including a computer-readable storage medium (e.g., optical disk, memory card, or hard drive) containing instructions executable by a processor included in CTC 404. FIG. 11B illustrates method 1100B including a feedback loop for CTC 404.

[0134] At 1122, the CTC 404 receives map segment and lane information for a plurality of interconnected traffic intersections within the transportation network.

[0135] At 1125, the CTC 404 receives feedback signals related to sensing and routing from the controlled, uncontrolled, and / or semi-controlled vehicles.

[0136] At 1135, the CTC 404 constructs matrices and vectors in the CTC 404's CP data for the objectives, equality constraints, and inequality constraints. In one embodiment, these matrices and vectors are constructed using received feedback signals related to sensing and routing and map segment and lane information.

[0137] At 1140, the CTC 404 solves the CP problem based on a convex relaxation of the non-convex traffic rules. In some embodiments, the CP includes a convex relaxation of one or more mixed-integer equality and / or inequality constraints that enforce each of a plurality of traffic rules for an entire transportation network of one or more interconnected traffic intersections. In some embodiments, the CP problem includes a convex optimization problem in the CTC 404. The convex optimization problem may be a convex linear programming (LP) problem that includes a linear objective and one or more linear equality and / or inequality constraints. In some embodiments, the convex optimization problem in the CTC 404 is a convex quadratic programming (QP) problem that includes a linear-quadratic objective and one or more linear equality and / or inequality constraints. In some embodiments, the convex optimization problem in the CTC 404 is a quadratically constrained quadratic programming (QCQP) problem that includes a linear-quadratic objective, one or more linear equality and / or inequality constraints, and one or more quadratic inequality constraints. In some embodiments, the convex optimization problem in CTC 404 is a convex cone programming problem that includes a linear objective and one or more linear equality and / or inequality constraints and one or more convex cone inequality constraints. Some embodiments of the present disclosure are based on the recognition that numerical optimization algorithms exist for computationally efficiently solving convex optimization problems in CTC 404. Examples of optimization algorithms for efficiently solving the CP in step 1140 include the active constraint method, the interior point method, the projected gradient method, the operator decomposition method, or the alternating method of multipliers (ADMM).

[0138] At 1145, the CTC 404 calculates an optimal sequence of high-level target values ​​for traffic movement in the multi-intersection transportation network over a prediction time window.

[0139] At 1150, the CTC 404 sends the calculated optimal sequence of high-level traffic movement targets to each ITC in the transportation network's hierarchical traffic control system 600A.

[0140] FIG. 11C illustrates a method for formulating and solving a constrained convex programming (CP) problem for computing an optimal sequence of high-level target values ​​for traffic flows in a transportation network of multiple interconnected traffic intersections, according to some embodiments of the present disclosure. The steps identified in FIG. 11C and their order are exemplary and may include various alternatives, equivalents, or derivations thereof, including, but not limited to, the order of execution thereof. The steps of method 1100C of FIG. 11C and its various alternatives may be embodied in hardware or software, including a computer-readable storage medium (e.g., optical disk, memory card, or hard drive) containing instructions executable by a processor included in hierarchical traffic control system 600A. In another embodiment, the steps of method 1100C of FIG. 11C and its various alternatives may be embodied in hardware or software, including a computer-readable storage medium (e.g., optical disk, memory card, or hard drive) containing instructions executable by a processor included in CTC 404. FIG. 11C illustrates method 1100C including a feedback loop for CTC 404.

[0141] At 1152, the CTC 404 receives map segment and lane information for a plurality of interconnected traffic intersections in the transportation network.

[0142] At 1154, the CTC 404 receives feedback signals related to sensing and routing from the controlled, uncontrolled, and / or semi-controlled vehicles.

[0143] At 1156, the CTC 404 constructs matrices and vectors in the CTC 404's convex QP data for the objectives, equality constraints, and inequality constraints. In one embodiment, these matrices and vectors are constructed using received feedback signals related to sensing and routing and map segment and lane information.

[0144] At 1158, the CTC 404 solves a convex QP based on a convex relaxation of the non-convex traffic rules. According to some embodiments, the convex QP includes a linear quadratic objective function 1158-1, one or more linear equality constraints 1158-2, and one or more linear inequality constraints 1158-3.

[0145] At 1160, the CTC 404 calculates and sends optimal traffic flow values ​​to each ITC in the transportation network's hierarchical traffic control system 600A.

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[0147] In some embodiments, the sampling period for the setback range realization of the CTC 404 is equal to or greater than the sampling period for the setback range realization of each ITC 408, 410 in the hierarchical traffic control system 600A. In some embodiments, the length of the prediction time window of the CTC 404 is equal to or greater than the length of the prediction time window of each ITC 408, 410 in the hierarchical traffic control system 600A.

[0148] In some embodiments of the present disclosure, the macroscopic traffic flow model in CTC 404 can be represented as a directed graph, where each node corresponds to a road segment and each edge corresponds to a connection between road segments, i.e., a direction across a traffic intersection in a transportation network controlled by a hierarchical traffic control system.

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[0161] 12A illustrates a method for formulating and solving a constrained optimization problem for computing a microscopic traffic flow motion plan for one or more traffic lights and connected autonomous vehicles (CAVs) in a local area around one or more interconnected traffic intersections in a transportation network, according to some embodiments of the present disclosure. The steps identified in FIG. 12A and their order are exemplary and may include various alternatives, equivalents, or derivations thereof, including, but not limited to, the order of execution thereof. The steps of method 1200A of FIG. 12A and its various alternatives may be embodied in hardware or software, including a computer-readable storage medium (e.g., an optical disk, memory card, or hard drive) containing instructions executable by a processor included in hierarchical traffic control system 600A. In another embodiment, the steps of method 1200A of Figure 12A and various alternatives thereof may be embodied in hardware or software, including a computer-readable storage medium (e.g., an optical disk, memory card, or hard drive) containing instructions executable by a processor included in an ITC, such as ITCs 408, 410 shown in Figure 6A. Figure 12A shows method 1200A including a feedback loop for an ITC.

[0162] At 1201, an ITC 408 or 410 receives mapping information, such as location data (eg, GPS data) for road segments, lanes, traffic intersections, and stopping zones within a transportation network.

[0163] At 1205, the ITC 408 or 410 receives additional input from the CAV, such as a feedback signal about status and planned routing information. In one example, the feedback signal also includes information from the infrastructure detection module 406.

[0164] At 1206, the ITC 408 or 410 receives additional input from the HDV, such as a feedback signal about status and predicted routing information. In some embodiments, the feedback signal is obtained directly or indirectly from the sensing infrastructure module 406 (e.g., an RSU) or from a connected vehicle, which may be an autonomous vehicle, a semi-autonomous vehicle, and / or a human-driven vehicle. The feedback signal about the status and planned routing information of the CAV may be referred to as a Type 1 feedback signal. The feedback signal about the status and predicted routing information of the HDV may be referred to as a Type 2 feedback signal.

[0165] At 1210, the ITC 408 or 410 constructs a constrained optimization problem based on a microscopic traffic model for the ITC's transportation network. In some embodiments, the constrained optimization problem is a mixed integer programming (MIP) problem constructed based on the microscopic traffic model.

[0166] At 1215, the ITC 408 or 410 solves the MIP problem to compute a microscopic traffic flow motion plan for the ITC 408 or 410 for a traffic light and one or more traffic lights and / or connected (semi-)automated vehicles in the transportation network. The ITC 408 or 410 computes a solution to the MIP at each sampling time step.

[0167] At 1220, the ITC 408 or 410 calculates an optimal sequence of target control commands and an optimal sequence of traffic light commands for each CAV in a local area around one or more traffic intersections in the transportation network over a prediction time window of the ITC 408 or 410.

[0168] At 1225, the ITC 408 or 410 sends commands to the multi-tier guidance and control architecture of each CAV, and the ITC sends control commands to each traffic light in a local area around one or more traffic intersections in the transportation network controlled by the hierarchical traffic control system 600A.

[0169] Some embodiments are based on the recognition that the hierarchical traffic control system 600A can be realized by solving a constrained optimization problem 1210 to calculate a motion plan for each CAV and to calculate optimal control commands for each TLC, taking into account input information from V2X communications. In some embodiments, the constrained optimization problem can be an MIP problem, such as a mixed integer linear programming (MILP) or mixed integer quadratic programming (MIQP) problem. In some embodiments, one or more MIP problems at each sampling time instant of the hierarchical traffic control system 600A can be solved by a global optimization algorithm, including, for example, branch and bound, branch and cut, and branch and price. In other embodiments of the present disclosure, heuristic techniques can be used to calculate feasible but suboptimal solutions to one or more MIP problems, including, for example, rounding schemes, feasibility pumping, approximate optimization algorithms, or (deep) machine learning, for example, using supervised learning.

[0170] 12B is a schematic diagram 1200B of a formulation of an MIP problem 1210 based on a microscopic traffic model for mixed traffic in a local area controlled by an ITC around one or more traffic intersections in a transportation network, according to some embodiments of the present disclosure. Figure 12B shows a schematic diagram 1200B of a formulation of an MIP problem 1210 based on a microscopic traffic model for mixed traffic in a local area controlled by an ITC around one or more traffic intersections in a transportation network. In some embodiments, the MIP problem 1210 is formulated based on multiple constraints, including, for example, a motion model 1211 for one or more CAVs, a motion model 1212 for one or more HDVs, a model 1213 for one or more TLCs, one or more physical and / or safety constraints 1214 for the CAVs, traffic rules and timing constraints 1215 for multi-lane road segments, collision avoidance constraints 1216, dynamic traffic rules and timing constraints 1217, and traffic rules for traversing one or more traffic intersections 1218. An MIP problem 1210 is formulated based on a cost function 1205 to be minimized or a reward function to be maximized to reduce congestion, travel time, emissions, and energy consumption in a local area controlled by the ITC, for example, around one or more traffic intersections in a transportation network. An optimal solution 1225 to the MIP problem defines optimal values ​​1222 of control commands sent to one or more CAVs and optimal values ​​1223 of control commands for states sent to one or more TLCs.

[0171] In some embodiments, a long-term future route plan is used for each CAV in a local area controlled by the ITC around one or more traffic intersections in the transportation network. Some embodiments recognize that, depending on the infrastructure system, obtaining an accurate future prediction 1212 for each HDV's route may be difficult. Therefore, in some embodiments, the hierarchical traffic control system 600A is implemented in a fallback range manner based on up-to-date information from sensing infrastructure (e.g., RSUs) and connected vehicles. Some embodiments recognize that an approximate short-term future route prediction 1212 for HDVs is sufficient, and that this prediction 1212 can generally be obtained relatively easily from, for example, each HDV's current position to the next traffic intersection, each HDV's current lane, and detection of one or more HDV's turn signals. Some embodiments of the present disclosure recognize that the inherent feedback mechanism of a fallback range strategy can adjust for discrepancies in predictions. For example, an update period of 1 second allows for real-time calculations of the hierarchical traffic control system 600A while providing sufficiently fast updates to the multi-layer guidance and control architecture of each CAV and sufficiently fast updates 1223 to each TLC to account for mispredictions of HDV behavior.

[0172] 12C shows a flow diagram 1200C of a switching function used in a microscopic traffic model for mixed traffic in a local area controlled by an ITC around one or more traffic intersections in a transportation network controlled by a hierarchical traffic control system, according to some embodiments of the present disclosure. The switching function for each of the one or more HDVs includes one or more motion models for one or more switching conditions. In one example, the one or more motion models include a first motion model for stopping maneuvers at stopping zones at each of a plurality of intersections of roads in the transportation network when the corresponding traffic sign is red in the cross direction and the HDV is within a first safe distance from the stopping zone; a second motion model for safe leading vehicle following behavior when a leading vehicle is within a second safe distance ahead of the HDV and is in the same lane of the same road section as the HDV; and / or a third motion model for traveling at a desired average speed when there is no leading vehicle within the second safe distance ahead of the HDV and the leading vehicle is not in the same lane as the HDV or when the HDV is not within the first safe distance from the stopping zone and the corresponding traffic sign is not red.

[0173] In some embodiments, the future driving behavior of the HDV is modeled using a switched dynamic system that can predict the HDV's response to estimated or predicted driving behaviors of one or more CAVs or HDVs in a local vicinity around the HDV, and that can predict the HDV's response to traffic rules or traffic lights within a transportation network. In particular, the HDV predictive motion model uses real-time information from the infrastructure detection module 406 to predict a new state of the HDV, taking into account the HDV's current state.

[0174] The steps and their order identified in Figure 12C are exemplary and may include various alternatives, equivalents, or derivations thereof, including but not limited to the order of execution thereof. The steps of method 1200C of Figure 12C and its various alternatives may be embodied in hardware or software, including a computer-readable storage medium (e.g., an optical disk, memory card, or hard drive) containing instructions executable by a processor included in hierarchical traffic control system 600A.

[0175] At 1231, the current state of the HDV is received and fed into the HDV predictive motion model.

[0176] At 1235, the HDV predictive motion model determines whether the traffic light is red in the crossing direction and the HDV is within a safe distance from the stopping zone. In some embodiments, the value of the safe distance may be predetermined based on empirical observations or may be set by a local government.

[0177] At 1236, the HDV predictive motion model predicts that the HDV will perform a stopping maneuver at a stopping zone at a traffic intersection if the traffic light is red in the crossing direction and the HDV is within a safe distance from the stopping zone.

[0178] At 1240, the HDV predictive motion model determines whether a vehicle preceding the HDV is within a safe distance ahead of the HDV if any of the conditions mentioned in step 1235 are not met, i.e., the traffic light is not red in the crossing direction or the HDV is not within a safe distance from the stopping zone.

[0179] At 1241, the HDV predictive motion model predicts that the HDV will perform a safe leading vehicle following behavior when the HDV is not within a safe distance from a stopping zone and / or the traffic light is not red, but a leading vehicle is within a safe distance ahead of the HDV and in the same lane as the HDV.

[0180] At 1242, the HDV predictive motion model predicts that the HDV will continue traveling at the desired average speed if there is no leading vehicle within a safe distance ahead of the HDV and / or if the leading vehicle is not in the same lane as the HDV.

[0181] FIG. 12D is a schematic diagram of a motion model for an HDV according to some embodiments of the present disclosure. FIG. 12D shows a schematic diagram of a motion model 1200D for an HDV. Different functions are formulated for different dynamic traffic rules. For example, a function 1248 for dynamic traffic rule 1, a function 1250 for dynamic traffic rule 2, and a function 1252 for dynamic traffic rule n are formulated. Each of the functions 1248-1252 represents a motion model for the corresponding dynamic traffic rule. In other words, each function represents the behavior of the HDV in response to the corresponding dynamic traffic rule. The motion model represented by the functions 1248-1252 is referred to as a rule-constrained motion model. In addition, a rule-free function 1246 is formulated, which represents a rule-free motion model. The rule-free motion model is not affected by the dynamic traffic rules.

[0182] The selection of a function to be active for the HDV depends on traffic sign state 1256, HDV state 1254, and other vehicle state 1258. HDV state 1254 includes at least one of the HDV's position, speed, acceleration, and lane. Thus, while the functions 1246-1252 themselves may not depend on traffic sign state 1256, the selection of a function to be active in a particular control step does depend on traffic sign state 1256. Functions 1246-1252 are collectively referred to herein as switching (discontinuous) functions that select a function representing a motion model for the HDV based on one or a combination of traffic sign state 1256, HDV state 1258, and other vehicle state 1258. Functions 1246-1252 individually represent dynamic traffic rules that the HDV should follow.

[0183] According to one embodiment, the selected function can be used as a motion model of the HDV for joint optimization of the CAV and the HDV. In particular, the traffic control system solves a MIP that optimizes a cost function for the values ​​of control commands that change the state of each CAV and the values ​​of control commands that change the state of each traffic sign. The cost function is optimized according to the motion model of each CAV and the motion model of each HDV.

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[0192] The collision avoidance rule (19) for the vehicle position is independent of other variables controlled by the traffic control system other than the position of the vehicle itself, and therefore the collision avoidance rule (19) is not a dynamic traffic rule, since for a fixed vehicle position, satisfying or violating a traffic rule is always the same.

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[0198] In some implementations, normalization may be omitted in both (24a) and (24b).

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[0202] FIG. 12E illustrates a method for constructing and solving a MIP problem based on mixed-integer equality and inequality constraints for a predictive motion model of one or more CAVs, HDVs, TLCs, and non-convex traffic rules in a transportation network controlled by a hierarchical traffic control system, according to some embodiments of the present disclosure. The steps and their order identified in FIG. 12E are exemplary and may include various alternatives, equivalents, or derivations thereof, including, but not limited to, the order of execution thereof. The steps of method 1200E of FIG. 12E and its various alternatives may be embodied in hardware or software, including a computer-readable storage medium (e.g., optical disk, memory card, or hard drive) containing instructions executable by a processor included in hierarchical traffic control system 600A. In another embodiment, the steps of method 1200E of FIG. 12E and its various alternatives may be embodied in hardware or software, including a computer-readable storage medium (e.g., optical disk, memory card, or hard drive) containing instructions executable by a processor included in ITC 408 or 410. FIG. 12E illustrates a method 1200E that includes a feedback loop for the ITC 408 or 410.

[0203] At 1260, the ITC 408 or 410 receives map segment and lane information for a plurality of interconnected traffic intersections in the transportation network.

[0204] At 1262, the ITC 408 or 410 receives feedback signals related to sensing and routing from controlled, uncontrolled, and / or semi-controlled vehicles.

[0205] At 1264, the ITC 408 or 410 constructs matrices and vectors in the ITC's MIP data for the objective, equality constraints, and inequality constraints.

[0206] At 1266, the ITC 408 or 410 solves the MIP problem based on mixed integer equality and inequality constraints for the predictive motion model of one or more CAVs, HDVs, and TLCs in the transportation network, and mixed integer equality and inequality constraints for the non-convex traffic rules.

[0207] At 1268, the ITC 408 or 410 calculates and sends optimal control commands to one or more CAVs and TLCs in the transportation network controlled by the hierarchical traffic control system 600A.

[0208] According to some embodiments of the present disclosure, the MIP problem includes a linear quadratic objective function 1266-1, one or more linear inequality constraints 1266-2, one or more linear equality constraints 1266-3, and one or more integer feasibility constraints 1266-4. Some embodiments are based on the recognition that the MIP problem is a mixed integer convex programming (MICP) problem, i.e., the MIP problem becomes a convex programming (CP) problem with fixed values ​​of the integer optimization variables, and that MICP can be solved computationally efficiently using, for example, branch and bound optimization methods.

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[0215] Also, in some embodiments of the present disclosure, the following MIP inequality constraints 1266-2 prevent both lane changes up and down in the same time step, preventing lane changes down from the lowest lane in a road segment of the transportation network, and preventing lane changes up from the highest lane in a road segment of the transportation network.

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[0229] In some embodiments of the present disclosure, the constraints of the MIP problem 1266 include one or more traffic light timing constraints to impose a minimum time between two consecutive traffic light change commands and an upper bound on the timer state variable, as follows:

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[0231] Some embodiments of the present disclosure are based on the recognition that by using a macroscopic traffic flow model and by using a convex relaxation of non-convex traffic rules in the CTC 404, which results in a convex optimization problem 1158 that is computationally much easier to solve compared to the MIP formulation 1266 solved in each ITC 408 or 410, the prediction time window of the CTC 404 can be longer than the prediction time window of each ITC 408 or 410 in a hierarchical traffic control system 600A that controls mixed traffic in a transportation network of multiple interconnected traffic intersections.

[0232] In some embodiments, the mixed integer optimization (minimization) problem 1266 can be solved using a branch and bound (B&B) optimization method that searches for a globally optimal solution within a search space to generate optimal control signals. B&B optimization iteratively divides the search space into a nested tree of regions to find a solution with a globally optimal (minimum) objective value. The B&B method iteratively solves a convex relaxation to calculate a lower bound for the objective value within a region from the nested tree of regions. One or more regions can be pruned if the corresponding lower bound is greater than the currently known upper bound for the globally optimal objective value. The upper bound for the globally optimal objective value can be updated if an integer feasible solution is found that has an objective value that is smaller than the currently known upper bound for the globally optimal objective value.

[0233] Some embodiments of the present disclosure are based on the recognition that redundant optimization variables may be automatically removed by a preprocessing routine in a numerical optimization algorithm used to solve the MIP problem 1266 in the hierarchical traffic control system 600A. In some embodiments, one or more redundant optimization variables may be explicitly fixed to particular values ​​by adjusting a corresponding simple bound for each redundant optimization variable in the MIP problem 1266. Some embodiments of the present disclosure are based on the recognition that after fixing one or more binary optimization variables, one or more of the corresponding inequality constraints may become redundant and may be removed by setting the corresponding lower bound to −∞ and / or the corresponding upper bound to ∞.

[0234] Figure 13 illustrates an example traffic situation in a transportation network of multiple interconnected traffic intersections including mixed traffic of CAVs and HDVs controlled by one CTC in combination with multiple ITCs in a hierarchical traffic control system, according to some embodiments of the present disclosure. Figure 10 illustrates an example traffic situation 1300 in a transportation network of multiple interconnected traffic intersections including mixed traffic controlled by one CTC 404 in combination with multiple ITCs 1311-1313 in a hierarchical traffic control system 600A, where each ITC is assigned the task of controlling the mixed traffic through one traffic intersection in the transportation network. In some embodiments, one or more rules are used to assign CAVs and / or HDVs to each of the ITCs 1011-1013 in the hierarchical traffic control system 600A to reduce the computational cost of solving the constrained optimization problem while maintaining good control performance and ensuring safety for all vehicles in the transportation network at all times.

[0235] Some embodiments of the present disclosure are based on the recognition that for both HDVs and CAVs controlled by different ITCs in a hierarchical traffic control system, a switched dynamic predictive model can be used at each ITC. For example, each CAV can be assigned to one "controlling" ITC, and the same CAV can be assigned to one or more other "predicting" ITCs to improve control performance and safety for all vehicles, especially as they transition from one ITC to the next in the transportation network.

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[0237] In some embodiments of the present disclosure, a CAV 1331 and / or HDV 1332 that is not currently within a predetermined distance of any traffic intersection in the transportation network is not currently assigned to any ITC in the hierarchical traffic control system and is therefore not included in any ITC's MIP formulation 1266. However, this CAV 1331 and / or HDV 1332 may be assigned to an ITC in a future time step once it is within a predetermined distance of any traffic intersection in the transportation network.

[0238] Some embodiments are based on the recognition that the latter set of rules for assigning vehicles to ITCs can ensure that speed and lane-change commands for each CAV are calculated by at most one ITC in the hierarchical traffic control system. According to some embodiments of the present disclosure, if a CAV is not assigned to any ITC, given a predetermined threshold distance, control is returned to the CAV's on-board control architecture. In some embodiments of the present disclosure, considering the area immediately following a traffic intersection, both HDVs and CAVs are treated equally in the ITC's MIP formulation 1266, and their behavior is predicted to prevent a possible collision with any vehicle further upstream. In some embodiments of the present disclosure, each ITC provides control commands to the CAV only prior to the traffic intersection and only while the vehicle is physically within the traffic intersection. Control is either returned to the vehicle or passed to the ITC corresponding to the next traffic intersection after the CAV exits the intersection.

[0239] 14A is a schematic diagram of an example of an integer optimization variable search tree representing a nested tree of search spaces for integer-feasible optimal solutions for hierarchical traffic control according to some embodiments of the present disclosure. FIG. 14A shows a schematic diagram of an example of a binary decision variable search tree 1400A representing a nested tree of search spaces for integer-feasible solutions to a MIP problem 1266 in a hierarchical traffic control system 600A. FIG. 14A shows a schematic diagram of a branch-and-bound method, which can be used to implement a hierarchical traffic control system in some embodiments by displaying a binary search tree 1400A at a particular iteration of a mixed-integer optimization algorithm. The main idea of ​​the branch-and-bound (B&B) method is to sequentially create partitions of the original MIP problem 1266 and then attempt to solve those partitions, with each partition corresponding to a particular region of the discrete optimization variable search space. In some embodiments of the present disclosure, the branch-and-bound method selects a partition or node and selects discrete optimization variables to branch this partition into smaller partitions or search areas, resulting in a nested tree of partitions or search areas.

[0240]

number

[0241] While solving each partition may still be difficult, it is quite efficient to find a local lower bound on the optimal objective value by solving a local relaxation of a mixed integer program (MIP) or by using duality. If the MIP solver happens to find an integer feasible solution while solving the local relaxation, the MIP solver can use it to find a global upper bound on the mixed integer solution of the original MIP problem in the hierarchical traffic control system. This can help avoid solving or branching certain partitions that have already been created; that is, these partitions or nodes can be pruned. This general algorithmic idea of ​​partitioning can be represented as a binary search tree 1400A that includes a root node at the top of the tree, e.g., P1 1401, and leaf nodes at the bottom of the tree, e.g., P4 1404 and P5 1405. Also, nodes P21402 and P31403 are generally referred to as direct children of node P11401, and node P11401 is generally referred to as the parent of nodes P21402 and P31403. Similarly, nodes P41404 and P51405 are children of their parent node P21402. In some embodiments of the present disclosure, the MIP problem may be a mixed integer linear programming (MILP) or a mixed integer quadratic programming (MIQP) problem.

[0242] Figures 14B and 14C , collectively, are block diagrams of a branch-and-bound mixed-integer optimization algorithm for searching for an integer-feasible optimal solution based on a nested tree of search regions and corresponding lower / upper bounds, according to some embodiments. The block diagram of the branch-and-bound mixed-integer optimization algorithm shown in Figures 14B and 14C can be used to implement a hierarchical traffic control system in some embodiments. The branch-and-bound method initializes 1410 branch search tree information for a mixed-integer program (MIP) in the current time step of the hierarchical traffic control system based on MIP data 1401, which is composed of matrices and vectors. In addition, this initialization can use the branch search tree information and MIP solution information from a previous time step 1412 to generate a warm-start initialization for the current time step 1410. The main goal of the optimization algorithm is to establish lower and upper bounds for the objective value of the mixed-integer solution. In step 1411, if the difference between the lower and upper bounds is less than a certain tolerance value, a mixed-integer optimal solution is found 1455.

[0243] As long as the difference between the lower and upper bounds in step 1411 is greater than a specified tolerance value and the optimization algorithm has not yet reached its maximum run time, the branch and bound method continues to iteratively search for a mixed integer optimal solution (1455). Each iteration of the branch and bound method begins by selecting (1415) the next node in the tree corresponding to the next region or partition of the integer variable search space, with possible variable fixes based on a pre-processing branching technique. After node selection, the corresponding integer relaxation problem is solved (1420), with possible variable fixes based on a post-processing branching technique.

[0244] If the integer relaxation problem has a feasible solution, the resulting relaxed solution provides a lower bound on the objective value for that particular region or partition of the integer variable search space. If, in step 1421, it is determined that the objective is greater than the currently known upper bound on the objective value of the optimal mixed integer solution, then the selected node is pruned or removed from the branching tree (1440). However, if, in step 1421, it is determined that the objective is lower than the currently known upper bound and the relaxed solution is integer feasible (1425), then, in step 1430, the currently known upper bound and the corresponding mixed integer solution estimate are updated.

[0245] If the integer relaxed problem has a feasible solution and the objective is lower than the currently known upper bound (1421), but the relaxed solution is not yet integer feasible, then the global lower bound on the objective may be updated to the minimum of the objective values ​​of the remaining leaf nodes in the branching tree (1435), and the selected node is pruned from the tree (1440). Also, starting from the current node, discrete variables with fractional values ​​are selected for branching according to a particular branching strategy (1445), with the objective to create resulting subproblems corresponding to regions or partitions of the discrete search space and append them as children of that node in the branching tree (1450).

[0246] A key step in the branch-and-bound method is how to create partitions, i.e., which nodes to select (1415) and which discrete variables to select for branching (1445). Some embodiments are based on branching one of the binary optimization variables that has a fractional value in the integer relaxation solution. For example, if a particular binary optimization variable d∈{0,1} has a fractional value as part of the integer relaxation optimal solution, some embodiments create two partitions of the mixed-integer problem by adding an equality constraint d=0 to one subproblem and an equality constraint d=1 to the other subproblem, respectively. Some embodiments are based on a reliability branching strategy for variable selection (1445), which aims to predict future branching behavior based on information from previous branching decisions.

[0247] Some embodiments are based on a branch-and-bound method using a depth-first node selection strategy, which can be implemented using a last-in-first-out (LIFO) buffer. The next node to be solved is selected as one of the children of the current node, and this process is repeated, followed by a backtracking procedure, until the node is pruned, i.e., the node becomes infeasible, optimal, or a currently known upper bound prevails. Alternatively, some embodiments are based on a branch-and-bound method using a best-first strategy, which selects the node with the currently lowest local lower bound. Some embodiments utilize a combination of depth-first and best-first node selection approaches, where a depth-first node selection strategy is used until an integer-feasible solution is found, and then a best-first node selection strategy is used in subsequent iterations of the branch-and-bound-based optimization algorithm. The latter implementation is motivated by seeking integer-feasible solutions early in the branch-and-bound procedure (depth-first), allowing for early pruning, followed by a more greedy search for better feasible solutions (best-first).

[0248] The branch-and-bound method continues to iterate until one or more of the following conditions are met:

[0249] The processor's maximum execution time is reached.

[0250] As a result of all the nodes in the branching search tree being pruned, no new nodes can be selected to solve the convex relaxation or perform branching.

[0251] The optimality difference between the global lower and upper bounds for the mixed integer solution objective is smaller than the tolerance.

[0252] Some embodiments recognize that optimization problems for CTC and / or ITC controllers can be solved exactly or inexactly. An exact solution is feasible and locally or globally optimal, while an inexact solution can be approximately feasible and / or suboptimal. Examples of exact optimization algorithms are interior point methods, active constraint methods, gradient methods, operator decomposition, sequential quadratic programming, sequential convex programming, branch and bound, branch and cut, and branch and price. Examples of inexact optimization algorithms are heuristic rules, early termination of exact optimization algorithms, rounding methods, machine learning-based approximations of optimal solutions, approximate dynamic programming, etc.

[0253] In some embodiments, the CTC and / or ITC control policies can be approximated by deep neural network architectures using, for example, reinforcement learning, to directly maximize reward functions for reducing congestion, travel times, emissions, and energy consumption within transportation networks. In other embodiments, the CTC and / or ITC control policies can be implemented using deep neural network architectures based on imitation learning, which aims to approximate expert solutions of corresponding optimization problems using exact optimization algorithms.

[0254] FIG. 15 is a block diagram of a hierarchical traffic control system 1500 for calculating motion plans for one or more control vehicles and one or more traffic light controllers in a transportation network of one or more interconnected traffic intersections, according to some embodiments of the present disclosure. The hierarchical traffic control system 1500 executes in the cloud or in one or more mobile edge computers (MECs). In addition, the system may require one or more edge devices (e.g., RSUs for infrastructure-based detection) configured with or operatively connected to a set of sensors to collect traffic information near one or more interconnected conflict zones in the transportation network. In some embodiments of the present disclosure, the hierarchical traffic control system is designed to transmit an optimal sequence 1522 of entry / exit times and average speeds, and / or a speed profile, one or more lane change commands, and a sequence 1524 of planned stops to each connected and autonomous vehicle (CAV) along a future planned route in the transportation network.

[0255] The hierarchical traffic control system 1500 comprises several interfaces connecting the decision-making system 1500 with other systems and devices. For example, the decision-making system 1500 comprises a network interface controller (NIC) 1502 adapted to connect the decision-making system 1500 via a bus 1504 to a network 1506 that connects the decision-making system 1500 with one or more devices 1508. Examples of such devices include, but are not limited to, vehicles, traffic lights, traffic sensors, roadside units (RSUs), mobile edge computers (MECs), and passenger mobile devices. Further, decision-making system 1500 includes a transmitter interface 1510 configured to transmit, using a transmitter 1512 and / or one or more devices 1508, an optimal sequence 1522 of entry / exit times and average speeds, and / or a speed profile, one or more lane change commands, and a sequence 1524 of planned stops, determined by one or more processors 1514, to each connected automated vehicle (CAV) along a future planned route in the transportation network. To improve the overall safety, time efficiency, and energy efficiency of traffic flow in the transportation network, in each CAV, the commands received from the hierarchical traffic control system can be used by a multi-layer guidance and control architecture to control the vehicle's motion.

[0256] In some embodiments of the present disclosure, the decision-making system 1500 includes a transmitter interface 1510, which is further configured to transmit, using a transmitter 1512 and / or one or more devices 1508, an optimal sequence of traffic light change commands determined by the one or more processors 1514 to each traffic light controller (TLC) in the transportation network of interconnected traffic intersections over a prediction time window.

[0257] The hierarchical traffic control system 1500 receives real-time traffic data 1532 via the network 1506 using a receiver interface 1528 connected to a receiver 1530. The decision-making system 1500 can receive traffic information for one or more of the interconnected conflict zones and road segments in the transportation network. The traffic data 1532 may include vehicle state (e.g., acceleration, position, heading, speed) information for each vehicle in the transportation network and planned and / or predicted future route (e.g., future road segments, truck lanes, desired destinations, wait time sequences). Additionally or alternatively, the decision-making system 1500 may include a control interface 1534 configured to send commands to one or more devices 1508 to change their respective states, such as acceleration, speed, etc. The control interface 1534 may use the transmitter 1512 and / or any other communication means to send these commands.

[0258] In some embodiments of the present disclosure, a human machine interface (HMI) 1540 connects the decision system 1500 to a keyboard 1536 and a pointing device 1538, which may include, among other things, a mouse, trackball, touchpad, joystick, pointing stick, stylus, or touch screen. The decision system 1500 may also be coupled via the bus 1504 to a display interface adapted to connect the decision system 1500 to a display device such as a computer monitor, camera, television, projector, or mobile device, among other things. The decision system 1500 may also be connected to an application interface adapted to connect the decision system 1500 to one or more devices for performing various power distribution tasks.

[0259] The decision-making system 1500 may include one or more processors 1514 configured to execute stored instructions and a memory 1516 storing instructions executable by the processor 1514. The processor 1514 may be a single-core processor, a multi-core processor, a computing cluster, a network of multiple connected processors, or any number of other configurations. The memory 1516 may include random access memory (RAM), read-only memory (ROM), flash memory, or any other suitable memory system. The processor 1514 may be connected to one or more input / output devices via a bus 1504. These instructions implement a method of hierarchical traffic control using a centralized traffic controller (CTC) and one or more intersection traffic controllers (ITCs) to control mixed traffic of CAVs and HDVs within a transportation network of multiple interconnected traffic intersections. In some embodiments of the present disclosure, the decision-making system 1500 includes a map configuration 1518. For example, the map configuration 1518 may include location data (eg, GPS data) for conflict-free road segments, traffic intersections, stopping zones, conflict zones, and lanes within each road segment of the transportation network.

[0260] The decision-making system 1500 includes constraints and objectives 1520 of one or more MIP problems 1266 and convex optimization problem 1158 that are solved at each time step of the hierarchical traffic control system. For example, the constraints and objectives 1520 may be configured to enforce physical limitations, vehicle speed limits, and / or safety constraints, and to minimize a weighted combination of travel time, waiting time, and / or energy consumption of each vehicle in the transportation network.

[0261] 16A is a schematic diagram of a vehicle 1601 including a multi-layer guidance and control architecture 1602 that controls the vehicle's motion based on a future route plan and a corresponding motion plan that can be computed by a hierarchical traffic control system for a transportation network, according to some embodiments of the present disclosure. As used herein, a vehicle 1601 may be any type of wheeled vehicle, such as a car, truck, shuttle, bus, or rover. The vehicle 1601 may also be an autonomous or semi-autonomous vehicle. For example, some embodiments control the motion of the vehicle 1601 based on a motion plan that can be computed by the hierarchical traffic control system. An example of the motion is the lateral motion of the vehicle, which is controlled by a steering system 1603 of the vehicle 1601. In some embodiments of the present disclosure, the steering system 1603 is controlled by the multi-layer guidance and control architecture 1602. Additionally or alternatively, the steering system 1603 can be controlled by a (human) driver of the vehicle 1601.

[0262] The vehicle may also include an engine 1606, which may be controlled directly by the multi-layer guidance and control architecture 1602 or by other components of the vehicle 1601. The vehicle may also include one or more on-board sensors 1604 for sensing the surrounding environment. Examples of sensors 1604 include range finders, radar, lidar, and cameras. The vehicle 1601 may also include one or more on-board sensors 1605 for sensing current motion quantities and internal conditions. Examples of sensors 1605 include a global positioning system (GPS), accelerometers, inertial measurement units, gyroscopes, shaft rotation sensors, torque sensors, deflection sensors, pressure sensors, and flow sensors. These on-board sensors provide information to the multi-layer guidance and control architecture 1602. The vehicle may be equipped with a transceiver 1608 that enables communication capabilities of the multi-tier guidance and control architecture 1602 via wired or wireless communication channels, for example, so that the vehicle 1601 communicates with a hierarchical traffic control system, in accordance with some embodiments of the present disclosure.

[0263] 16B is a schematic diagram of the interaction between the multi-layer guidance and control architecture 1610 (i.e., layers of algorithms and techniques for decision-making, motion planning, vehicle control, and / or estimation) and other controllers 1320 of the vehicle 1601, according to some embodiments of the present disclosure. For example, in some embodiments, the controllers 1620 of the vehicle 1601 are a steering controller 1625 and a brake / throttle controller 1630, which control the rotation and acceleration of the vehicle 1601, respectively. In such a case, the multi-layer guidance and control architecture 1610 outputs control inputs to the controllers 1625 and 1630 for controlling the state of the vehicle 1601. The controller 1620 may also include a higher-level controller, such as a lane-keeping assist controller 1635, that further processes the control inputs of the multi-layer guidance and control architecture 1602. In either case, controller 1620 uses the output of multi-layer guidance and control architecture 1610 to control at least one actuator of vehicle 1601, such as the steering wheel and / or brakes of vehicle 1601, to control the motion of vehicle 1601. In some embodiments of the present disclosure, vehicle 1601 is one of multiple CAVs in a transportation network, and multi-layer guidance and control architecture 1610 determines inputs to vehicle 1601 based on a motion plan calculated by a hierarchical traffic control system, and the inputs to vehicle 1601 may include one or a combination of acceleration of vehicle 1601, engine torque, brake torque, and steering angle of vehicle 1601.

[0264] The following description provides exemplary embodiments only and is not intended to limit the scope, applicability, or configuration of the present disclosure. Rather, the following description of exemplary embodiments will provide those skilled in the art with an enabling description for implementing one or more exemplary embodiments. Contemplated are various changes that may be made in the function and arrangement of elements without departing from the spirit and scope of the disclosed subject matter as set forth in the appended claims.

[0265] Specific details are set forth in the following description to provide a thorough understanding of the embodiments. However, those skilled in the art will understand that the embodiments may be practiced without these specific details. For example, systems, processes, and other elements of the disclosed subject matter may be shown as components in block diagram form so as not to obscure the embodiments in unnecessary detail. In other instances, well-known processes, structures, and techniques may be shown without unnecessary detail so as to avoid obscuring the embodiments. Furthermore, like reference numbers and names in the various drawings indicate like elements.

[0266] Also, particular embodiments may be described as a process that is depicted as a flowchart, a flow diagram, a data flow diagram, a structure diagram, or a block diagram. While a flowchart may describe operations as a sequential process, many of these operations can be performed in parallel or simultaneously. Also, the order of these operations may be rearranged. A process may terminate when its operations are completed, or may have additional steps not discussed or included in the diagram. Moreover, not all operations in any specifically described process are performed in all embodiments. A process may correspond to a method, a function, a procedure, a subroutine, a subprogram, etc. When a process corresponds to a function, the end of the function may correspond to the function returning to the calling function or the main function.

[0267] Furthermore, embodiments of the disclosed subject matter may be implemented at least in part manually or automatically. The manual or automatic implementation may be performed or at least assisted by the use of machines, hardware, software, firmware, middleware, microcode, hardware description languages, or any combination thereof. When implemented in software, firmware, middleware, or microcode, the program code or code segments to perform the necessary tasks may be stored on a machine-readable medium. A processor may perform the necessary tasks.

[0268] The various methods or processes outlined herein may be coded as software executable on one or more processors utilizing any one of a variety of operating systems or platforms. Additionally, such software may be written using any of a number of suitable programming languages ​​and / or programming or scripting tools, and compiled as executable machine language code or intermediate code that runs on a framework or virtual machine. Typically, the functionality of the program modules may be combined or distributed as desired in various embodiments.

[0269] The above-described embodiments of the present disclosure can be implemented in any of numerous ways. For example, these embodiments may be implemented using hardware, software, or a combination thereof. If implemented in software, the software code may be executed on any suitable processor or collection of processors, whether provided on a single computer or distributed among multiple computers. Such a processor may be implemented as an integrated circuit, with one or more processors being in an integrated circuit component. However, a processor may be implemented using circuitry in any suitable format.

[0270] Embodiments of the present disclosure may be embodied as a method, of which an example is provided. The acts performed as part of this method may be ordered in any suitable manner. Thus, embodiments may be constructed in which acts are performed in an order different from that shown, which may include performing some acts simultaneously even though they are shown as sequential acts in the example embodiment.

[0271] Although the present disclosure has been described with reference to certain preferred embodiments, it is to be understood that various other adaptations and modifications may be made within the spirit and scope of the disclosure. It is, therefore, the aspect of the appended claims to cover all such variations and modifications that come within the true spirit and scope of the disclosure.

Claims

1. 1. A traffic control system for cooperatively controlling one or more connected and automated vehicles (CAVs) and one or more human-driven vehicles (HDVs) traversing a plurality of intersections of a road according to an integer constraint for traversing each of the intersections, the traffic control system comprising: at least one processor; and a memory storing instructions, the instructions, when executed by the at least one processor, causing the traffic control system to: collecting digital representations of the status of each said CAV, each said HDV, and each traffic sign regulating traffic on said road; solving an optimization problem to jointly optimize traffic flow based on a macroscopic traffic flow model in a Centralized Traffic Controller (CTC) for the plurality of intersections using convex optimization subject to convex relaxation of the integer constraints for traversing each of the plurality of intersections; and solving a multivariable mixed-integer programming (MIP) problem in each of a plurality of intersection traffic controllers (ITCs), individually for each of the plurality of intersections, to generate control command values ​​for changing the state of each of the CAVs associated with an intersection of the plurality of intersections and control command values ​​for changing the state of each of the traffic signs associated with the intersection, the multivariable MIP problem optimizing a cost function according to the integer constraints to minimize a tracking error in traffic flow values ​​of a microscopic traffic flow model relative to relaxed traffic flow values ​​from the ITC, the cost function being optimized according to a motion model of the CAVs described by differential equations relating control commands for the CAVs associated with the intersections to changes in the state of the CAVs, and according to a motion model of the HDVs described by switching functions relating dynamic traffic rules for HDVs to the state of the HDVs and the states of corresponding traffic signs; and when executed by the at least one processor, the instructions further cause the traffic control system to: a traffic control system causing the optimized value of the control command to be transmitted to the corresponding CAV and a corresponding traffic sign;

2. The switching function for each of the HDVs includes one or more motion models under one or more switching conditions, the one or more motion models being: a first motion model for a stopping maneuver at a stopping zone when a corresponding traffic sign is red in a cross direction and the HDV is within a first safety distance from the stopping zone at each of the plurality of intersections of roads in a transportation network; a second motion model for safe leading vehicle following behavior when a leading vehicle is within a second safe distance ahead of the HDV and is in the same lane on the same road segment as the HDV; and a third motion model for traveling at a desired average speed when there is no preceding vehicle within the second safe distance ahead of the HDV and the preceding vehicle is not in the same lane as the HDV, or when the HDV is not within the first safe distance from the stopping zone and the corresponding traffic sign is not red.

3. 2. The traffic control system of claim 1, wherein the multivariable MIP problem at each of the plurality of ITCs includes a mapping between a plurality of collision-free states of the traffic sign and a value of the traffic sign for each cross direction of the plurality of intersections in a transportation network controlled by a hierarchical traffic control system.

4. the multivariable MIP problem at each of the plurality of ITCs includes a plurality of mixed-integer equality constraints and mixed-integer inequality constraints for enforcing traffic rules for the CAVs and the HDVs traveling near each of the plurality of intersections in the transportation network controlled by the hierarchical traffic control system; 4. The traffic control system of claim 3, wherein the traffic rules include constraints for crossing an intersection among the plurality of intersections based on a collision-free state of a corresponding traffic sign, capacity limit constraints for each of the plurality of intersections or each road segment within the transportation network, collision avoidance constraints between vehicle pairs, lane change constraints for overtaking vehicles, speed limit constraints, and traffic sign timing constraints.

5. 2. The traffic control system of claim 1, wherein the cost functions of the multivariable MIP problem at each of the plurality of ITCs include maximizing the distance traveled for each of the CAVs and HDVs traveling near one or more intersections of the plurality of intersections in a transportation network, minimizing the error between a current lane value and a preferred lane value for each of the CAVs and HDVs, minimizing the number of lane changes for each of the CAVs and HDVs, minimizing slack variables due to one or more constraint violations, and minimizing the least-squares tracking error between predicted traffic flow values ​​and reference CTC traffic flow values ​​in a cost function fitting method for a hierarchical traffic control system.

6. The macroscopic traffic flow model in the CTC is represented as a directed graph, each node of the directed graph corresponds to a road section among a plurality of road sections, and each edge of the directed graph corresponds to a connection between two road sections among the plurality of road sections; 2. The traffic control system of claim 1, wherein the connection between two road segments indicates a direction across an intersection of the plurality of intersections in a transportation network controlled by the hierarchical traffic control system.

7. The macroscopic traffic flow model in the CTC is a set of discrete-time differential equations including one or more differential state variables and one or more control input variables; The traffic control system of claim 6 , wherein each of the one or more differential state variables and one or more control input variables is included in an optimization variable of a convex optimization problem solved in the CTC.

8. the one or more differential state variables include a vehicle density variable that defines the number of vehicles for each pair of a road segment and a traffic movement maneuver among the plurality of road segments at each time step within a prediction time window of the CTC; 8. The traffic control system of claim 7, wherein the one or more control input variables include an inflow variable and an outflow variable that define the number of entering and exiting vehicles, respectively, for each pair of the road segment and the traffic movement maneuver at each time step within the prediction time window of the CTC.

9. the solution of the convex optimization problem is used by the CTC to calculate a set of optimal traffic flow probability values ​​according to the convex relaxation of mixed-integer constraints for vehicles crossing each of the plurality of intersections, for the switching behavior of the traffic signs, or for the collision-free status of the traffic signs at each of the plurality of intersections; 9. The traffic control system of claim 8, wherein the optimal traffic flow probability values ​​of the CTCs are used by a cost function fitting method at each of the plurality of ITCs to minimize tracking error between predicted traffic flow values ​​and CTC traffic flow values ​​over a forecast time range of the ITC for each crossing direction of the plurality of intersections.

10. 2. The traffic control system of claim 1, wherein the CTC solves a convex optimization problem having a cost function including at least one of maximizing a sum of traffic flow variables or minimizing a sum of traffic congestion variables within a transportation network controlled by the hierarchical traffic control system.

11. 2. The traffic control system of claim 1, wherein in the macroscopic traffic flow model, the CTC predicts the number of external vehicles entering the transportation network from each incoming direction at each time step within a prediction time window based on historical data collected for a similar transportation network during a past period similar to the prediction time window.

12. 2. The traffic control system of claim 1, wherein the CTC calculates at least one of a vehicle density or a vehicle routing probability value for each pair of road segment and traffic movement operation in the transportation network in the prediction time window based on historical data collected for a similar transportation network during a past period similar to the prediction time window.

13. 2. The traffic control system of claim 1, wherein a sampling period for realizing the setback range of the CTC is equal to or greater than a sampling period for realizing the setback range of each of the ITCs in the hierarchical traffic control system, and a length of a prediction time window of the CTC is equal to or greater than a length of a prediction time window of each of the ITCs in the hierarchical traffic control system.

14. 2. The traffic control system of claim 1, wherein the at least one processor causes the traffic control system to assign a set of CAVs from the one or more CAVs and a set of HDVs from the one or more HDVs to each ITC in a hierarchical traffic control system based on one or more rules.

15. an ITC of the plurality of ITCs calculates a speed command and a lane change command for each CAV of the one or more CAVs in the hierarchical traffic control system based on the one or more rules for the allocation of vehicles to the plurality of ITCs; 15. The traffic control system of claim 14, wherein if a CAV of the one or more CAVs is not assigned to any of the plurality of ITCs, authority to control the speed commands and the lane change commands is returned to the CAV's on-board control architecture.

16. 15. The traffic control system of claim 14, wherein each CAV of the one or more CAVs is assigned to an ITC of the plurality of ITCs for control, and the same CAV is assigned to one or more other ITCs for prediction based on a switching dynamic model similar to a switching dynamic model of the one or more HDVs.

17. The convex optimization problem solved in the CTC is a convex linear programming (LP) problem or a convex quadratic programming (QP) problem, 2. The traffic control system of claim 1, wherein the convex LP problem or the convex QP problem is solved using an active set method, an interior point method, a gradient method, an operator decomposition method, or an alternating direction method of multipliers (ADMM).

18. 2. The traffic control system of claim 1, wherein the CTC is implemented using a reinforcement learning (RL) policy, model-based or model-free RL technique, to maximize a reward function for reducing congestion, travel time, emissions, or energy consumption for each of one or more CAVs and one or more HDVs in the transportation network, and the RL policy is trained to calculate optimal traffic flow actions taking into account one or more state feedback signals from the transportation network.

19. the multivariable MIP problem for each of the plurality of ITCs is solved using a branch-and-bound (B&B) optimization method, which searches for a global optimum within a search space to generate optimal control signals; The traffic control system of claim 1 , wherein the B&B optimization method iteratively divides the search space into a nested tree of regions to find a solution with a globally optimal objective value at each ITC of the traffic control system.

20. the multivariable MIP problem for each of the plurality of ITCs is solved using heuristic techniques; The traffic control system of claim 1 , wherein the heuristic technique includes a rounding scheme, a feasibility pumping method, an approximate optimization algorithm, or a machine learning technique to predict an optimal solution to the multivariable MIP problem.

21. 1. A method for jointly controlling one or more connected autonomous vehicles (CAVs) and one or more human-driven vehicles (HDVs) traversing a plurality of intersections of a road according to integer constraints for traversing each of the intersections, the method comprising: collecting digital representations of the state of each said CAV, each said HDV, and each traffic sign regulating traffic on said road; solving an optimization problem to jointly optimize traffic flow based on a macroscopic traffic flow model in a centralized traffic controller (CTC) for the plurality of intersections using convex optimization subject to convex relaxation of the integer constraints for traversing each of the plurality of intersections; and solving a multivariable mixed integer programming (MIP) problem in each of a plurality of intersection traffic controllers (ITCs), individually for each of the plurality of intersections, to generate control command values ​​for changing the state of each of the CAVs associated with an intersection among the plurality of intersections and control command values ​​for changing the state of each of the traffic signs associated with the intersection, wherein the multivariable MIP problem optimizes a cost function according to the integer constraints to minimize a tracking error in traffic flow values ​​of a microscopic traffic flow model relative to relaxed traffic flow values ​​from the CTC, the cost function being optimized according to a motion model of the CAV described by differential equations relating control commands for the CAVs associated with the intersection to changes in the state of the CAVs, and according to a motion model of the HDV described by switching functions relating dynamic traffic rules for the HDVs to the state of the HDVs and the states of corresponding traffic signs; and wherein the method further comprises: transmitting the optimized value of the control command to the corresponding CAV and a corresponding traffic sign.

22. 1. A non-transitory computer-readable storage medium having embodied thereon a program executable by a processor for performing a method for cooperatively controlling one or more connected autonomous vehicles (CAVs) and one or more human-driven vehicles (HDVs) traversing a plurality of intersections of a road according to integer constraints for traversing each of the intersections, the method comprising: collecting digital representations of the state of each said CAV, each said HDV, and each traffic sign regulating traffic on said road; solving an optimization problem to jointly optimize traffic flow based on a macroscopic traffic flow model in a centralized traffic controller (CTC) for the plurality of intersections using convex optimization subject to convex relaxation of the integer constraints for traversing each of the plurality of intersections; and solving a multivariable mixed integer programming (MIP) problem in each of a plurality of intersection traffic controllers (ITCs), individually for each of the plurality of intersections, to generate control command values ​​for changing the state of each of the CAVs associated with an intersection among the plurality of intersections and control command values ​​for changing the state of each of the traffic signs associated with the intersection, wherein the multivariable MIP problem optimizes a cost function according to the integer constraints to minimize a tracking error in traffic flow values ​​of a microscopic traffic flow model relative to relaxed traffic flow values ​​from the CTC, the cost function being optimized according to a motion model of the CAV described by differential equations relating control commands for the CAVs associated with the intersection to changes in the state of the CAVs, and according to a motion model of the HDV described by switching functions relating dynamic traffic rules for the HDVs to the state of the HDVs and the states of corresponding traffic signs; and wherein the method further comprises: a non-transitory computer-readable storage medium, comprising: transmitting the optimized value of the control command to the corresponding CAV and a corresponding traffic sign;

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