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] This disclosure relates to optimization-based control in general, and more specifically to methods and apparatus for optimization-based hierarchical cooperative control of dynamic traffic rules and mixed traffic in a transport network of multiple interconnected traffic intersections. [Background technology]

[0002] The automation of transportation systems, even partially, leads to a reduction in road accidents and more efficient use of the road network. Therefore, connected and automated vehicles (CAVs) have great potential to improve safety and traffic flow, and as a result, have great potential to reduce congestion, travel time, emissions, and energy consumption. This has been known for decades, but most of the successful developments have been achieved in recent years through technological advancements in sensing, computing, control, and connectivity. Road conditions are often extremely dynamic, meaning that vehicle participants and their behavior change rapidly and significantly, but vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) communication (also known as vehicle-to-everything (V2X) communication) enables efficient planning and decision-making by providing access to real-time information about all vehicles within a specific planning area.

[0003] Significant advances have been made in planning and control for autonomous driving, which generally requires multi-layered guidance and control architectures implemented in vehicles. At the highest level, an intelligent navigation system finds a route through the transport network from the vehicle's current location to the requested destination. Decision-makers, using automata combined with, for example, collective reachability or formal language and optimization, select appropriate driving behavior at any given time, considering the route plan, current environmental conditions, and the behavior of other traffic participants. Considering target behaviors including lane following, lane changing, or stopping, motion planning algorithms calculate dynamically feasible and safe trajectories that can be tracked in real time by low-level feedback controllers. A common approach uses a combination of a sampling-based motion planner and Model Predictive Control (MPC) for reference tracking. While the guidance and control architecture of a CAV may appear similar to standard guidance and control architectures for autonomous driving, some of its modules can be implemented within the infrastructure, for example, in a mobile edge computer (MEC), to provide decisions to multiple vehicles in an area, while other modules can continue to be implemented individually on each vehicle.

[0004] By coordinating cooperative agents, it becomes possible to achieve socially optimal behavior for the transportation network. As an example, we describe a First Come, First Serve (FCFS) policy for autonomous traffic management at intersections. Recently, cooperative strategies for intersection control using nonlinear optimization or mixed-integer linear programming (MILP) have been proposed. The latter has been extended to distributed MILP algorithms for planning grids of interconnected intersections. Also, an 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 be noted that intersection and merging control problems are essentially very similar.

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

[0006] However, in most situations, it is reasonable to expect that autonomous vehicles will share the roads with conventional vehicles, i.e., human-driven vehicles (HDVs), for many years, and possibly indefinitely. Therefore, ensuring appropriate interaction between autonomous and human-driven vehicles is crucial for optimizing traffic behavior across the entire transport network. In these cases, the CTC only needs to directly control the CAV while anticipating the specific behavior of the HDVs. In some approaches, the HDVs will always be prioritized because nothing will change their behavior, and the CAVs will always adjust their actions to match the expected behavior of the HDVs. However, this solution is inherently suboptimal because only partial control of the vehicles is possible in this situation.

[0007] In other HDV-only scenarios, HDV traffic flow is controlled via controllable road infrastructure elements such as traffic lights. HDV flow is influenced by the timing and ordering of traffic lights so that the overall operation of the transport network is positively affected. However, in such models, since vehicles are driven by human drivers, the control effect on vehicles is limited to stopping them at specific times and locations. Thus, the control over the transport network is limited because only traffic lights can be controlled. To address this problem, centralized coordinated systems and methods are used to coordinate the operation of CAVs and achieve overall optimization of transport networks with multiple connected traffic intersections, as well as mixed CAVs and HDVs, using controllable infrastructure elements such as traffic lights that can influence HDV traffic. However, the resulting centralized optimization problem is a large-scale mixed-integer programming (MIP) problem that is computationally difficult to solve in real time.

[0008] Therefore, it is necessary to consider computationally traceable, optimization-based, hierarchical systems and methods that coordinate the real-time operation of CAVs and controllable infrastructure elements that can affect HDV traffic, such as traffic signals, by solving one or more isolated optimization problems, thereby achieving overall optimization of a transportation network that includes multiple connected traffic intersections and where CAVs and HDVs coexist. [Overview of the Initiative]

[0009] Some embodiments are based on the recognition that there is a need for a computationally traceable solution for the overall optimization of transportation networks with mixed traffic, which is computationally more efficient than the conventional solutions described above.

[0010] The objective of some embodiments is to provide an optimization-based hierarchical system and method for dynamic traffic rules and the coordinated operation and control of mixed traffic, including connected automated vehicles (CAVs) and human-driven vehicles (HDVs), in a transit network of multiple connected traffic intersections. In some embodiments of the Disclosure, the hierarchical system calculates dynamic traffic rules affecting HDVs over a predicted range, using controllable infrastructure elements referred herein as traffic signs. Examples of traffic signs include traffic signals, lane-activating electronic displays, and variable speed limits. In some embodiments of the Disclosure, the hierarchical system calculates a sequence of speed targets over a predicted range for each CAV in the transit network, and these target trajectories may be executed by the on-board planning and control architecture of each CAV.

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

[0012] In one embodiment, the hierarchical system is based on a multi-layer guidance and control architecture in which some modules are mounted and implemented on each CAV, while other modules operate centrally or decentralized within the transportation network infrastructure, for example, in a mobile edge computer, to take advantage of V2X connectivity. Specifically, in each CAV, considering target behaviors representing actions such as lane following, lane changing, or stopping, a motion planning algorithm calculates a dynamically feasible and safe trajectory that can be tracked in real time by the vehicle controller of the corresponding CAV. Some embodiments are based on a probabilistic sampling-based motion planner and MPC algorithm for reference tracking in each CAV.

[0013] Some embodiments are based on the recognition that obtaining accurate predictions for HDVs may be difficult depending on the infrastructure of the transportation network. Therefore, in some embodiments, hierarchical vehicle coordination and scheduling modules are implemented in a reverse-range manner based on the latest information. Some embodiments are based on the recognition that CTC controllers may calculate high-level targets over medium- or long-term prediction ranges at a relatively low frequency, while ITC controllers may calculate control trajectories over short- or medium-term prediction ranges at a relatively high frequency, for example, with each ITC controller using an update period of 0.5 to 1 second, while the global CTC controller uses an update period of 1 to 2 seconds. Any discrepancies in predictions can be adjusted by the inherent feedback mechanism of the coordination system's reverse-range strategy.

[0014] Some embodiments are based on the understanding that the presence of other traffic participants, such as bicycles and pedestrians, can be managed as obstacles by on-board modules within each CAV's multi-layer guidance and control architecture, such as motion planning and / or vehicle control algorithms. Because their computational cost is relatively low compared to hierarchical vehicle coordination systems, motion planning and vehicle control algorithms can be run at relatively fast sampling rates, with the aim of having a quick response time to unexpected changes in the behavior of other traffic participants, such as bicycles, pedestrians, and other vehicles, within the transport network. For example, vehicle control algorithms are often run with update intervals of 50-100 milliseconds.

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

[0016] In some embodiments, a simplified macroscopic traffic model may be obtained based on representing the transport network as, for example, a directed graph, in which each road section 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 that are scheduled to go straight, turn left, or turn right in each road section represented as a node in the directed graph. Inputs to the macroscopic traffic model may include the directed graph and the number of vehicles moving from one road section to the next, taking into account the maximum capacity of each traffic intersection and time delay constraints that enforce the expected travel time of vehicles within each road section. 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 in which a global optimal solution can be computed 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, and as a result, can solve a convex linear programming (LP) problem using an LP optimization algorithm, such as the simplex method, the effective constraint method, or the interior point method. In some embodiments, the optimization problem of the global CTC controller is a non-convex smoothing nonlinear programming (NLP) or mixed integer programming (MIP) optimization problem in which a local optimal or suboptimal solution can be computed at each time step of the global CTC controller.

[0018] In some embodiments, each ITC controller solves a short-term or medium-term range optimization problem that computes a speed target and a sequence of lane change commands for each CAV, as well as a sequence of commands for one or more dynamic traffic rules, e.g., traffic signals, near a traffic intersection. The resulting optimization problem is a MIP, e.g., a mixed-integer linear programming (MILP) or mixed-integer quadratic programming (MIQP) problem. Some embodiments of this disclosure are based on the understanding 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 transport network.

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

[0020] In some embodiments, the microscopic traffic model includes predicting the behavior of HDVs using a switching dynamic system to represent the reaction of HDVs to traffic rules that may change in some cases. In one example, the state-dependent switching dynamics are as follows: (1) when the traffic signal for the desired traffic direction of the HDV is red and the HDV is within a predetermined distance from the stop zone of a particular intersection, the HDV stops at the traffic signal of this intersection; (2) otherwise, when a leading vehicle is within a particular predetermined distance ahead of the HDV within the transportation network, the HDV follows the leading vehicle and maintains a safe following distance; (3) otherwise, the HDV travels within the transportation network at the desired target speed.

[0021] In some embodiments, HDV modeling can be used to model both HDVs and CAVs controlled by different ITCs. For this purpose, each CAV can be assigned to a particular ITC for control or prediction only. This technology 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 done in the following given steps, but is not limited thereto. (1) Each HDV is assigned to the prediction ITC of the next traffic intersection when it is within a predetermined distance.

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

[0023] (3) Each CAV is assigned to the prediction ITC of the previous traffic intersection when it is within a predetermined distance. That is, it will be regarded as an HDV by the corresponding ITC controller.

[0024] In some embodiments of the present disclosure, each ITC calculates the CAV speed and lane change trajectory, as well as the signal phase switching trajectory of its specific traffic intersection, and these calculations of each ITC can be executed in parallel on separate computing units.

[0025] Some embodiments are based on the recognition that the optimization problems of the CTC controller and the ITC controller may be solved accurately or inaccurately. An accurate solution is executable and locally or globally optimal, while an inaccurate solution may be approximately executable or sub-optimal. Examples of accurate optimization algorithms include, but are not limited to, the interior point method, the active constraint method, the gradient method, the operator splitting method, the sequential quadratic programming method, the sequential convex programming method, the branch and bound method, the branch and cut method, and the branch and price method. Examples of inaccurate optimization algorithms include, but are not limited to, heuristic rules, early termination of accurate optimization algorithms, rounding methods, machine learning-based approximations of optimal solutions, or approximate dynamic programming methods.

[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 example, reinforcement learning may be used, but is not limited to, directly maximizing a reward function for reducing congestion, travel time, exhaust gas, and energy consumption within the transportation network. In other embodiments, one or both of the CTC and ITC control policies may be realized using a deep neural network architecture based on imitation learning aimed at approximating an expert solution to the corresponding optimization problem using an accurate optimization algorithm.

[0027] Accordingly, some embodiments disclose a traffic control system 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, subject to integer constraints for traversing each of the intersections. The traffic control system includes at least one processor and a memory storing instructions, which, when executed by the at least one processor, cause the traffic control system to collect digital representations of the state 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 for jointly optimizing traffic flow based on a macroscopic traffic flow model in a centralized traffic controller (CTC) for the plurality of intersections, using convex optimization that undergoes 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 for each of the multiple intersections in each of the multiple intersection traffic controllers (ITCs) to generate control command values ​​that change the state of each of the CAVs associated with one of the multiple intersections, and control command values ​​that change 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 the tracking error in the traffic flow values ​​of the microscopic traffic flow model for the relaxed traffic flow values ​​from the CTC, wherein the cost function is 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 state of the 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 the corresponding traffic signs.

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

[0029] Accordingly, yet another embodiment discloses a non-temporary computer-readable storage medium embodying a processor-executable program for performing 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, subject to integer constraints for traversing each of the plurality of intersections. The method includes the step of collecting digital representations of the state of each of the CAVs, each of the HDVs, and each traffic sign regulating traffic on the road. The method further includes the step of solving an optimization problem for jointly optimizing traffic flow based on a macroscopic traffic flow model in a centralized traffic controller (CTC) for the plurality of intersections, using a convex optimization that undergoes a convex relaxation of the integer constraints for traversing each of the plurality of intersections. The method further includes the step of individually solving a multivariable mixed integer programming (MIP) problem for each of the multiple intersections in each of the multiple intersection traffic controllers (ITCs) to generate values ​​for control commands that change the state of each of the above CAVs associated with one of the multiple intersections, and values ​​for control commands that change the state of each of the above traffic signs associated with the above intersection, wherein the multivariable MIP problem optimizes a cost function according to the integer constraints to minimize the tracking error in the traffic flow values ​​of the microscopic traffic flow model for relaxed traffic flow values ​​from the above CTC, wherein the cost function is optimized according to a motion model of the above CAVs described by differential equations relating control commands for the above CAVs associated with the intersection to changes in the state of the above CAVs, and according to a motion model of the above HDVs described by switching functions relating dynamic traffic rules for HDVs to the state of the above HDVs and the state of the corresponding traffic signs. The method further includes the step of transmitting the optimized values ​​of the above control commands to the corresponding CAVs and the corresponding traffic signs. The embodiments disclosed herein will be further described with reference to the attached drawings. The drawings shown are not necessarily drawn to a specific scale, and instead, the emphasis is on illustrating the principles of the embodiments disclosed herein as a whole. [Brief explanation of the drawing]

[0030] [Figure 1] This block diagram shows an exemplary network environment for optimization-based hierarchical traffic control of controlled and uncontrolled vehicles, according to some embodiments of the present disclosure. [Figure 2] This flowchart shows an exemplary method for optimization-based hierarchical traffic control of controlled and uncontrolled vehicles, according to one embodiment of the present disclosure. [Figure 3] This figure shows 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] This figure shows an example of controlling traffic in a local area of ​​multiple interconnected traffic intersections using dynamic traffic rules and mixed traffic optimization-based hierarchical cooperative control, according to some embodiments of the present disclosure. [Figure 4B] This figure shows an example of traffic conditions in a local area of ​​an interconnected intersection and routing information for multiple connected autonomous vehicles, according to some embodiments of the present disclosure. [Figure 5] This diagram shows possible interactions between a hierarchical traffic control system, a mapping and navigation system, one or more control vehicles and human-driven vehicles, roadside units, a traffic signal controller, and a mobile edge computer, according to some embodiments of the present disclosure. [Figure 6A] This is a schematic diagram of a feedback loop for a hierarchical traffic control system in a transport network, according to some embodiments of the present disclosure. [Figure 6B] This is a schematic diagram of a feedback loop for one intersection traffic controller (ITC) in a hierarchical traffic control system within a transport network, according to some embodiments of the present disclosure. [Figure 6C] This is a schematic diagram of a feedback loop for a hierarchical traffic control system in a transport network, according to some embodiments of the present disclosure. [Figure 7] This figure shows an exemplary operation for optimization-based hierarchical traffic control of controlled and uncontrolled vehicles, according to one embodiment of the present disclosure. [Figure 8A] This is an illustrative diagram of a four-way traffic intersection in a transport network controlled by a hierarchical traffic control system, according to some embodiments of the present disclosure. [Figure 8B] This figure shows an example of a mapping between multiple collision-free states and signal values ​​for each crossing direction of a traffic intersection in a transport network controlled by a hierarchical traffic control system, according to some embodiments of the present disclosure. [Figure 8C] This figure shows an example of a traffic flow plan calculated by a Central Traffic Coordinator (CTC) using a table of traffic flow values ​​for each transverse direction at a traffic intersection in a transport network controlled by a hierarchical traffic control system, according to some embodiments of the present disclosure. [Figure 9] This figure shows an exemplary cost function fitting method for a hierarchical traffic control system according to some embodiments of the present disclosure. [Figure 10A] This figure shows an example of a multi-lane road section in a transportation network according to some embodiments of the present disclosure. [Figure 10B] This figure shows an example of vehicle density values ​​over a predicted time range for multi-lane road sections within a transport network, used in a macroscopic traffic flow model of a hierarchical traffic control system according to some embodiments of the present disclosure. [Figure 10C] This figure shows an example of multiple transverse directions over a predicted time range for a three-way traffic intersection in a transport network, according to some embodiments of the present disclosure. [Figure 10D] This figure shows an example of traffic flow values ​​in multiple transverse directions over a predicted time range for a three-way traffic intersection in a transport network, used in a macroscopic traffic flow model of a hierarchical traffic control system according to some embodiments of the present disclosure. [Figure 10E] This figure shows an example of multiple transverse directions over a predicted time range for a three-way traffic intersection in a transport network, according to some embodiments of the present disclosure. [Figure 10F] This figure shows an example of vehicle density values ​​in multiple transverse directions over a predicted time range for a three-way traffic intersection in a transport network, used in a macroscopic traffic flow model of a hierarchical traffic control system according to some embodiments of the present disclosure. [Figure 11A] This figure shows a method for constructing and solving a constrained optimization problem for calculating a macroscopic traffic flow motion plan for one or more traffic signals and connected autonomous vehicles (CAVs) in a transport network including a plurality of interconnected traffic intersections, according to some embodiments of the present disclosure. [Figure 11B] This figure shows a method for constructing and solving a constrained convex programming (CP) problem for calculating the optimal sequence of high-level target values ​​for traffic flow in a transport network of multiple interconnected traffic intersections, according to some embodiments of the present disclosure. [Figure 11C] This figure shows a method for constructing and solving a constrained convex programming (CP) problem for calculating an optimal sequence of high-level target values ​​for traffic flow in a transport network of multiple interconnected traffic intersections, according to some embodiments of the present disclosure. [Figure 12A] This figure shows a method for constructing and solving a constrained optimization problem for calculating a microscopic traffic flow motion plan for one or more traffic signals and connected autonomous vehicles (CAVs) in a local area around one or more interconnected traffic intersections in a transport network, according to some embodiments of the present disclosure. [Figure 12B] This is a schematic diagram of a formulation of a MIP problem based on a microscopic traffic model for mixed traffic in local areas controlled by ITC around one or more traffic intersections in a transport network, according to some embodiments of the present disclosure. [Figure 12C]This is a flowchart of a switching function in a predictive motion model of one or more HDVs used in a microscopic model for mixed traffic in an ITC-controlled local area around one or more traffic intersections in a transport network controlled by a hierarchical traffic control system, according to some embodiments of the present disclosure. [Figure 12D] This is a schematic diagram of an HDV motion model according to some embodiments of the present disclosure. [Figure 12E] This figure shows a method for constructing and solving a MIP problem based on mixed integer equality and mixed integer inequality constraints for a predictive motion model of one or more CAVs, HDVs, TLCs and non-convex traffic rules in a transport network controlled by a hierarchical traffic control system, according to some embodiments of the present disclosure. [Figure 13] This figure shows an example of traffic conditions in a transport network of multiple interconnected traffic intersections, including mixed CAV and HDV traffic controlled by a single CTC in combination with multiple ITCs in a hierarchical traffic control system, according to some embodiments of the present disclosure. [Figure 14A] This is a schematic diagram of an example of an integer optimization variable search tree representing a nested tree of search domains for integer feasible optimal solutions for hierarchical traffic control, according to some embodiments of the present disclosure. [Figure 14B] This is a block diagram of a branch-bound mixed integer optimization algorithm for searching for an integer feasible optimal decision solution based on a nested tree of search domains and corresponding lower / upper bounds, according to some embodiments of the present disclosure. [Figure 14C] This is a block diagram of a branch-bound mixed integer optimization algorithm for searching for an integer feasible optimal decision solution based on a nested tree of search domains and corresponding lower / upper bounds, according to some embodiments of the present disclosure. [Figure 15] This is a block diagram of a hierarchical traffic control system for calculating motion plans for one or more control vehicles in a transport network of one or more interconnected conflict zones, according to some embodiments of the present disclosure. [Figure 16A] This is a schematic diagram of a vehicle including a multi-layer induction and control architecture according to some embodiments of the present disclosure. [Figure 16B] This is a schematic diagram illustrating the interaction between a multilayer induction and control architecture and other controllers in a vehicle, according to some embodiments of the present disclosure. [Modes for carrying out the invention]

[0031] Some embodiments of this disclosure provide systems and methods for controlling one or more connected autonomous vehicles (CAVs) within a transport network comprising one or more interconnected traffic intersections and including a dynamic environment. The dynamic environment includes, but is not limited to, one or more human-driven vehicles, traffic participants, or dynamic obstacles.

[0032] The terms “for example,” “for instance,” and “such as,” as used herein and in the claims, as well as the verbs “comprising,” “having,” and “including,” and any other forms thereof, should be interpreted as open-ended, meaning that when used with an enumeration of one or more components or other items, the enumeration should not be considered to exclude any further components or items. The term “based on” means based at least in part. Furthermore, it should be understood that the phrasing and terminology used herein are for illustrative purposes only and should not be considered limiting. Any headings used in this description are for convenience only and have no legal or limiting effect.

[0033] Figure 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 Figure 1, the network environment 100 is shown. The network environment 100 may include a hierarchical traffic control system 102 and a transport network 104 communicably coupled to the hierarchical traffic control system 102. A communication network 106 and a database 108 accessible to the hierarchical traffic control system 102 via the communication network 106 are further shown. In Figure 1, the hierarchical traffic control system 102, the communication network 106 and the database 108 are shown as separate devices, but in some embodiments, the entire functionality of the hierarchical traffic control system 102, the communication 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 preferred logic, circuits, codes and / or interfaces that can be configured to generate control commands that change the state of a controlled vehicle and control commands that change the state of traffic signs or signals associated with multiple intersections within the transport network 104. The hierarchical traffic control system 102 transmits the generated control commands to the controlled vehicle and traffic signs or signals. Examples of the hierarchical traffic control system 102 include, but are not limited to, servers, computer workstations, mainframe machines and / or laptops.

[0035] The transport network 104 may include a control vehicle 110, a human-driven vehicle 112, a traffic controller 114, and a sensor 116. In Figure 1, the sensor 116 is shown as separate from the control vehicle 110 and the human-driven vehicle 112, but in some embodiments, the entire functionality of the sensor 116 may be individually incorporated into the control vehicle 110 or the human-driven vehicle without departing from the scope of this disclosure. Examples of the control vehicle 110 include, but are not limited to, an unmanned vehicle, a connected autonomous vehicle (CAV), and / or a connected semi-autonomous vehicle. Examples of the human-driven vehicle 112 include, but are not limited to, a manually driven vehicle that is largely controlled and managed by a human. Examples of the traffic controller 114 include, but are not limited to, traffic signals or traffic signs that control the movement of traffic on roads and across intersections within the transport network 104. The color of traffic lights or signs defines whether a vehicle moving on a road or at an intersection within the transport network 104 should be stopped, allowed to continue moving, or slowed down. Examples of sensors 116 include, but are not limited to, rangefinders, radar, lidars, or cameras for accurately detecting the state of a vehicle, as well as the dynamic environment, including connected and unconnected vehicles, autonomous vehicles, semi-autonomous vehicles, and manually operated vehicles, and other traffic participants such as bicycles and pedestrians.

[0036] The communication network 106 may include a communication medium through which the hierarchical traffic control system 102 can communicate with the transport network 104 and other devices omitted from this disclosure for brevity. The communication network 106 may be either a wired or wireless connection. Examples of the communication network 106 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). Various devices within 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 include, but are not limited to, at least one of the following: 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), terminal-to-terminal communication, cellular communication protocols, and Bluetooth (BT) communication protocols.

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

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

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

[0040] In 200-2, an optimization problem for co-optimizing traffic flow based on a macroscopic traffic flow model in a centralized traffic controller (CTC) for multiple intersections is solved using convex optimization with convex relaxation of integer constraints for crossing each of multiple intersections. In one embodiment, optimizing traffic flow involves optimizing traffic flow values ​​by convex relaxation of integer constraints for crossing each of multiple intersections. Optimizing traffic flow values ​​results in relaxed traffic flow values. Integer constraints are carefully designed and incorporated into the optimization problem, for example, to avoid collisions while crossing intersections. Integer constraints restrict some or all variables in the optimization problem to accept only integer values. This makes it possible to accurately model the optimization problem involving discrete quantities such as discrete representations of the state of each CAV, each HDV, and each traffic sign or signal regulating traffic on the road. Convex optimization with integer constraints is a problem where 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 refers simply to the technique of removing a particular constraint from an optimization problem. Specifically, convex relaxation means that the problem becomes convex when relaxed or when certain constraints are removed. In one embodiment, convex relaxation of integer constraints enforcing multiple traffic rules includes convex relaxation of integer constraints for the switching behavior of vehicles crossing each intersection and for traffic signals. For this purpose, traffic flow values ​​are relaxed using convex relaxation, which involves removing certain constraints, to obtain relaxed traffic flow values, and these relaxed traffic flow values ​​make the optimization problem convex.

[0041] In 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 ​​that change the state of each CAV associated with a given intersection and control command values ​​that change the state of each traffic sign associated with that intersection. To generate the control command values ​​that change the state of each CAV associated with that intersection and control command values ​​that change the state of each traffic sign associated with that intersection, the multivariable MIP problem optimizes a cost function according to integer constraints to minimize the tracking error in the traffic flow values ​​of the microscopic traffic flow model relative to the 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 a differential equation relating the control command for the CAV to the change in the state of the CAV, and according to a motion model of the HDV described by a switching function relating the dynamic traffic rules for the HDV to the state of the HDV and the state of the corresponding traffic sign.

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

[0043] While flowchart 200 is shown as individual operations such as 200-1, 200-2, 200-3, and 200-4, the disclosure is not limited in that way. 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] Figure 3 shows an example of a 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. Figure 3 shows an example of a traffic situation that illustrates the need for optimization-based hierarchical coordination and control of traffic rules, signals, controlled vehicles and human-driven vehicles in a local area of ​​multiple interconnected conflict zones, for example, an interconnected intersection of a road section. 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 merging point where vehicles can travel from one conflict zone to another. An example of a communicatively interconnected conflict zone is a traffic intersection or merging point where traffic information is shared from one conflict zone to another via a communication channel.

[0045] The example of traffic conditions in Figure 3 shows a transport network including multiple interconnected traffic intersections 101 and 103 that are physically interconnected to one another via road section 105. This transport network further includes road sections 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 signal display 150, and a lane access status display 151.

[0046] The transport network may include one or more conflict zones and one or more conflict-free zones. Multiple interconnected traffic intersections 101 and 103 are examples of one or more conflict zones or merging points within the transport network. Multiple interconnected traffic intersections 101 and 103 may connect multiple lanes or road sections 105, 107, 109, 111, 113, 114, and 116. An example of one or more conflict-free zones is road sections 105, 107, 109, 111, 113, 114, and 116 consisting of one or more lanes that allow traffic in either a single direction or multiple directions.

[0047] In one embodiment, each of the vehicles 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, and 146 in the transport network may be an autonomous vehicle, a semi-autonomous vehicle, or a manually operated vehicle. In one example, autonomous and semi-autonomous vehicles are connected automated vehicles (CAVs). Alternatively, autonomous and semi-autonomous vehicles may be referred to as controlled vehicles. In one example, a manually operated vehicle or other traffic participant may be an example of a human-driven vehicle (HDV). In another example, 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 automobiles, or vehicles with four or more wheels such as trucks.

[0048] In one embodiment, vehicles 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, and 146 are subject to general traffic rules. In one example, general traffic rules include, but are not limited to, rules regarding crossing intersections, avoiding collisions with adjacent vehicles, occupying empty lanes, or meeting lane speed limits. In one embodiment, general traffic rules may include dynamic traffic rules that change dynamically upon receiving corresponding control commands. In one example, general traffic rules include constraints for crossing one of several intersections based on the collision-free state of corresponding traffic signs, capacity limit constraints for each of several intersections or each road section in the transport network, collision avoidance constraints between vehicle pairs, lane change constraints for vehicle overtaking, 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 of when more or fewer vehicles pass through a particular crossing; variable speed limits that can receive control commands to change the maximum speed of vehicles in a particular lane; and dynamically activated lanes that can receive control commands to open or close access to a lane. Dynamic traffic rules may be displayed on digital displays on road sections 105, 107, 109, 111, 113, 114, and 116 to notify vehicles 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, and 146 of the status of the dynamic traffic rules. For example, a traffic light display 150 may be configured to display the status of traffic lights at multiple interconnected traffic intersections 101, and a lane speed display may be configured to display lane speed limits. In one example, a lane access status display 151 may be configured to display a status indicating whether access to a lane 153 of the transport 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 within a local area around each RSU 122, 124. In one embodiment, the traffic situation in Figure 3 shows one RSU 122 and another RSU 124, a core network 120 and a cloud network 118 for establishing an Internet of Vehicles (IoV) environment, including vehicle-to-vehicle (V2V) communication and vehicle-to-infrastructure (V2I) communication, also known as vehicle-to-anything (V2X) communication.

[0050] In one embodiment, multi-hop communication is established between different vehicles within a transport network, for example, between vehicles 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, and 146. Communication between the cloud network 118 and vehicles such as vehicle 126 on road section 105 needs to propagate through RSU 122 or RSU 124 and the core network 120. In some embodiments, the safe 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, the cloud network 118 and the 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 of implementation, the MEC may be incorporated as part of one or more RSUs 122,124, or it 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, but is not limited to these. Embodiments of the present disclosure include solving one or more constrained optimization problems at each sampling time step for the coordinated control of dynamic rules, signals, and vehicles in a transport network, which can be computed on either the cloud network 118 or one or more MECs.

[0051] In some embodiments, the traffic conditions 300 in Figure 3 correspond to a public metropolitan area where road sections 105, 107, 109, 111, 113, 114, and 116 form multiple interconnected traffic intersections, such as 101 and 103. In this metropolitan area, traffic conditions at the multiple interconnected traffic intersections 101 and 103 determine the traffic flow because traffic congestion typically starts at a traffic intersection, such as intersection 103, and propagates further to road sections, such as 105, 107, 109, 111, 113, 114, and 116. The traffic conditions at the interconnected traffic intersections 101 and 103 are interdependent such that a change at one intersection, such as intersection 103, propagates further to other interconnected intersections, such as intersection 101, which is a neighboring intersection to intersection 103.

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

[0053] In the transportation network of traffic condition 300 shown in Figure 3, the on-board control devices of vehicles such as vehicle 146 cannot acquire information about nearby vehicles such as vehicle 142, pedestrians, and environmental conditions 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 the intersection 101, and a smaller vehicle such as vehicle 142 is also entering intersection 101. In this situation, as shown in Figure 5, the visibility of vehicle 142 to vehicle 146 is obstructed by vehicle 144. 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 will 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 would be unacceptable in the real-time context of cloud-based vehicle control.

[0054] Some embodiments are based on the understanding that different communication technologies can be used to support vehicle communication. Examples include the IEEE Dedicated Short-Range Communication / Wireless Access (DSRC / WAVE) standards for vehicle environments for vehicle networks, and 3GPP C-V2X (Cellular-Vehicle-to-Anything). However, due to high costs, it is impractical for vehicles, such as vehicles 126, 128, 130, 132, 134, 136, 138, 140, 142, 144, and 146, to support two or more short-range communication technologies, which would create compatibility issues between communicating vehicles. Therefore, 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 by the on-board multi-layer guidance and control architecture in each individual vehicle will be severely affected because the real-time decisions will be based on incomplete information about the traffic conditions shown in Figure 3. To this end, embodiments of the present disclosure use an optimization-based hierarchical traffic control system that utilizes real-time information from vehicles, dynamic traffic rules, and traffic signals within the transport network to ensure safety, time efficiency, and energy efficiency.

[0055] Some embodiments of this disclosure are based on the recognition that edge infrastructure devices, such as RSU122 and RSU124, have advantages with respect to multi-vehicle traffic control compared to using only cloud networks or only in-vehicle devices including multi-layer guidance and control architectures. For example, edge infrastructure devices may be installed at intersections or merging points, such as multiple interconnected traffic intersections 101, 103, and can communicate directly with vehicles approaching the intersections or merging points. 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 enabled to provide reliable communication with vehicles and to collect relatively high-quality environmental data.

[0056] Edge infrastructure devices can continuously monitor multi-vehicle traffic and the environment for accurate decision-making. For example, an edge infrastructure device might use sensors to accurately detect vehicle status and the dynamic environment, including connected and disconnected vehicles, autonomous vehicles, semi-autonomous vehicles, and manually operated vehicles, as well as other traffic participants such as bicycles and pedestrians. These sensors are not limited to rangefinders, radar, lidar, or cameras. In another example, an edge infrastructure device might use sensor fusion technology to accurately detect vehicle status and the dynamic environment. Therefore, edge infrastructure devices are suitable for use in the coordinated control of dynamic traffic rules and mixed traffic within a transport network of multiple interconnected traffic intersections.

[0057] In one embodiment, a CAV can be continuously controlled from edge infrastructure equipment at any given time and space to achieve optimization of the transport network, such as minimizing average or worst-case travel time, overall idling time, etc. In contrast, an HDV is an uncontrolled vehicle. In other words, it is impossible, or at least impractical, to control the motion of an HDV at each point in time and space. In different traffic situations with only HDVs, the motion of the HDV is controlled via traffic signs. For example, the flow of HDVs is influenced by the timing and sequencing of traffic signals so that the overall operation of the transport 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, the control of HDVs is limited to specific locations, thus restricting control over the transport network.

[0058] Some embodiments are based on the recognition that it may be beneficial to jointly control CAVs and HDVs to optimize the overall benefits for CAVs and HDVs, such as minimizing average or worst-case driving time, overall idling time, etc. To that end, an objective of some embodiments is 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, one or more MECs 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, a cloud network 118, or a core network 120.

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

[0060] In the exemplary traffic situation 400A shown in Figure 4A, north-south traffic at intersections 203 and 205 is much more congested than east-west traffic at intersections 207 and 209. The traffic control system controls the planned future timing and speed trajectory for CAVs such as vehicle 219, which plans to cross intersection 201 and travel in the north-south direction of the very congested intersection 203. To improve the overall safety, time efficiency, and energy efficiency of traffic flow in the transport network, the traffic control system generates commands for vehicle 219 to slow down before and after crossing intersection 201, so that vehicle 219 is expected to arrive at intersection 203 at a later time, with the aim of reducing traffic congestion at intersection 203 and reducing the overall waiting time for one or more vehicles in the transport network.

[0061] In addition, the traffic control system also controls CTR signals or signs. For example, the traffic control system may increase the green light period in the north-south direction by decreasing the green light period of east-west CTR signals 211, 213, and 215, thereby reducing traffic congestion by allowing more traffic to flow in the more congested north-south direction. However, the traffic control system may also allow the green light to be turned on at 211, 213, and 215 at precisely the moment when a specific vehicle, such as vehicle 219, can pass, in contrast to the manner associated with average traffic. This makes it possible to activate the green light when necessary according to the purpose of a particular vehicle. For example, a CTR signal or sign 211 may be green in the east-west direction, but may be turned red when both HDV 221 and vehicle 219 are approaching intersection 201, resulting in HDV 221 stopping and vehicle 219 passing.

[0062] Figure 4B shows an example of traffic conditions and routing information for multiple connected autonomous vehicles in a local area of ​​an interconnected intersection according to some embodiments of the present disclosure. Figure 4B shows an exemplary traffic scene 400B in a transport network of multiple interconnected intersections and merging points. The transport network includes one or more controlled vehicles referred to as CAVs, e.g., vehicles 223, 225, 227, and 229. The transport network further includes one or more uncontrolled traffic participants referred to as HDVs, e.g., 231, 233, 235, and 237. The transport network itself may include multiple interconnected intersections such as 239(I1), 241(I2), and 243(I3), and multiple interconnected merging points such as 245(M1), 247(M2), and 249(M3). Both intersections and merging points are referred to as conflict zones. The conflict zones are interconnected by multiple conflict-free road sections, each potentially containing one or more lanes, e.g., 251 (L6), 253 (L47), and 255 (L36). Figure 4B also shows stop lines, e.g., stop lines 257 (S1), 259 (S2), and 261 (S3), indicating positions where vehicles may wait for a certain period before entering the intersection. Furthermore, parts of the intersection have controlled traffic signals, CTR263, 265, 267, and 269.

[0063] In addition, Figure 4B shows routing information that may be provided by a routing or navigation module for each CAV, for example, vehicle 223. For vehicle 223, which is currently at location 271 and has a 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, identical or different individual routing or navigation modules can provide other vehicles, for example, CAVs 225, 227, and 229, with a sequence of roads and turns from their current location to a desired destination. Some embodiments of this disclosure are based on the understanding that for one or more uncontrolled traffic participants, such as HDVs 231, 233, 235, and 237, a relatively short sequence of roads and turns starting from their current location can be accurately predicted.

[0064] However, it is noteworthy that each of the road and corner sequences 275a, 275b, 275c, 275d, 275e, 276f, 275g, and 275h does not, in itself, yet determine a motion plan or route for the vehicle 223. There are numerous discontinuous decisions to be made, such as which lane the vehicle should travel in, whether the vehicle should change lanes or stay in its current lane, whether the vehicle should begin to decelerate to stop at a stop line, and whether the vehicle is permitted to cross an intersection. Furthermore, there are numerous continuous decisions to be made, such as a timed sequence of position and orientation that the vehicle should achieve during the predicted journey from its initial position to its destination. In addition, it is 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 discontinuous and / or continuous decisions described above along a route from the 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 control vehicles and human-driven vehicles, roadside units, traffic light controllers, and a mobile edge computer, according to some embodiments of the present disclosure. Figure 5 shows an exemplary Figure 500 of possible interactions between a traffic control system 302, a 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 understanding that the traffic control system 302 can be efficiently implemented using a hierarchical traffic control architecture that includes a central traffic controller (CTC) and one or more intersection traffic controllers (ITCs) to compute future control commands for each CAV and each TLC. The CTC computes a high-level plan based on a macroscopic traffic flow model for a transport network of multiple interconnected intersections. One or more ITCs execute this high-level plan by calculating control commands for CAV306 and TLC312 based on a microscopic traffic model, thereby minimizing the average travel time, waiting time, and fuel consumption of all vehicles in the transport 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 a 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 CAV 306. The routing information for each CAV is transmitted 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 signal commands for each TLC 312, and a rough motion plan for each CAV 306 in the transport 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 transmitted from the hierarchical traffic control system 302 to each CAV 306. In another example, the motion plan may be transmitted indirectly from the hierarchical traffic control system 302 to each CAV 306 via communication with one or more MEC 314 that provide updated information from the hierarchical traffic control system to the CAV 306. Similarly, the sequence of signal commands is transmitted from the hierarchical traffic control system to each TLC 312, either directly or indirectly via communication with one or more MEC 314 that provide updated information from the hierarchical traffic control system 302 to the TLC 312.

[0068] In one embodiment, real-time information may be transmitted directly from the CAV306, HDV308, RSU310, and TLC312 to the hierarchical traffic control system 302. In another embodiment, real-time information may be transmitted indirectly from the MEC314 via the communication interface 301. In some embodiments, the MEC314 may collect real-time information about the state of traffic participants and the dynamic environment within the local area of ​​the transport network by communicating with the CAV306, HDV308, RSU310, and TLC312 currently present within the local area of ​​the transport network. In some embodiments, the RSU310 uses additional sensors, such as rangefinders, radar, lidar, or cameras, to accurately detect the state of the vehicles as well as the dynamic environment, including the CAV306, HDV308, and other traffic participants such as bicycles or pedestrians. In another embodiment, sensor fusion technology may also be used to accurately detect the state of the vehicles and the dynamic environment.

[0069] Some embodiments are based on the understanding that in the hierarchical traffic control system 302, the number of MEC314, CAV306, HDV308, RSU310, and TLC312 may change at each sampling time step. Most importantly, the number of vehicles can change significantly because traffic participants enter and exit the transport network in which the hierarchical traffic control system 302 operates.

[0070] Figure 6A is a schematic diagram of a feedback loop for a hierarchical traffic control system in a transport 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 sensing module 406 to calculate a sequence of future control commands for each CAV306 and each TLC312 in the transport 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 mixed traffic of CAV306 and HDV308 in a transport network of multiple interconnected intersections. The hierarchical traffic control system 600A further includes one or more intersection traffic controllers (ITCs) 408,410, which execute the high-level plan based on the microscopic traffic model by calculating control commands for the CAV306 and TLC312 assigned to each ITC 408,410. In one example, ITC408 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 ITC408. Group 412 of CAVs may include, but is not limited to, CAV1, CAV2, and CAV3. ITC408 directly or indirectly controls traffic flow in local areas around one or more intersections in the transport network. Similarly, ITC410 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 ITC410. Group 416 of CAVs includes CAV4, CAV5, and CAV6. Group 418 of TLCs includes TLC4, TLC5, and TLC6. ITC410 directly or indirectly controls traffic flow in local areas around one or more intersections in the transport network.

[0071] In one embodiment, CTC404 performs one or more calculations. The calculations in CTC404 involve solving a convex optimization problem according to a macroscopic traffic flow model for an entire transit network of multiple interconnected intersections, and according to a convex relaxation of mixed integer constraints enforcing each of multiple traffic rules. In one example, the convex relaxation of mixed integer constraints enforcing each of multiple traffic rules may include, but is not limited to, the convex relaxation of mixed integer constraints for the switching behavior of vehicles crossing each intersection or for traffic signals. In one embodiment, the macroscopic traffic flow model defines a high-level approximate representation of traffic flow in the transit network, in which the modeling of individual vehicle behavior is omitted, and instead, the general behavior of vehicles at the transit network level is modeled using traffic flow values, density values, and average speed values ​​of the traffic flow. In some embodiments, by using the macroscopic traffic flow model in combination with a convex relaxation of multiple mixed integer traffic constraints, CTC404 can efficiently compute a high-level traffic flow plan for an entire transit network of multiple interconnected intersections. The operations performed for the efficient calculation of high-level traffic flow plans for the entire transport network are described in detail with reference to Figure 7.

[0072] In some embodiments of this disclosure, the calculations in each ITC408,410 involve 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 transport network, and according to mixed-integer constraints enforcing each of several traffic rules in the transport network. In one example, the mixed-integer constraints enforcing each of several traffic rules in the transport network include mixed-integer constraints for vehicles crossing each intersection, collision avoidance constraints, and mixed-integer constraints for signal switching behavior. In one embodiment, the microscopic traffic flow model is a detailed representation of traffic flow in the transport network, including modeling the behavior of each individual vehicle using a motion model for controlling and predicting the behavior of CAVs and a switching dynamic model for predicting the behavior of HDVs and predicting responses to CAVs and changing signals. Some embodiments of this disclosure are based on the understanding that for each ITC 408, 410, using a microscopic traffic flow model in a limited local area around one or more intersections in the transport network allows for the efficient calculation of low-level motion plans and future control command sequences for each CAV in group 412, 416 and each TLC in group 414, 418 by minimizing the average travel time, wait time, and fuel consumption of all vehicles in the local area of ​​the transport network assigned to ITC 408, 410.

[0073] In one embodiment, a specific ITC may be assigned to a set of CAVs and a set of TLCs located in a local area around a particular traffic intersection, such that the set of CAVs and TLCs has the specific ITC within a transport network of multiple interconnected intersections. For example, if group 412 of CAVs and group 414 of TLCs are located in a local area around a traffic intersection to which ITC 408 belongs, 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 located in a local area around a traffic intersection to which ITC 410 belongs, 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 transport network. In another embodiment, each ITC may be assigned to a local area around a group of multiple traffic intersections in the transport network. For example, in some embodiments of this disclosure, traffic intersections within a transport network may be divided into disjoint subsets of traffic intersections, where the CAV and TLC in each of these subsets are controllable by a single ITC. As a result, the total number of ITCs is less than the number of traffic intersections.

[0074] In some embodiments, calculations in CTC404 and each ITC408,410 are performed in real time to take into account dynamically changing traffic conditions within the transport network. For example, the sampling period of CTC404 may be the same as or different from the sampling period of each ITC408,410. For example, in some embodiments, the sampling period of CTC404 and the sampling period of each ITC408,410 may be set to be equal to 1 second, meaning that CTC404 calculates a new traffic flow plan every second, and each ITC408,410 individually calculates a new control command for each CAV and TLC every second. In some embodiments of this disclosure, the sampling period of CTC404 may be longer than the sampling period of each ITC408,410. For example, in some embodiments, the sampling period of CTC404 may be in the range of 1 to 2 seconds, and the sampling period of each ITC408,410 may be in the range of 0.5 to 1 second.

[0075] In one embodiment, the CTC404 predicts in a macroscopic traffic model the number of external vehicles entering the transport network from each inflow direction at each time step within the prediction time window, based on historical data collected for a similar transport network over a similar past period to the prediction time window. In another embodiment, the CTC404 calculates at least one of the values ​​for each pair of road sections and traffic flow operations within the transport network in the prediction time window, based on historical data collected for a similar transport network over a similar past period to the prediction time window.

[0076] In some embodiments, the convex optimization problem in CTC404 is a convex linear programming (LP) problem with linear objectives, linear equality constraints, and linear inequality constraints, or a convex quadratic programming (QP) problem with linear quadratic objectives, linear equality constraints, and linear inequality constraints. Examples of optimization algorithms for efficiently solving convex LPs or QPs include, but are not limited to, effective constraint methods, interior point methods, projection gradient methods, operator partitioning methods, or alternating direction methods of multipliers (ADMM).

[0077] In some embodiments, the MIP problem in each ITC is a mixed-integer linear programming (MILP) or mixed-integer quadratic programming (MIQP) problem. Some embodiments of this disclosure are based on the understanding that MILP or MIQP can be efficiently solved when formulated as a mixed-integer convex programming (MICP) problem. In other words, MILP or MIQP can be efficiently solved when the optimization problem becomes convex when each of the integer feasibility constraints is relaxed. For example, when the integer feasibility constraints are relaxed, MILP becomes a convex LP, or 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 methods.

[0078]

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[0079]

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[0080]

number

[0081] In some embodiments, heuristic search techniques may be used in CTC404 and each ITC408,410 to compute a feasible but possibly suboptimal solution to the MICP, and the heuristic search techniques include, for example, rounding schemes, feasibility pumping methods, approximate optimization algorithms, or the use of deep learning or supervised learning. For example, in some embodiments, a deep neural network may be used in CTC404 or each ITC408,410 to predict optimal values ​​for each of the binary or integer optimization variables, thereby solving one or more convex design (CP) problems after fixing each of the binary or integer optimization variables.

[0082] Figure 6B is a schematic diagram of a feedback loop for one ITC in a hierarchical traffic control system according to some embodiments of the present disclosure. Figure 6B shows an exemplary schematic diagram 600B of a feedback loop for ITC408, which is one of several ITCs 408, 410 in a hierarchical traffic control system 600A. ITC408 uses real-time information from infrastructure sensing module 406 and high-level traffic flow plans 420 from CTC404 to calculate a sequence of future control commands for each CAV in a group of CAVs 412 and a sequence of future control commands for each TLC in a group of TLCs 414 assigned to the individual ITC408 in the local vicinity of the transport network. Group of CAVs 412 may include CAVs 422, 424, 426. Group of TLCs 414 may include TLCs 452, 454, 456. In some embodiments, the ITC408 calculates a solution to the MIP according to a microscopic traffic flow model for local areas around one or more traffic intersections in the transport network, and according to mixed integer constraints that enforce each of several traffic rules in the transport network, the mixed integer constraints include, for example, mixed integer constraints for vehicles crossing each intersection, mixed integer constraints for collision avoidance constraints, and mixed integer constraints for the switching behavior of traffic signals.

[0083] At each control time step, taking into account 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 on a microscopic scale, and these control commands are sent to each of the TLCs 452, 454, 456 and each of the CAVs 422, 424, 426. In some embodiments, each of the TLCs 452, 454, 456 controls one or more signal lights for a traffic intersection in the transport network. For example, in some embodiments, the TLC 452 controls the timing of one signal light in a particular transverse direction of a traffic intersection. In other embodiments of the present disclosure, the TLC 454 controls the timing of multiple signal lights in multiple transverse directions of a traffic intersection in the transport network.

[0084] Some embodiments are based on the recognition that planning and control for (semi) autonomous driving can be effectively realized using a multilayer guidance and control architecture, generally mounted and implemented on each individual vehicle, which includes one or more layers of algorithms and techniques for decision-making, motion planning, vehicle control, or estimation. In some embodiments, the multilayer 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 on-board sensors 434, 442, 450 in each individual CAV 422, 424, 426.

[0085] For example, CAV422,424,426 includes decision layers 428,436,444, motion planner or motion planning algorithms 430,438,446, vehicle controllers 432,442,450, and one or more on-board sensors 434,442,450, respectively. The decision layer 428 of CAV422 selects an appropriate driving behavior at any given time, taking into account a motion plan 460 from the ITC, current environmental conditions, and the behavior of other traffic participants, for example, using an automaton combined with collective reachability or formal language and optimization for vehicle decision-making. Considering the target behavior from the decision 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 a low-level vehicle controller 432 can track in real time. To provide feedback to high-level algorithms for decision-making, motion planning, and control, real-time sensor fusion and estimation using on-board and infrastructure sensing information may be performed in each vehicle, e.g., CAV422,424,426. Similar but different multi-layer guidance and control architectures may be used for (semi-)autonomous driving in one or more CAVs within a transport network.

[0086] In one example, an approach for (semi-)autonomous driving uses a combination of a finite-state machine (FSM) for decision-making in decision layers 428, 436, 444, a sampling-based motion planning algorithm in motion planners 430, 438, 446, and a model predictive control (MPC) algorithm for reference trajectory tracking in vehicle controllers 432, 440, 448. An example of a sampling-based motion planning algorithm samples the input space using probabilistic particle filtering and adds further modification terms based on one or more driving requirements. An example of a predictive algorithm for vehicle control solves linear time-varying or nonlinear MPC problems in real time using one or more iterations of a sequential quadratic programming (SQP) method. Several embodiments are based on the recognition that the use of predictive algorithms for motion planning and reference trajectory tracking control for (semi-)autonomous 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 are not limited to, moving horizontal estimation (MHE), augmented or linear regression Kalman filtering, or particle filtering.

[0087] In some embodiments, different components of the multi-layer guidance and control architectures 428, 430, 432, 434 may be mounted and implemented on each control vehicle, such as the 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 decision or feedback information to multiple connected vehicles in the transport network.

[0088] In some embodiments of the present disclosure, the infrastructure sensing 406 corresponds to one or more RSUs, such as RSUs 122, 124, which include one or more sensors, e.g., rangefinders, radar, lidar, or cameras and sensor fusion technology, to accurately detect the status of vehicles as well as the dynamic environment within the transport network, including connected and unconnected vehicles, autonomous vehicles, semi-autonomous vehicles and manually operated vehicles, bicycles and pedestrians.

[0089] Some embodiments are based on the recognition that safety constraints for other dynamic traffic participants, such as vehicles, bicycles, or pedestrians, can be addressed by obstacle avoidance techniques in the on-board modules of each CAV's multi-layer guidance and control architecture. Obstacle avoidance techniques can be implemented, for example, by motion planning or vehicle control algorithms. Motion planning and vehicle control algorithms can be run at relatively fast sampling rates because their computational costs are relatively small compared to the hierarchical traffic control system 600A, with the aim of having a fast response time to unexpected changes in the dynamic behavior of other vehicles or other traffic participants. For example, real-time vehicle control algorithms are generally run with update periods of 50 to 100 milliseconds, but in some embodiments of the present disclosure, the sampling period of 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 understanding that different vehicle motion models having different modeling accuracy or computational complexity may be used by one or more components within the architecture shown in Figure 4B. Some embodiments are based on the understanding that vehicle motion models having higher modeling accuracy and possibly higher computational complexity may be used by components at lower levels of the multilayer induction and control architecture shown in Figure 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 RSU310, while a higher-dimensional or nonlinear motion model may be used to describe the motion of each individual vehicle 422, 424, and 426 in the decision units 428, 436, 444, motion planners 430, 438, 446, vehicle controllers 432, 440, 448, or on-board sensors 434, 442, 450.

[0091] Alternatively, one or more of the lower levels of the multi-layer induction and control architecture may use a higher-dimensional or nonlinear dynamic model to describe the motion of a vehicle based on the 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, in which the state is described by the two-dimensional position, longitudinal and lateral velocities, yaw angle, and yaw rate of the vehicle. 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 so that it can accurately model the longitudinal and lateral load transfer between the four wheels of the vehicle. In some embodiments, the nonlinear relationship between longitudinal and lateral tire friction forces, slip ratio, and slip angle may be modeled using Paseika's Magic Formula, which exhibits general saturation behavior in tire forces. Combined with slip conditions, the coupling between longitudinal and lateral tire forces can be modeled using friction ellipses or weighting functions.

[0092] Figure 6C is a schematic diagram of a feedback loop for a hierarchical traffic control system in a transport network according to some embodiments of the present disclosure. Figure 6C shows an exemplary schematic diagram 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 transport network, taking into account real-time information from an infrastructure sensing 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 a high-level plan based on a microscopic traffic model by calculating control commands for CAVs such as group 412, 416 and TLCs such as group 414, 418, which are assigned to each ITC 408, 410. For example, group 412 of CAVs and group 414 of TLCs are assigned to ITC 408. Group 416 of the CAV and Group 418 of the TLC are assigned to ITC410.

[0093] For example, ITC408 calculates future control commands 464 for group 412 of CAVs and group 414 of TLCs assigned to ITC408, taking into account real-time information from infrastructure detection 406 and CTC traffic flow values ​​460 for each transverse direction of one or more intersections assigned to ITC408 in the transport network. Similarly, another ITC, such as ITC410, calculates future control commands 466 for group 416 of CAVs and group 418 of TLCs assigned to ITC410, taking into account real-time information from infrastructure detection 406 and CTC traffic flow values ​​462 for each transverse direction of one or more intersections assigned to ITC410 in the transport network.

[0094] Figure 7 shows an exemplary operation for optimization-based hierarchical traffic control of controlled and uncontrolled vehicles according to one embodiment of the present disclosure. Figure 7 is described in relation to elements from Figures 5, 6A, 6B, and 6C. Referring to Figure 7, a block diagram 700 illustrating exemplary operations 702 and 704 described herein is shown.

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

[0096] In 702, traffic flow is jointly optimized for all intersections using convex optimization with convex relaxation of integer constraints for multiple interconnected intersections. In one embodiment, the CTC404 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, e.g., CTC traffic flow values ​​460 or 462 associated with ITC408 or 410 shown in Figure 6C. Convex optimization of integer constraints is a problem where 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. Generally, relaxation refers to the technique of simply removing a particular constraint from the optimization problem. Specifically, convex relaxation means that the problem becomes convex when relaxed. In one embodiment, convex relaxation of integer constraints enforcing multiple traffic rules includes convex relaxation of integer constraints for the switching behavior of vehicles and signals crossing each intersection. By using a macroscopic traffic flow model in combination with convex relaxation of integer constraints that enforce multiple traffic rules, CTC404 can efficiently compute high-level traffic flow plans for entire transit networks of multiple interconnected intersections. For example, convex relaxation of traffic flow values ​​460 or 462 associated with ITC408 or 410 yields relaxed traffic flow values. Details of relaxed approximations of pure integer values ​​due to convex relaxation of integer constraints that enforce hybrid dynamic behavior of vehicles are further explained, for example, with reference to Figure 8C.

[0097] In 704, the cost function of the MIP problem in each ITC is optimized for relaxed traffic flow values ​​from CTC404, subject to integer constraints, in order to generate control command values ​​that change the state of each CAV associated with the intersection and control command values ​​that change the state of each traffic sign associated with the intersection.

[0098] Figure 8A is an exemplary situational diagram of a four-way traffic intersection in a transport network controlled by a hierarchical traffic control system, according to some embodiments of the present disclosure. Figure 8A shows an exemplary situational diagram 800A of a traffic intersection 800 in a transport 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 TLC820 shown in Figure 8A. More specifically, Figure 8A shows a four-way traffic intersection in which vehicles, including both CAVs and HDVs, may arrive from any of the following directions: North 815, East 816, South 817, or West 818, and each vehicle may pass through the traffic intersection 800 in one of several crossing directions. For example, a vehicle arriving from one of four entry directions, including North 815, East 816, South 817, and West 818, may turn right, go straight, or turn left, resulting in 12 crossing directions for each traffic intersection.

[0099] A vehicle arriving from North 815 may cross direction d1801 by turning right, cross direction d2802 by going straight, or cross direction d3803 by turning left. A vehicle arriving from East 816 may cross direction d4804 by turning right, cross direction d5805 by going straight, or cross direction d6806 by turning left. A vehicle arriving from South 817 may cross direction d7807 by turning right, cross direction d8808 by going straight, or cross direction d9809 by turning left. A vehicle arriving from West 818 may cross direction d 10 810 can be brought about by moving straight ahead in the transverse direction d 11 This may result in 811, or by turning left, crossing direction d 12 This could result in 812.

[0100] In some embodiments, the TLC820 determines whether and when to switch one or more traffic signal values, for example, from green to red or red to green, in order to avoid collisions and to reduce traffic congestion and fuel consumption. Traffic participants are permitted to cross the intersection in a particular direction if the traffic signal is green for that direction, but must stop and wait if the traffic signal is red for the desired direction. Some embodiments are based on the recognition that there are multiple collision-free states for the intersection traffic signal, i.e., the current state of the traffic signal is equal to one of multiple collision-free states at each time step, in order to allow the intersection traffic signal to be either red or green for one or more directions while avoiding collisions between vehicles arriving at the traffic intersection from different directions.

[0101] Figure 8B shows an example of a mapping between multiple no-collision states and signal values ​​for each crossing direction of a traffic intersection in a transport network controlled by a hierarchical traffic control system according to some embodiments of the present disclosure. Figure 8B shows an example of a mapping 830 between multiple no-collision states 821-829 and signal values ​​for each crossing direction 801-812 of a traffic intersection in a transport network controlled by a hierarchical traffic control system 600A. For example, if the current state of the intersection's signal is equal to no-collision state 821, the signal value is red for each crossing direction. In no-collision state 821, traffic participants are not permitted to cross the intersection in any direction. If the current state of the intersection's signal is equal to no-collision state 822, the signal values ​​are red for crossing directions d4804, d5805, d 10 810 and d 11 811 is blue, and the signal value is red for all other crossing directions. In collision-free condition 822, traffic participants are in crossing directions d4804, d5805, d 10 810 and d 11It is only permitted to cross the intersection at 811. Similarly, a traffic participant is only permitted to cross the intersection in the crossing directions d1801, d2802, d3803, and d4804 when the current state of the traffic signal at the intersection is equal to the collision-free state 829.

[0102] Some embodiments of the present disclosure are based on the recognition that there is no collision between a vehicle traveling from the east 816 via the crossing direction d4804 or d5805 and a vehicle traveling from the west 818 via the crossing direction d 10 810 or d 11 8I1, so the signal state 822 is collision-free. For example, there is no collision between a vehicle traveling from the south 817 via the crossing directions d7807, d8808, or d9809 and a vehicle traveling from the west 818 via the crossing direction d 10 810, so the signal state 828 is collision-free. Similarly, there is no collision between a vehicle traveling from the north 815 via the crossing directions d1801 or d2802 and a vehicle traveling from the south 817 via the crossing directions d7807 or d8808, so the signal state 824 is collision-free.

[0103] Figure 8C shows an example of a traffic flow plan calculated by a Central Traffic Coordinator (CTC) using a table of traffic flow values ​​for each transverse direction of a traffic intersection in a transport network controlled by a hierarchical traffic control system, according to some embodiments of the present disclosure. Figure 8C shows an example of a CTC traffic flow plan 800C calculated by a CTC 404 in a hierarchical traffic control system 600A, where the CTC flow plan 800C is represented in Figure 8C as a table 840 of traffic flow values ​​for each of the transverse directions 801-812. In some embodiments, the CTC traffic flow plan 800C consists of traffic flow values ​​at future time steps 841-844 that satisfy relaxed traffic flow constraints over a predicted range for each of the transverse directions 801-812 of one or more traffic intersections in the transport network. Some embodiments of the present disclosure are based on the understanding that such relaxed traffic flow values ​​840 can be calculated by the CTC404 by solving a convex optimization problem according to a macroscopic traffic flow model for the entire transit network of multiple interconnected intersections and according to a convex relaxation of mixed integer constraints that enforce each of multiple traffic rules over the prediction range of the CTC404, where the convex relaxation of mixed integer constraints includes, for example, a convex relaxation of mixed integer constraints for the switching behavior of vehicles and signals crossing each intersection, or a convex relaxation of mixed integer constraints that enforces individual collision-free states for signal signals at each traffic intersection, as shown in Figure 8B.

[0104] In some embodiments, the traffic flow value 840 is a relaxed real-valued approximation of a pure integer value. The pure integer value is relaxed based on a convex relaxation of a mixed-integer constraint that enforces the hybrid dynamic behavior of vehicles crossing one or more traffic intersections. For example, in Figure 8C, the future CTC traffic flow value at time step 841 is a real-valued control value representing that 2.3 vehicles cross the traffic intersection in transverse direction d1801, 1.0 vehicle crosses in direction d2802, and 0.7 vehicles cross in direction d3803. At time step 842, the future CTC traffic flow value 840 represents that 1.1 vehicles cross the traffic intersection in transverse direction d1801, 1.5 vehicles cross in direction d2802, and 1.4 vehicles cross in direction d3803. Similarly, at time step 843, the future CTC traffic flow value 840 represents 0.3 vehicles crossing the intersection in direction d1801, 1.2 vehicles crossing in direction d2802, 0.8 vehicles crossing in direction d7807, and 1.7 vehicles crossing in direction d8808.

[0105] In some embodiments of this disclosure, the CTC traffic flow value 840 satisfies a macroscopic traffic flow model and satisfies convex relaxation of one or more mixed integer constraints that enforce each of a plurality of traffic rules for the entire transport network of one or more interconnected traffic intersections. In some embodiments, the sum of the CTC traffic flow values ​​840 is not permitted to exceed the maximum capacity limit at each time step for each traffic intersection in the transport network. Similarly, the CTC traffic flow value 840 is not permitted to exceed the number of vehicles arriving at the traffic intersection that are expected to cross the traffic intersection in a particular transverse direction. For example, considering the future CTC traffic flow value 840 in Figure 8C, a total of 2.3 + 1.0 + 0.7 = 4 vehicles arrive at the traffic intersection from the north 815 direction and then cross the traffic intersection at time step 841.

[0106] Figure 9 shows an exemplary cost function fitting method for a hierarchical traffic control system according to some embodiments of the present disclosure. The cost fitting method 900 is based on traffic flow values ​​calculated by CTC 404 to fit a cost function that is minimized by a constrained optimization problem solved in one or more ITCs, such as ITC 408, 410, of the hierarchical traffic control system 600A. The steps and their order identified in Figure 9 are exemplary and may include various alternatives, equivalents, or derivatives thereof, including, but not limited to, their execution order. The steps of the method in Figure 9 and their 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 the hierarchical traffic control system 600A.

[0107] In 901, microscopic traffic models of ITCs, such as ITC408 shown in Figure 6A, may be obtained from database 108 or, in some embodiments, calculated. More specifically, future CTC traffic flow values ​​over a predicted time range for each transverse direction of a traffic intersection may be used in combination with the microscopic traffic model of ITC408 in the hierarchical traffic control system 600A to fit the cost function of the constrained optimization problem solved by ITC408.

[0108] In 902, the microscopic traffic model of ITC408 can be used to calculate predictions of future traffic flow values ​​over a predicted time range.

[0109] In 903, future CTC traffic values ​​can be calculated by the CTC404 of a hierarchical traffic control system, such as the hierarchical traffic control system 600A shown in Figure 6A.

[0110] In step 904, the tracking error between the predicted future traffic flow calculated in step 902 and the future CTC traffic flow value calculated in step 903 is calculated. In one embodiment, the optimal traffic flow probability value of CTC 404 is used in ITC 408 to minimize the tracking error between the predicted future traffic flow calculated in step 902 and the future CTC traffic flow value calculated in step 903 over the predicted time range of ITC for each transverse direction of a plurality of intersections.

[0111] In step 905, the tracking error 603 over the predicted time range calculated in step 904 is minimized in the cost function of ITC 408. Some embodiments of the present disclosure are based on the understanding that minimizing the difference in traffic flow prediction 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 value calculated in 902 and the reference CTC traffic flow value 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, e.g., minimizing fuel consumption over the predicted time range 906-1, minimizing traffic congestion over the predicted time range 906-2, maximizing the distance traveled by one or more vehicles in the local vicinity of the transport network over the predicted time range 906-3, and maximizing the safety of one or more vehicles in the local vicinity of the transport network over the predicted time range 906-4.

[0112] In step 906, the fitting of a cost function for a constrained optimization problem solved by ITC408 is performed. The cost function fitting method 900 is based on a direct policy mapping from real-time information of CTC traffic flow values ​​and infrastructure detection 406 calculated in step 905 to one or more parameter values ​​in the cost function of ITC408. In one example, one or more parameter values ​​may include one or more weight values ​​that quantify a penalty for higher traffic flow values ​​in one or more transverse directions for each traffic intersection in the transport network. In some embodiments, the direct policy mapping can be implemented using a deep neural network architecture, for example, using reinforcement learning (RL), to directly maximize a reward function for reducing congestion, travel time, emissions, and energy consumption in the transport network. For example, in some embodiments of this disclosure, CTC404 is implemented by training an RL policy based on model-free or model-based RL techniques. In other embodiments, the policy mapping may be implemented using a deep neural network architecture based on imitation learning aimed at approximating an expert or heuristic solution.

[0113] A deep neural network architecture may be based on one or more layers, including 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 exemplary figure 1000A of a multi-lane road section in a transport network according to some embodiments of the present disclosure. Figure 10A shows a multi-lane road section 1005 in which four vehicles plan to turn left at the following intersection 1006 (1011). Similarly, Figure 10A shows six vehicles in road section 1005 in which they plan to go straight at the following traffic intersection 1006 (1012). Furthermore, Figure 10A shows five vehicles in road section 1005 in which they plan to turn right at the following traffic intersection 1006 (1013).

[0115] Figure 10B shows an example of vehicle density values ​​over a predicted time range for a multi-lane road section in a transport network, used in a macroscopic traffic flow model of a hierarchical traffic control system in some embodiments of the present disclosure. Figure 10B shows an example of vehicle density value 1000B over a predicted time range 1015-1018 for a multi-lane road section 1005 in a transport network, and in some embodiments, the vehicle density value 1000B can be used as part of a state information vector in a macroscopic traffic flow model used in a constrained optimization problem solved by the CTC404 in the hierarchical traffic control system 600A to compute a high-level traffic flow plan. In one example, Figure 10A shows four vehicles in road section 1005 (1011) planning to turn left at the next traffic intersection 1006, and as a result, the vehicle density value s k,1 1001 becomes equal to 4 in the first time step 1015, and the dynamic behavior of this vehicle density value can be predicted between subsequent time steps 1016-1018 based on a macroscopic traffic flow model of the transport network. Similarly, Figure 10A shows 6 vehicles in road section 1005 planning to proceed straight through the next traffic intersection 1006 (1012), resulting in a vehicle density value s k,21002 becomes equal to 6 in the first time step 1015, and the dynamic behavior of this vehicle density value can be predicted between subsequent time steps 1016-1018 based on a macroscopic traffic flow model of the transport network. Furthermore, Figure 10A shows five vehicles in road section 1005 planning to turn right at the next traffic intersection 1006 (1013), resulting in the vehicle density value s k,3 1003 becomes equal to 5 in the first time step 1015, and the dynamic behavior of this vehicle density value can be predicted between subsequent time steps 1016-1018 based on a macroscopic traffic flow model of the transport network.

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

[0117] Figure 10C shows an example of multiple transverse directions over a predicted time range for a three-way traffic intersection in a transport network, according to some embodiments of the present disclosure.

[0118] Figure 10D shows an example of traffic flow values ​​in multiple transverse directions over a predicted time range for a three-way traffic intersection in a transport network, used in a macroscopic traffic flow model of a hierarchical traffic control system according to some embodiments of the present disclosure.

[0119] Figure 10E shows an example of multiple transverse directions over a predicted time range for a three-way traffic intersection in a transport network, according to some embodiments of the present disclosure.

[0120] Figure 10F shows an example of vehicle density values ​​in multiple transverse directions over a predicted time range for a three-way traffic intersection in a transport network, used in a macroscopic traffic flow model of a hierarchical traffic control system in some embodiments of the present disclosure. Figure 10F shows an example of vehicle density values ​​1020 over a predicted time range 1035-1038 and traffic flow values ​​1040 over a predicted time range 1055-1057 for a three-way traffic intersection 1050 connecting multiple two-lane road sections in a transport network. In some embodiments, both the vehicle density values ​​1020 and the traffic flow values ​​1040 can be used as part of a state information vector in a macroscopic traffic flow model used in a constrained optimization problem solved by a CTC in a hierarchical traffic control system 600A to compute a high-level traffic flow plan. As shown in Figures 10C and 10E, the three-way intersection results in six transverse directions 1060, namely d11061, d21062, d31063, d41064, d51065 and d61066.

[0121] For example, the traffic flow value in the transverse direction d1 of 2.3 in the first time step 1055 is in 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 through this area. This shows the dynamic behavior of this traffic flow value 1041 and s11021,s 11 1031 and s 12 The vehicle density value at 1032 can be predicted for subsequent time steps 1055-1057 and 1035-1038, respectively, based on a macroscopic traffic flow model of the transport network. For example, the transverse traffic flow value d1 of 2.3 at the first time step 1055 is equal to the vehicle density value s1 of 8 at the first time step 1035 minus 5.7 at the second time step 1036. Also, the road section s from the first time step to the second time step 11 and s 12The vehicle inflow into (5.15-4)+(3.15-2)=2.3 is equal to the sum of the traffic flow value in the transverse direction d1 of 2.3 and the traffic flow value in the transverse direction d4 of 744, which is 0 at the first time step 1055. In Figure 10C, similar dynamic traffic behavior can be observed for the traffic flow value 1040 and the corresponding vehicle density value 1020, each transverse direction at the traffic intersection 1050, and each time step within the prediction range of CTC404.

[0122] For example, the transverse traffic flow value of 1.7 in the first time step 1055 represents the number of vehicles predicted to flow in direction d21062, i.e., from road section s2 to road section s7 or s8. The dynamic behavior of this traffic flow value 1042 and the vehicle density values ​​for s21022, s71027, and s81028 can be predicted between subsequent time steps 1055-1057 and 1035-1038, respectively, based on a macroscopic traffic flow model of the transport network. For example, the transverse traffic flow value of 1.7 in the first time step 1055 is equal to the vehicle density value for s2 of 4 in the first time step 1035 minus 2.3 in the second time step 1036. Furthermore, 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 sum of the transverse d2 traffic flow value of 1.7 and the transverse d5 traffic flow value of 745 at the first time step 1055, which is within the prediction range of CTC404.

[0123] In some embodiments, the state information vector in the macroscopic traffic flow model includes a vehicle density value 1020, a traffic flow value 1040 passing through one or more intersections, and the position of vehicles within each road section of the transport network. In some embodiments, to improve the accuracy of the macroscopic traffic flow model in the hierarchical traffic control system 600A, each road section is divided into one or more smaller subsections, for each subsection a current vehicle density value is estimated and a future vehicle density value is predicted. In some embodiments, vehicles are expected to travel from one subsection to the next within one sampling period, and vehicles can only enter a traffic intersection from a road subsection that is sufficiently close to the traffic intersection in the transport network. This allows for a more accurate modeling of the travel time of each vehicle traveling from the beginning to the end of a road section, taking into account the desired or estimated average speed of each vehicle.

[0124] In some embodiments, historical data is collected from a database 108 to improve the performance of a hierarchical traffic control system 600A within a transport network and used to estimate and predict vehicle density values ​​1020 and traffic flow values ​​1040. For example, considering a transverse direction d31063 from road section s5 to road section s3 or s4, the percentage of vehicles in the traffic flow of transverse direction d31063 entering either road section s3 or s4 can be predicted based on vehicle density values ​​1020 and traffic flow values ​​1040 in the same or similar transport network over a similar period in the past. Similarly, the number of external vehicles entering the transport network from each inflow direction at each time step within the prediction range can be predicted based on historical data collected for the same or similar transport network over a similar period in the past. For example, historical data may be used to predict general traffic inflow values ​​or general routing of vehicles entering a particular transport network at 8 a.m. on Monday versus 2 p.m. on Saturday, and historical data can be used to improve the prediction of the macroscopic traffic flow model in the hierarchical traffic control system 600A.

[0125] Figure 11A shows a method for constructing and solving a constrained optimization problem for calculating a macroscopic traffic flow motion plan for one or more traffic signals and connected autonomous vehicles (CAVs) in a transport network including a plurality of interconnected traffic intersections, according to some embodiments of the present disclosure. The steps and their order identified in Figure 11A are illustrative and may include various alternatives, equivalents, or derivatives thereof, including, but not limited to, their execution order. The steps of method 1100A in Figure 11A and their various alternatives may be embodied in hardware or software including a computer-readable storage medium (e.g., optical disc, memory card, or hard drive) containing instructions executable by a processor included in a hierarchical traffic control system 600A. In another embodiment, the steps of method 1100A in Figure 11A and their various alternatives may be embodied in hardware or software including a computer-readable storage medium (e.g., optical disc, memory card, or hard drive) containing instructions executable by a processor included in a CTC 404. Figure 11A shows method 1100A including a feedback loop for CTC404.

[0126] In 1101, the CTC404 receives mapping information, such as location data (e.g., GPS data) about road sections, lanes, traffic intersections, and stop zones within the transport network.

[0127] In 1105, the CTC404 receives additional inputs from the CAV, such as feedback signals about status and planned routing information. In one example, the feedback signals may also include information from the infrastructure sensing module 406.

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

[0129] In 1110, CTC404 constructs a constrained optimization problem based on CTC404's macroscopic traffic flow model.

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

[0131] In step 1120, CTC404 calculates the optimal sequence of high-level control target values ​​for traffic flow across CTC404's predicted time window within the transport network, based on the solution to a constrained optimization problem. CTC404 controls mixed traffic within the transport network.

[0132] In 1121, the CTC404 sends a calculated optimal sequence of high-level control target values ​​for traffic flow to each of one or more ITC821s in the hierarchical traffic control system 600A that controls mixed commons within the transport network.

[0133] Figure 11B shows a method for constructing and solving a constrained convex design (CP) problem for calculating an optimal sequence of high-level target values ​​for traffic flow in a transport network of multiple interconnected traffic intersections, according to some embodiments of the present disclosure. The steps and their sequence specified in Figure 11B are illustrative and may include various alternatives, equivalents, or derivatives thereof, including, but not limited to, their execution sequence. The steps and their various alternatives of method 1100B in Figure 11B may be embodied in hardware or software including a computer-readable storage medium (e.g., optical disc, memory card, or hard drive) containing instructions executable by a processor included in a hierarchical traffic control system 600A. In another embodiment, the steps and their various alternatives of method 1100B in Figure 11B may be embodied in hardware or software including a computer-readable storage medium (e.g., optical disc, memory card, or hard drive) containing instructions executable by a processor included in a CTC 404. Figure 11B shows method 1100B including a feedback loop for the CTC 404.

[0134] In 1122, CTC404 receives map segments and lane information for multiple interconnected traffic intersections within the transport network.

[0135] In 1125, the CTC404 receives feedback signals related to detection and routing from the controlled vehicle, the uncontrolled vehicle, and / or the semi-controlled vehicle.

[0136] In 1135, CTC404 constructs matrices and vectors in the CP data of CTC404 for purpose, equality constraints, and inequality constraints. In one embodiment, these matrices and vectors are constructed using received feedback signals related to detection and routing, as well as map segments and lane information.

[0137] In 1140, CTC404 solves the CP problem based on convex relaxation of non-convex traffic rules. In some embodiments, the CP includes convex relaxation of one or more mixed integer equality and / or mixed integer inequality constraints that enforce each of a plurality of traffic rules for an entire transit network of one or more interconnected traffic intersections. In some embodiments, the CP problem includes a convex optimization problem in CTC404. The convex optimization problem may be a convex linear programming (LP) problem, which includes a linear objective and one or more linear equality constraints and / or linear inequality constraints. In some embodiments, the convex optimization problem in CTC404 is a convex quadratic programming (QP) problem, which includes a linear quadratic objective and one or more linear equality constraints and / or linear inequality constraints. In some embodiments, the convex optimization problem in CTC404 is a quadratically constrained quadratic programming (QCQP) problem, which includes a linear quadratic objective and one or more linear equality constraints and / or linear inequality constraints and one or more quadratic inequality constraints. In some embodiments, the convex optimization problem in CTC404 is a convex cone programming problem comprising a linear objective and one or more linear equality constraints and / or linear inequality constraints and one or more convex cone inequality constraints. Some embodiments of this disclosure are based on the understanding that numerical optimization algorithms exist for computationally efficient solving of the convex optimization problem in CTC404. Examples of optimization algorithms for efficiently solving CP in step 1140 include effective constraint methods, interior point methods, projection gradient methods, operator partitioning methods, or alternating multiplier methods (ADMMs).

[0138] In step 1145, CTC404 calculates the optimal sequence of high-level target values ​​for traffic flow in a multi-intersection transport network across a predicted time window.

[0139] At 1150, the CTC404 sends the calculated optimal sequence of high-level target values ​​for traffic flow to each ITC within the hierarchical traffic control system 600A of the transport network.

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

[0141] At 1152, CTC404 receives map segments and lane information for multiple interconnected traffic intersections within the transport network.

[0142] In 1154, the CTC404 receives feedback signals related to detection and routing from the controlled vehicle, the uncontrolled vehicle, and / or the semi-controlled vehicle.

[0143] In 1156, CTC404 constructs matrices and vectors in the convex QP data of CTC404 for purpose, equality constraints, and inequality constraints. In one embodiment, these matrices and vectors are constructed using received feedback signals related to detection and routing, as well as map segments and lane information.

[0144] In 1158, CTC404 solves the convex QP based on the 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, CTC404 calculates the optimal traffic flow values ​​and sends them to each ITC within the hierarchical traffic control system 600A of the transport network.

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

[0148] In some embodiments of this disclosure, the macroscopic traffic flow model in CTC404 can be represented as a directed graph, where each node corresponds to a road section and each edge corresponds to a connection between road sections, i.e., a direction traversing a traffic intersection in a transport network controlled by a hierarchical traffic control system.

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[0161] Figure 12A shows a method for constructing and solving a constrained optimization problem for calculating a microscopic traffic flow motion plan for one or more traffic signals and connected autonomous vehicles (CAVs) in a local area around one or more interconnected traffic intersections in a transport network, according to some embodiments of the present disclosure. The steps and their order identified in Figure 12A are illustrative and may include various alternatives, equivalents, or derivatives thereof, including, but not limited to, their execution order. The steps of method 1200A in Figure 12A and their 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 a hierarchical traffic control system 600A. In another embodiment, the steps of Method 1200A shown in Figure 12A and its various alternatives may be embodied in hardware or software including a computer-readable storage medium (e.g., optical disc, memory card, or hard drive) containing instructions executable by a processor included in an ITC such as ITC408,410 shown in Figure 6A. Figure 12A shows Method 1200A including a feedback loop for the ITC.

[0162] In 1201, ITC408 or 410 receives mapping information, such as location data (e.g., GPS data) about road sections, lanes, traffic intersections, and stop zones within the transport network.

[0163] In 1205, ITC408 or 410 receives additional inputs from the CAV, such as feedback signals about status and planned routing information. For example, the feedback signals may also include information from the infrastructure sensing module 406.

[0164] In 1206, ITC408 or 410 receives additional inputs from the HDV, such as feedback signals about the state and predicted routing information. In some embodiments, the feedback signals are obtained directly or indirectly from a sensing infrastructure module 406 (e.g., RSU) or from a connected vehicle, which may be an autonomous vehicle, a semi-autonomous vehicle, and / or a human-driven vehicle. Feedback signals about the state and planned routing information of the CAV may be referred to as Type 1 feedback signals. Feedback signals about the state and predicted routing information of the HDV may be referred to as Type 2 feedback signals.

[0165] In 1210, ITC408 or 410 constructs a constrained optimization problem based on a microscopic traffic model for the ITC's transport network. In some embodiments, the constrained optimization problem is a mixed-integer programming (MIP) problem constructed based on the microscopic traffic model.

[0166] In 1215, ITC408 or 410 solves the MIP problem for calculating the microscopic traffic flow motion plan for ITC408 or 410 for traffic signals and one or more traffic signals and / or connected (semi) autonomous vehicles in a transit network. ITC408 or 410 calculates the solution to the MIP at each sampling time step.

[0167] In 1220, ITC408 or 410 calculates the optimal sequence of target control commands and signal commands for each CAV in the local area around one or more traffic intersections in the transport network, over the predicted time window of ITC408 or 410.

[0168] In 1225, ITC408 or 410 sends commands to the multi-layer guidance and control architecture of each CAV, and ITC sends control commands to each signal in the local area around one or more traffic intersections in the transport network controlled by the hierarchical traffic control system 600A.

[0169] Some embodiments are based on the understanding 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 an optimal control command for each TLC, taking into account input information from V2X communication. In some embodiments, the constrained optimization problem may be a 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 point of the hierarchical traffic control system 600A can be solved by a global optimization algorithm, which includes, for example, branch-and-bound, branch-and-cut, and branch-and-price methods. In other embodiments of the present disclosure, heuristic techniques may be used to compute a feasible but suboptimal solution to one or more MIP problems, which include, for example, rounding schemes, feasibility pumping methods, approximate optimization algorithms, or (deep) machine learning with, for example, supervised learning.

[0170] Figure 12B is a schematic diagram of a formulation of an MIP problem based on a microscopic traffic model for mixed traffic in an ITC-controlled local area around one or more traffic intersections in a transport 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 an ITC-controlled local area around one or more traffic intersections in a transport network. In some embodiments, the MIP problem 1210 is formulated based on a plurality of constraints, which include, 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 CAVs, traffic rules and timing constraints 1215 for multi-lane road sections, collision avoidance constraints 1216, dynamic traffic rules and timing constraints 1217, and traffic rules 1218 for crossing one or more traffic intersections. The MIP problem 1210 is formulated based on a cost function 1205 to be minimized or a reward function to be maximized in order to reduce congestion, travel time, emissions, and energy consumption in a local area controlled by an ITC, for example, around one or more traffic intersections in a transport network. The optimal solution 1225 for the MIP problem defines the optimal values ​​1222 of control commands sent to one or more CAVs and the optimal values ​​1223 of control commands for a state 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 transport network. Some embodiments are based on the recognition that, depending on the infrastructure system, it may be difficult to obtain accurate future predictions 1212 for each HDV's route. For this reason, in some embodiments, the hierarchical traffic control system 600A is implemented in a reverse range manner based on the latest information from the sensing infrastructure (e.g., RSU) and connected vehicles. Some embodiments are based on the recognition that an approximate short-term future route prediction 1212 for the HDVs is sufficient, and that this prediction 1212 can generally be obtained relatively easily from, for example, the current position of each HDV to the next traffic intersection, the current lane of each HDV, and the detection of the turn signals of one or more HDVs. Some embodiments of the present disclosure are based on the recognition that discrepancies in predictions can be adjusted by an inherent feedback mechanism of the reverse range strategy. For example, a 1-second update interval allows for real-time computation of the hierarchical traffic control system 600A while providing sufficiently fast updates for each CAV's multi-layer guidance and control architecture, as well as for each TLC, in order to account for prediction errors in HDV behavior.

[0172] Figure 12C is a flowchart of a switching function in a predictive motion model of one or more HDVs used in a microscopic model for mixed traffic in an ITC-controlled local area around one or more traffic intersections in a transport network controlled by a hierarchical traffic control system, according to some embodiments of the present disclosure. Figure 12C shows flowchart 1200C of a switching function used in a microscopic traffic model for mixed traffic in an ITC-controlled local area around one or more traffic intersections in a transport network controlled by a hierarchical traffic control system. 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, one or more motion models include a first motion model for stopping in stop zones at each of several intersections of roads in a transport network, where the corresponding traffic sign is red in the transverse direction and the HDV is within a first safe distance from the stop zone; a second motion model for safe preceding vehicle following behavior, where the preceding vehicle is within a second safe distance ahead of the HDV and is in the same lane on the same road section as the HDV; and / or a third motion model for driving at a desired average speed, where 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 the HDV is not within the first safe distance from the stop zone and the corresponding traffic sign is not red.

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

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

[0175] In step 1231, the current state of the HDV is received and sent to the HDV predictive motion model.

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

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

[0178] In step 1240, the HDV predictive motion model determines whether a vehicle preceding the HDV is within a safe distance in front 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 stop zone.

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

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

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

[0182] Selecting a function to be active for the HDV depends on the traffic sign state 1256, the HDV state 1254, and the other vehicle state 1258. The 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 the traffic sign state 1256, selecting a function to be active in a particular control step depends on the traffic sign state 1256. Hereinafter, functions 1246-1252 are collectively referred to as switching (discontinuous) functions that select a function representing a motion model for the HDV based on one or a combination of the traffic sign state 1256, the HDV state 1258, and the other vehicle state 1258. Each of the functions 1246-1252 individually represents a dynamic traffic rule that the HDV should follow.

[0183] According to one embodiment, the selected function can be used as the motion model of the HDV for the joint optimization of the CAV and HDV. In particular, the traffic control system solves a MIP that optimizes the cost function with respect to the values ​​of the control commands that change the state of each CAV and the values ​​of the 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) concerning the position of a vehicle is independent of other variables controlled by the traffic control system other than the position of the vehicle itself, and therefore, since satisfying or violating the traffic rule is always the same for a fixed vehicle position, the collision avoidance rule (19) is not a dynamic traffic rule.

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

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[0202] Figure 12E shows a method for constructing and solving a MIP problem based on mixed integer equality and mixed integer inequality constraints for a predictive motion model of one or more CAVs, HDVs, TLCs and non-convex traffic rules in a transport network controlled by a hierarchical traffic control system, according to some embodiments of the present disclosure. The steps and their order identified in Figure 12E are illustrative and may include various alternatives, equivalents or derivatives thereof, including, but not limited to, their execution order. The steps of method 1200E in Figure 12E and its various alternatives may be embodied in hardware or software including a computer-readable storage medium (e.g., optical disc, memory card or hard drive) containing instructions executable by a processor included in the hierarchical traffic control system 600A. In another embodiment, the steps of method 1200E in Figure 12E and its various alternatives may be embodied in hardware or software including a computer-readable storage medium (e.g., optical disc, memory card or hard drive) containing instructions executable by a processor included in ITC 408 or 410. Figure 12E shows Method 1200E including a feedback loop for ITC408 or 410.

[0203] In 1260, ITC408 or 410 receives map segments and lane information for multiple interconnected traffic intersections within the transport network.

[0204] In 1262, ITC408 or 410 receives feedback signals related to detection and routing from the controlled vehicle, uncontrolled vehicle, and / or semi-controlled vehicle.

[0205] In 1264, ITC408 or 410 constructs matrices and vectors in the ITC's MIP data for objective, equality constraints, and inequality constraints.

[0206] In 1266, ITC408 or 410 solves the MIP problem based on mixed integer equality and mixed integer inequality constraints for predictive motion models of one or more CAVs, HDVs, and TLCs in a transport network, as well as mixed integer equality and mixed integer inequality constraints for non-convex traffic rules.

[0207] In 1268, ITC408 or 410 calculates the optimal control command and sends it to one or more CAVs and TLCs in the transport network controlled by the hierarchical traffic control system 600A.

[0208] According to some embodiments of this 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 understanding 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 integer optimization variables, and that the MCP can be solved computationally efficiently using, for example, a branch-bound optimization method.

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[0215] Also, in some embodiments of the present disclosure, the following MIP inequality constraint 1266-2 prevents both a lane change up and a lane change down at the same time step, prevents a lane change down from the lowest lane in a road section of the transportation network, and prevents a lane change up from the highest lane in a road section 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 signal timing constraints for imposing a minimum time between two consecutive signal 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 understanding that the prediction time window of CTC404 may be longer than the prediction time window of each ITC408 or 410 in a hierarchical traffic control system 600A that controls mixed traffic in a transport network of multiple interconnected traffic intersections, by using a macroscopic traffic flow model and by using a convex relaxation of a non-convex traffic rule in CTC404, which results in a convex optimization problem 1158 that is computationally much easier to solve compared to the MIP formulation 1266 solved in each ITC408 or 410.

[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 global optimal solution in the search space and generates an optimal control signal. B&B optimization iteratively divides the search space into a nested tree of domains to find a solution with a global optimal (minimum) objective value. The B&B method iteratively solves convex relaxations to compute a lower bound for the objective value in a given domain from the nested tree of domains. If the corresponding lower bound is greater than the currently known upper bound for the global optimal objective value, one or more domains can be pruned. If an integer feasible solution is found with an objective value smaller than the currently known upper bound for the global optimal objective value, the upper bound for the global optimal objective value can be updated.

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

[0234] Figure 13 shows an example of a traffic situation in a transit 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 shows an exemplary traffic situation 1300 in a transit 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 mixed traffic passing through one traffic intersection in the transit network. In some embodiments, one or more rules are used for assigning CAVs and / or HDVs to each of the ITCs 1011-1013 in the hierarchical traffic control system 600A in order to reduce the computational cost of solving a constrained optimization problem while maintaining excellent control performance and ensuring safety for all vehicles in the transit network at all times.

[0235] Some embodiments of this disclosure are based on the understanding that a switchable dynamic predictive model can be used at each ITC for both HDVs and CAVs controlled by different ITCs within a hierarchical traffic control system. For example, each CAV may be assigned to one ITC "for control" and the same CAV may be assigned to one or more other ITCs "for prediction" in order to improve the control performance and safety of all vehicles, particularly when vehicles move from one ITC to the next in the transport network.

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[0237] In some embodiments of this disclosure, CAV1331 and / or HDV1332 that are not currently within a predetermined distance from any traffic intersection in the transport network are not currently assigned to any ITC in the hierarchical traffic control system and are therefore not included in any ITC's MIP formulation 1266. However, if CAV1331 and / or HDV1332 become within a predetermined distance from any traffic intersection in the transport network, they may be assigned to an ITC at a future time step.

[0238] Some embodiments are based on the recognition that a set of the latter rules for assigning vehicles to ITCs can ensure that speed and lane change commands for each CAV are calculated by at most one ITC within a hierarchical traffic control system. According to some embodiments of the present disclosure, if a CAV is not assigned to any ITC, taking into account a predetermined threshold distance, control is returned to the CAV's onboard control architecture. In some embodiments of the present disclosure, given 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 expected to prevent potential collisions with any vehicles further upstream. In some embodiments of the present disclosure, each ITC provides control commands to the CAV only before the traffic intersection and only while the vehicle is physically within the traffic intersection. Control is returned to the vehicle or passed to the ITC corresponding to the next traffic intersection after the CAV has exited the intersection.

[0239] Figure 14A is a schematic diagram of an example of an integer optimization variable search tree representing a nested tree of the search domain for integer feasible solutions for hierarchical traffic control, according to some embodiments of the present disclosure. Figure 14A shows a schematic diagram of an example of a binary decision variable search tree 1400A representing a nested tree of the search domain for integer feasible solutions to MIP problem 1266 in a hierarchical traffic control system 600A. Figure 14A shows a schematic diagram of the branch and bound method, which can be used to implement a hierarchical traffic control system in some embodiments by displaying the 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 specific region of the discrete optimization variable search space. In some embodiments of the present disclosure, the branch-and-bound method obtains a nested tree of partitions or search regions by selecting a partition or node and then selecting discrete optimization variables to branch this partition into smaller partitions or search regions.

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[0241] While solving each partition can still be difficult, finding a local lower bound for the optimal objective is quite efficient by solving the local relaxations of the mixed-integer program (MIP) or by using duality. If the MIP solver happens to find an integer feasible solution while solving the local relaxations, it can use this to find a global upper bound for the mixed-integer solution to the original MIP problem in a hierarchical traffic control system. This can help avoid solving or branching certain partitions that have already been created, i.e., these partitions or nodes can be pruned. This general algorithmic idea of ​​partitioning can be represented as a binary search tree 1400A containing a root node at the top of the tree, e.g., P11401, and leaf nodes at the bottom of the tree, e.g., P41404 and P51405. Furthermore, nodes P21402 and P31403 are generally referred to as direct children of node P11401, and node P11401 is 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 this disclosure, the MIP problem may be a mixed-integer linear programming (MILP) or mixed-integer quadratic programming (MIQP) problem.

[0242] Figures 14B and 14C together are block diagrams of a branch-bound mixed integer optimization algorithm for searching for an integer feasible optimal solution based on a nested tree of search domains and corresponding lower / upper bounds, according to several embodiments. The block diagrams of the branch-bound mixed integer optimization algorithm shown in Figures 14B and 14C can be used to implement a hierarchical traffic control system in several embodiments. The branch-bound method initializes branch search tree information for the mixed integer program (MIP) at the current time step of the hierarchical traffic control system based on MIP data 1401, which consists of matrices and vectors (1410). 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 construct lower and upper bounds for the target 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, the mixed integer optimal solution is found (1455).

[0243] In step 1411, unless the difference between the lower and upper bounds is greater than a certain tolerance value and the optimization algorithm has not yet reached its maximum execution 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 the next node in the tree corresponding to the next region or partition of the integer variable search space by possible variable fixing based on preprocessing branching techniques (1415). After node selection, the corresponding integer relaxation problem is solved by possible variable fixing based on postprocessing branching techniques (1420).

[0244] If the integer relaxation problem has a feasible solution, the resulting relaxed solution provides a lower bound on the objective value to that particular region or partition of the integer variable search space. In step 1421, if the objective is determined to be greater than the currently known upper bound on the objective value of the optimal mixed integer solution, the selected node is pruned or removed from the branch tree (1440). However, in step 1421, if the objective is determined to be 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 an integer relaxation problem has a feasible solution and the objective is lower than the currently known upper bound (1421), but the relaxation solution is not yet integer feasible, 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). Alternatively, starting from the current node, discrete variables with decimal values ​​are selected for branching according to a specific branching strategy (1445), whose objective is to create the resulting subproblem corresponding to a region or partition of the discrete search space and to be added as a child of that node in the branching tree (1450).

[0246] A crucial step in the branch-and-bound method is determining 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 have decimal values ​​in the integer-relaxed solution. For example, if a particular binary optimization variable d ∈ {0,1} has decimal values ​​as part of the integer-relaxed 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 branch-and-bound algorithms using a depth-first node selection strategy that 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 until the node is pruned, i.e., until the node becomes unfeasible, optimal, or a currently known upper bound prevails, followed by a backtracking procedure. Alternatively, some embodiments are based on branch-and-bound algorithms using a best-first strategy that selects the node with the lowest currently known local lower bound. Some embodiments utilize a combination of depth-first and best-first node selection approaches, where the depth-first node selection strategy is used until an integer feasible solution is found, and then the best-first node selection strategy is used in subsequent iterations of the branch-and-bound-based optimization algorithm. Implementations of the latter are motivated by seeking an integer feasible solution early in the branch-and-bound procedure (depth-first) to enable early pruning, and then aiming to search for better feasible solutions more greedily (best-first).

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

[0249] The processor reaches its maximum execution time.

[0250] As a result of pruning all nodes in the branch search tree, it becomes impossible to select a new node to solve the convex relaxation or perform a branch.

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

[0252] Some embodiments are based on the recognition that the optimization problem of CTC controllers and / or ITC controllers may or may not be solved exactly. Exact solutions are feasible and locally or globally optimal, while inaccurate solutions may be approximately feasible and / or suboptimal. Examples of exact optimization algorithms include interior-point methods, effective constraint methods, gradient methods, operator partitioning methods, successive quadratic programming, successive convex programming, branch-and-bound methods, branch-and-cut methods, and branch-and-price methods. Examples of inaccurate optimization algorithms include heuristic rules, early termination of exact optimization algorithms, rounding methods, machine learning-based approximations of optimal solutions, and approximate dynamic programming.

[0253] In some embodiments, CTC and / or ITC control policies can be approximated by a deep neural network architecture, for example using reinforcement learning, to directly maximize a reward function for reducing congestion, travel time, emissions, and energy consumption within the transport network. In other embodiments, CTC and / or ITC control policies can be implemented using a deep neural network architecture based on imitation learning, aiming to approximate expert solutions to the corresponding optimization problems using precise optimization algorithms.

[0254] Figure 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 signal controllers in a transit network of one or more interconnected traffic intersections, according to some embodiments of the present disclosure. The hierarchical traffic control system 1500 runs 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 sensing) consisting of or operationally connected to a set of sensors to collect traffic information near one or more interconnected conflict zones in the transit 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 speed, as well as / or a sequence 1524 of speed profiles, one or more lane change commands, and planned stops along a future planned route in the transit network to each connected autonomous vehicle (CAV).

[0255] The hierarchical traffic control system 1500 includes several interfaces for connecting the decision-making system 1500 with other systems and devices. For example, the decision-making system 1500 includes 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 to 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. Furthermore, the decision-making system 1500 includes a transmitter interface 1510, which is configured to transmit to each connected autonomous vehicle (CAV) along a future planned route within the transport network, using transmitters 1512 and / or one or more devices 1508, an optimal sequence 1522 of entry / exit times and average speed, as well as / 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 improve the overall safety, time efficiency, and energy efficiency of traffic flow within the transport network, commands received from the hierarchical traffic control system may be used in each CAV by a multi-layered 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 use transmitters 1512 and / or one or more devices 1508 to transmit an optimal sequence of signal change commands determined by one or more processors 1514 to each signal controller (TLC) in an interconnected traffic intersection transport network over a predicted 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 interconnected conflict zones and road sections within the transport network. The traffic data 1532 may include information on the vehicle status (e.g., acceleration, position, direction of travel, speed) for each vehicle in the transport network, and information on planned and / or predicted future routes (e.g., future road sections, track lanes, desired destinations, and waiting 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 each of the respective states, such as acceleration and speed. The control interface 1534 may use a transmitter 1512 and / or any other means of communication to send these commands.

[0258] In some embodiments of this disclosure, a Human Machine Interface (HMI) 1540 connects the decision-making system 1500 to a keyboard 1536 and a pointing device 1538, the pointing device 1538 may include, among other things, a mouse, trackball, touchpad, joystick, pointing stick, stylus, or touchscreen. The decision-making system 1500 may also be connected via a bus 1504 to a display interface adapted to connect the decision-making system 1500 to a display device such as a computer monitor, camera, television, projector, or mobile device. The decision-making system 1500 may also be connected to an application interface adapted to connect the decision-making 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 (at least one memory) 1516 that stores instructions executable by the processors (at least one processor) 1514. The processors 1514 may be single-core processors, multi-core processors, computing clusters, networks 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 processors 1514 may be connected to one or more input / output devices via a bus 1504. These instructions realize a hierarchical traffic control method using one central traffic controller (CTC) and one or more intersection traffic controllers (ITCs) for controlling mixed CAV and HDV traffic in a transport 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, map configuration 1518 may include location data (e.g., GPS data) for conflict-free road sections, traffic intersections, stop zones, conflict zones, and lanes within each road section of the transport network.

[0260] The decision-making system 1500 includes constraints and objectives 1520 of one or more MIP problems 1266 and constraints and objectives 1520 of a convex optimization problem 1158, which 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 limits, vehicle speed limits and / or safety constraints, and to minimize a weighted combination of travel time, waiting time and / or energy consumption for each vehicle in the transport network.

[0261] Figure 16A is a schematic diagram of a vehicle 1601 that includes a multilayer guidance and control architecture 1602 that controls the motion of the vehicle based on a future route plan and corresponding motion plan that a hierarchical traffic control system can compute for a transport network, according to some embodiments of the present disclosure. The vehicle 1601 used herein may be any type of wheeled vehicle, such as a passenger 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 a hierarchical traffic control system can compute. An example of motion is the lateral motion of the vehicle 1601, which is controlled by the steering system 1603 of the vehicle 1601. In some embodiments of the present disclosure, the steering system 1603 is controlled by the multilayer guidance and control architecture 1602. Additionally or alternatively, the steering system 1603 may be controlled by the (human) driver of the vehicle 1601.

[0262] The vehicle may also include an engine 1606, which can be directly controlled by a multilayer induction 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 a rangefinder, radar, lidar, and camera. The vehicle 1601 may also include one or more on-board sensors 1605 for sensing the current amount of motion and internal state. Examples of sensors 1605 include a Global Positioning System (GPS), accelerometer, inertial measurement unit, gyroscope, shaft rotation sensor, torque sensor, deflection sensor, pressure sensor, and flow sensor. These on-board sensors provide information to the multilayer induction and control architecture 1602. The vehicle may be equipped with a transceiver 1608 that enables communication functions of a multilayer induction and control architecture 1602 via a wired or wireless communication channel, for example, so that the vehicle 1601 can communicate with a hierarchical traffic control system, according to some embodiments of the present disclosure.

[0263] Figure 16B is a schematic diagram of the interaction between a multilayer induction 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 cases, the multilayer induction and control architecture 1610 outputs control inputs to controllers 1625 and 1630 for controlling the state of the vehicle 1601. Controller 1620 may also include high-level controllers, such as a lane-keeping assist controller 1635, which further process the control inputs of the multilayer induction and control architecture 1602. In any case, the controller 1620 controls at least one actuator of the vehicle 1601, such as the steering wheel and / or brakes, using the output of the multilayer induction and control architecture 1610 to control the motion of the vehicle 1601. In some embodiments of the present disclosure, the vehicle 1601 is one of several CAVs in a transport network, and the multilayer induction and control architecture 1610 determines inputs to the vehicle 1601 based on a motion plan calculated by a hierarchical traffic control system, and the inputs to the vehicle 1601 may include the acceleration of the vehicle 1601, the engine torque of the vehicle 1601, the brake torque and steering angle, or a combination thereof.

[0264] The following description provides only exemplary embodiments and is not intended to limit the scope, applicability, or configuration of the present disclosure. Rather, the following description of exemplary embodiments provides a practical description for realizing one or more exemplary embodiments for those skilled in the art. The subject matter to be considered is a variety of modifications that may be made in terms of the function and arrangement of the elements without departing from the spirit and scope of the subject matter disclosed as described in the appended claims.

[0265] Specific details are given in the following description to ensure a full understanding of the embodiments. However, those skilled in the art will understand that embodiments can be carried out without these specific details. For example, systems, processes, and other elements of the disclosed subject matter may be shown as components in the form of block diagrams so as not to obscure the embodiments with unnecessary details. In other examples, well-known processes, structures, and technologies may be shown without unnecessary details to avoid obscuring the embodiments. Furthermore, similar reference numbers and names in different drawings refer to similar elements.

[0266] Furthermore, individual embodiments may be described as processes shown as flowcharts, flow diagrams, data flow diagrams, structural diagrams, or block diagrams. While flowcharts may describe operations as sequential processes, many of these operations can be performed in parallel or simultaneously. The order of these operations may also be reordered. A process may terminate when its operations are complete, but it may have additional steps not discussed or included in the diagrams. Moreover, not all operations in any specifically described process occur in all embodiments. A process may correspond to a method, function, procedure, subroutine, subprogram, etc. If a process corresponds to a function, the termination of the function may correspond to the function returning to the calling function or main function.

[0267] Furthermore, embodiments of the disclosed subject matter may be implemented at least partially manually or automatically. Manual or automatic implementation may be performed, or at least assisted, by using a machine, hardware, software, firmware, middleware, microcode, hardware description language, or any combination thereof. If implemented in software, firmware, middleware, or microcode, program code or code segments for performing the required tasks may be stored in a machine-readable medium. A processor may then perform the required tasks.

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

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

[0270] Embodiments of this disclosure may be embodied as an example provided. The actions performed as part of this method may be ordered in any preferred manner. Thus, embodiments may be constructed in which the actions are performed in an order different from that shown, which may include performing some actions simultaneously, even if they are shown as sequential actions in the exemplary embodiments.

[0271] While this disclosure has been described with reference to certain preferred embodiments, it should be understood that various other adaptations and modifications may be made within the spirit and scope of this disclosure. Therefore, it is an aspect of the appended claims to cover all such variations and modifications that fall within the true spirit and scope of this disclosure.

Claims

1. A traffic control system for jointly controlling one or more connected and automated vehicles (CAVs) and one or more human-driven vehicles (HDVs) crossing a plurality of intersections of a road, according to integer constraints for crossing each of the intersections, comprising at least one processor and a memory storing instructions, wherein when an instruction is executed by the at least one processor, the traffic control system... To collect digital representations of the state of each CAV, each HDV, and each traffic sign regulating traffic on the road, The objective is to solve an optimization problem that co-optimizes traffic flow based on a macroscopic traffic flow model in a Centralized Traffic Controller (CTC) for the aforementioned intersections, using a convex optimization that undergoes convex relaxation of the integer constraints for traversing each of the aforementioned intersections, For each of the plurality of intersections, a Mixed-Integer Programming (MIP) problem is solved individually in each of the plurality of Intersection Traffic Controllers (ITCs) to generate values ​​for control commands that change the state of each of the CAVs associated with one of the plurality of intersections, and values ​​for control commands that change the state of each of the traffic signs associated with the intersection, the multivariable MIP problem optimizes the cost function according to the integer constraints to minimize the tracking error in the traffic flow values ​​of the microscopic traffic flow model relative to the relaxed traffic flow values ​​from the CTC, the cost function is optimized according to the 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 the motion model of the HDV, described by switching functions relating dynamic traffic rules for the HDVs to the state of the HDVs and the state of the corresponding traffic signs, and the instructions are further executed by the at least one processor in the traffic control system, A traffic control system that transmits the optimized value of the control command to the corresponding CAV and the corresponding traffic sign.

2. Each of the above HDVs' switching function includes one or more motion models for one or more switching conditions, and the one or more motion models are A first motion model for stopping in a stop zone, in which the corresponding traffic sign is red in the cross direction and the HDV is within a first safe distance from the stop zone at each of the plurality of intersections on the roads within the transport network, A second motion model for safe preceding vehicle following behavior when the preceding vehicle is within a second safe distance in front of the HDV and the preceding vehicle is in the same lane on the same road section as the HDV, and The traffic control system according to claim 1, comprising at least one of the following: a third motion model for traveling at a desired average speed when there is no preceding vehicle within the second safe distance in front 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 stop zone and the corresponding traffic sign is not red.

3. The traffic control system according to claim 1, wherein the multivariable MIP problem in each of the plurality of ITCs includes a mapping between a plurality of collision-free states of the traffic signs and the values ​​of the traffic signs for each transverse direction of the plurality of intersections in a transport network controlled by a hierarchical traffic control system.

4. Each of the above-mentioned multivariable MIP problems in the above-mentioned ITC includes a plurality of mixed integer equality constraints and mixed integer inequality constraints for enforcing traffic rules for the CAVs and HDVs traveling near each of the above-mentioned intersections in the transport network controlled by the hierarchical traffic control system, The traffic control system according to claim 3, wherein the traffic rules include constraints for crossing any of the plurality of intersections based on the collision-free state of the corresponding traffic signs, capacity limit constraints for each of the plurality of intersections or each road section within the transport network, collision avoidance constraints between vehicle pairs, lane change constraints for vehicle overtaking, speed limit constraints, and traffic sign timing constraints.

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

6. The macroscopic traffic flow model in the aforementioned CTC is represented as a directed graph. Each node in the directed graph corresponds to a road section among a plurality of road sections, and each edge in the directed graph corresponds to a connection between two road sections among the plurality of road sections. The traffic control system according to claim 1, wherein the connection between two road sections indicates a direction that crosses one of the plurality of intersections in a transport network controlled by a 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 according to claim 6, wherein each of the one or more differential state variables and the one or more control input variables is included in the optimization variables of the 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 section and a traffic flow operation at each time step within the prediction time window of the CTC. The traffic control system according to claim 7, wherein the one or more control input variables include inflow and outflow variables that define the number of inflowing and outflowing vehicles, respectively, for each pair of road section and traffic flow operation in each time step within the predicted time window of the CTC.

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

10. The traffic control system according to claim 1, wherein the CTC solves a convex optimization problem having a cost function that includes at least one of maximizing the sum of traffic flow variables or minimizing the sum of traffic congestion variables in a transport network controlled by a hierarchical traffic control system.

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

12. The traffic control system according to claim 1, wherein the CTC calculates at least one of vehicle density or vehicle routing probability values ​​for each pair of road section and traffic flow operation within the transport network in a predicted time window, based on historical data collected for a similar transport network over a similar past period to the predicted time window.

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

14. The traffic control system according to 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 of the ITCs in the hierarchical traffic control system based on one or more rules.

15. One of the plurality of ITCs calculates speed commands and lane change commands for each of the one or more CAVs in the hierarchical traffic control system based on the one or more rules for assigning vehicles to the plurality of ITCs. If one of the one or more CAVs is not assigned to any of the multiple ITCs, the authority to control the speed command and the lane change command is returned to the on-board control architecture of the CAV, according to claim 14.

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

17. The convex optimization problem solved in the aforementioned CTC is either a convex linear programming (LP) problem or a convex quadratic programming (QP) problem. The traffic control system according to claim 1, wherein the convex LP problem or the convex QP problem is solved using the effective constraint method, the interior point method, the gradient method, the operator partitioning method, or the alternating direction method of multipliers (ADMM).

18. The traffic control system according to 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, exhaust emissions or energy consumption for each of one or more CAVs and one or more HDVs in the transport network, and the RL policy is trained to calculate an optimal traffic flow action taking into account one or more state feedback signals from the transport network.

19. The multivariable MIP problem in each of the aforementioned ITCs is solved using a branch-and-bound (B&B) optimization method, which searches for a global optimal solution in the search space to generate the optimal control signal. The traffic control system according to claim 1, wherein the B&B optimization method repeatedly divides the search space into nested tree structures in order to find a solution having a globally optimal target value in each of the ITCs of the traffic control system.

20. The multivariable MIP problem in each of the aforementioned ITCs is solved using heuristic techniques. The traffic control system according to 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 the optimal solution to the multivariable MIP problem.

21. A method for jointly controlling one or more connected autonomous vehicles (CAVs) and one or more human-driven vehicles (HDVs) crossing a plurality of intersections of a road, in accordance with integer constraints for crossing each of the intersections, A step of collecting digital representations of the state of each CAV, each HDV, and each traffic sign regulating traffic on the road, The steps include solving an optimization problem for jointly optimizing traffic flow based on a macroscopic traffic flow model in a centralized traffic controller (CTC) for the multiple intersections, using a convex optimization that undergoes convex relaxation of the integer constraints for traversing each of the multiple intersections, The method comprises the steps of individually solving a multivariable mixed integer programming (MIP) problem for each of the plurality of intersections in each of the plurality of intersection traffic controllers (ITCs) to generate values ​​for control commands that change the state of each of the CAVs associated with one of the plurality of intersections, and values ​​for control commands that change 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 the tracking error in the traffic flow values ​​of the microscopic traffic flow model for relaxed traffic flow values ​​from the CTC, wherein the cost function is 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 state of corresponding traffic signs, and the method further, A method comprising the step of transmitting the optimized value of the control command to the corresponding CAV and the corresponding traffic sign.

22. A non-temporary computer-readable storage medium embodying a processor-executable program for performing a method for jointly controlling one or more connected autonomous vehicles (CAVs) and one or more human-driven vehicles (HDVs) crossing a plurality of intersections of a road, according to integer constraints for crossing each of the said intersections, wherein the method is: A step of collecting digital representations of the state of each CAV, each HDV, and each traffic sign regulating traffic on the road, The steps include solving an optimization problem for jointly optimizing traffic flow based on a macroscopic traffic flow model in a centralized traffic controller (CTC) for the multiple intersections, using a convex optimization that undergoes convex relaxation of the integer constraints for traversing each of the multiple intersections, The method comprises the steps of individually solving a multivariable mixed integer programming (MIP) problem for each of the plurality of intersections in each of the plurality of intersection traffic controllers (ITCs) to generate values ​​for control commands that change the state of each of the CAVs associated with one of the plurality of intersections, and values ​​for control commands that change 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 the tracking error in the traffic flow values ​​of the microscopic traffic flow model for relaxed traffic flow values ​​from the CTC, wherein the cost function is 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 state of corresponding traffic signs, and the method further, A non-temporary computer-readable storage medium comprising the step of transmitting the optimized value of the control command to the corresponding CAV and the corresponding traffic sign.

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