Trajectory optimization model based on vehicle fleet and vehicle fleet formation trajectory optimization method at signalized intersection

Abstract

This invention proposes a vehicle-based trajectory optimization model and a method for optimizing vehicle formation trajectories at signalized intersections. The method includes vehicle detection, congestion determination, and state tracking. The vehicle-based trajectory optimization model takes effect when congestion is detected, and its decision-making is based on the speed, passenger capacity, location information, and signal timing data of approaching vehicles. A three-stage solution is proposed: the first stage employs a multi-stage nonlinear programming process to search for the trajectory that minimizes the average travel time; the second and third stages optimize the results using mixed-integer linear programming to minimize the average idling time and speed fluctuations of the vehicle fleet, further reducing vehicle driving energy consumption and environmental impact; with the help of wireless communication technology, the system can acquire the location speed and signal information of each vehicle in real time, thereby predicting future traffic conditions.

Description

Technical Field

[0001] This invention relates to the field of autonomous driving trajectory planning technology, and in particular to a fleet-based trajectory optimization model and a method for optimizing fleet formation trajectories at signalized intersections. Background Technology

[0002] Signalized intersections are a crucial component of urban transportation systems. With the growth of urban areas and populations, limited road space and ever-increasing traffic demand often prevent signalized intersections from providing satisfactory service levels, leading to excessively long travel times and ecological problems. In the United States, the transportation sector consumes nearly 75% of the world's oil, and due to operational inefficiencies, its transportation industry ranks second globally in carbon dioxide emissions. Research has found that poor driving behavior caused by severe congestion is a major driver of carbon emissions and oil consumption. Traditional research on the operational efficiency of signalized intersections has yielded limited results, thus innovative technologies are urgently needed to address these challenges.

[0003] A literature review of existing technologies revealed the following main methods for optimizing vehicle trajectories at signalized intersections: 1. Zheng et al. proposed a real-time parallel trajectory optimization with spatiotemporal safety constraints for autonomous driving under congested traffic conditions. They developed a spatiotemporal safety module to address trajectory prediction errors caused by the multimodal behavior of surrounding vehicles and ensure safe interaction between autonomous vehicles and surrounding vehicles (Zheng et al., 2024).

[0004] 2. M. Ramezani and N. Geroliminis combined the collective effect of dispersed vehicle data with traffic flow shockwave analysis and data mining techniques to estimate vehicle platoon characteristics (Ramezani and Geroliminis, 2005).

[0005] 3. Wang et al. proposed a nonlinear model predictive control (MPC) emission reduction scheme based on the longitudinal control of intelligent vehicle fleets. Through a series of simulations, the fleet control strategy confirmed that implementing local instantaneous control on a small number of intelligent vehicles can effectively reduce the overall emissions of the fleet (Wang et al., 2013).

[0006] 4. A few studies focus on trajectory optimization at intersections under real-time communication conditions. Li and Wang proposed a safe vehicle trajectory that minimizes latency (Li and Wang, 2016).

[0007] 5. Chen et al. developed an algorithm that assumes vehicles can receive traffic light information in advance via DSRC and adjust their speed to minimize idling time before the stop line (Chen et al., 2011).

[0008] 6. Zohdy and Rakha developed a game theory-based algorithm that enables each vehicle to avoid conflicts and minimize delays in a cooperative adaptive cruise control system at intersections.

[0009] 7. Lee and Park developed a cooperative vehicle intersection control algorithm that does not require signal control using vehicle-to-everything (V2X) technology (Lee and Park, 2012).

[0010] 8. Abu-Lebdeh proposed an algorithm to study the benefits of intelligent driving technology in terms of vehicle delays (Abu-Lebdeh, 2013).

[0011] 9. Guler et al. proposed an algorithm that uses connected vehicle technology to enumerate various vehicle emission patterns in front of the stop line and minimize vehicle delays (Guler et al., 2014).

[0012] 10. Wan et al. (2016) proposed a speed suggestion system (SAS) for predictive traffic lights and obtained the most fuel-efficient driving strategy by solving the fuel consumption minimization problem (Wan et al., 2016).

[0013] 11. Wei et al. proposed a set of integer programming and dynamic programming models to plan longitudinal driving trajectories while taking into account both the overall system safety and throughput requirements. However, research on cooperative trajectory optimization to actively eliminate bottleneck section intersection conflicts by adjusting vehicle arrival patterns is still very limited (Wei et al., 2017).

[0014] 12. Other studies focus on connected autonomous vehicles at isolated intersections (Yang et al., 2016; Yue et al., 2018; Feng et al., 2018).

[0015] Existing research indicates that previous studies on vehicle speed control algorithms have mostly focused on designing a single optimization objective, while research on collaborative trajectory optimization that aims to improve overall driving economy by actively eliminating bottleneck area conflicts by changing vehicle arrival patterns, minimizing travel time, and reducing speed fluctuations and idling time. Summary of the Invention

[0016] The purpose of this invention is to propose a vehicle-based trajectory optimization model and a vehicle formation trajectory optimization method for signalized intersections, which can effectively shorten the average travel time, idling time and speed fluctuation of vehicles passing through signalized intersections, significantly reduce the energy consumption of autonomous driving vehicles, and improve the operating efficiency of intersections.

[0017] To achieve the above objectives, this invention proposes a trajectory optimization model based on a vehicle fleet, wherein the decision variable of the model is the speed curve of each vehicle in the fleet. The objective functions of the model include: a) minimizing the average travel time of vehicles in the fleet; b) minimizing the average idling time while satisfying objective a; and c) minimizing the average speed fluctuation while satisfying objectives b and a. The constraints of the model include: the vehicle speed must not exceed the maximum speed limit; if the vehicle is in cruise mode, its speed should exceed the minimum cruise speed; the vehicle's acceleration and deceleration rates should be within a reasonable range; and a safe distance should always be maintained between vehicles to avoid rear-end collisions.

[0018] Furthermore, regarding the constraint that vehicles should always maintain a safe distance to avoid rear-end collisions, the "two-second rule" is adopted, requiring drivers to maintain an ideal following distance of at least two seconds from the vehicle in front.

[0019] Furthermore, the trajectory optimization model is solved using a three-stage algorithm. The first stage uses multi-stage nonlinear programming to minimize the average driving time of the fleet. The second stage, based on the driving time of each vehicle determined in the first stage, constructs a mixed-integer programming model to further minimize the average idle time. The third stage, under the constraints of the results of the first and second stages, finally minimizes the average speed fluctuation of the fleet through another mixed-integer programming model.

[0020] Furthermore, in the first stage, a multi-stage decision-making process is employed to optimize the average travel time. Specifically, a time-rolling algorithm is used to estimate the travel time based on the feasible speed of the current stage, implementing phased updates. In each stage, nonlinear programming (NLP) is used to find the optimal speed for each vehicle in the platoon that minimizes the average travel time. Regarding the time interval H between two consecutive stages, this interval should be as short as possible, while ensuring that all vehicles have sufficient time to switch between idling and maximum speed limit driving states. The multi-stage NLP terminates when all vehicles in the platoon leave the intersection. Otherwise, it is assumed that vehicles that have already crossed the stop line are still participating in the optimization process.

[0021] Furthermore, the state transition function of the multi-stage decision-making process includes updating the speed, updating the cumulative travel distance, and updating the travel time; Update rate: Within the time interval H, the time indices of the s-th stage and the (s+1)-th stage are sH and sH+H, respectively; therefore, the estimated rate per second for stages s to s+1 is: ; in, It can be expressed by the following formula: ; Based on the above formula, the speed update process is shown: when updating the speed, the vehicle uses the maximum acceleration / deceleration rate, and if there is still time remaining to enter the next stage, it maintains the cruise state. Update cumulative driving distance: The cumulative driving distance in stage s+1 can be updated using the following formula: ; The updated travel time is given by the following formula: ; Where y is the idle speed indicator, given by the following formula, if If the value is zero, then the travel time will be assigned a very large value; ; From the formula It can be seen that if the vehicle has already left the intersection in stage s, then Taking a negative value results in a travel time less than sH; given the travel time for each stage, it can be updated in stage s+1 using the following formula: ; in:

[0022] Therefore, the update of the average travel time of the fleet is given by the following formula: .

[0023] Furthermore, the objective function of the multi-stage decision-making process is to minimize the average travel time stage by stage; In the (s+1)th stage, the objective function can be expressed as: .

[0024] Furthermore, the constraints of the multi-stage decision-making process include speed limit constraints, cruise speed limit constraints, and safe distance maintenance constraints.

[0025] This invention also proposes a method for optimizing the platoon formation trajectory at signalized intersections, characterized by using a platoon-based trajectory optimization model as described in any one of claims 1-7; the method for optimizing the platoon formation trajectory at signalized intersections includes the following steps: S1: Fleet Detection: Activated when the fleet leader vehicle enters the control range. The control range is the initially determined range. If the range is too short, it will not provide enough space for the vehicle to change its state according to the control command, while if it is too long, it may cause a waste of time and space resources. S2: Congestion Determination: Based on the following prediction: the current speed of the formation will be blocked by downstream vehicles or signal control, and the prediction should satisfy any of the following formulas: ; ; In the formula, x' is the current position of the nearest downstream vehicle; t is the initial speed of the first vehicle; t is the travel time of the vehicle leaving the intersection, which can be obtained by the system control from the downstream convoy; TTR is the red light countdown time when the convoy enters the control range. This value is negative, and its absolute value is equal to the duration after the red light is on. If the traffic light is red at this moment; if congestion is confirmed, the control logic will switch to the trajectory optimization model to optimize the convoy trajectory; otherwise, the control logic will jump to the unused component, i.e., state tracking. S3: State Tracking: If no congestion occurs or the trajectory optimization is completed, the system will continuously track the fleet status to detect whether the state constraints are violated; if a violation is found, the control logic will backtrack to the congestion determination and re-execute the subsequent steps until the fleet has completely left the intersection.

[0026] Compared with existing technologies, the advantages of this invention are: the autonomous vehicle trajectory optimization method proposed in this invention can effectively shorten the average travel time, idling time and speed fluctuation of the fleet passing through signalized intersections, significantly reduce the energy consumption level of autonomous vehicle fleets, and improve the operating efficiency of intersections. Attached Figure Description

[0027] Figure 1 Schematic diagram of route optimization to prevent congestion Figure 2 For control logic architecture Figure 3 Red light duration range under different initial signal information Figure 4 Three-stage algorithm architecture Figure 5 Average travel time optimization multi-stage process Figure 6 Excessive idling time and speed fluctuation pattern Figure 7 Travel time differs between controlled and uncontrolled environments. Figure 8 The movement trajectory of the formation in the control environment under different scenarios Figure 9 The movement trajectory of the formation in the control environment under different scenarios Figure 10 Fuel consumption rate of the lead vehicle in controlled and uncontrolled states in scenarios 1 and 3. Figure 11 The effect of initial speed on average travel time Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions of the present invention will be further described below.

[0029] This invention proposes a method for optimizing vehicle platooning trajectories at signalized intersections, such as... Figure 1 As shown, this method can effectively and simultaneously shorten the average transit time, idling time, and speed fluctuation of a fleet passing through a signalized intersection, significantly reduce the energy consumption of autonomous driving fleets, and improve intersection operating efficiency; it includes the following steps, such as... Figure 2 As shown: Step 1: Fleet Detection. This is the initial step of the control mechanism, activated when the convoy leader enters the control range. The control range here should be the initially determined range, because a range that is too short will not provide enough space for the vehicles to change their state according to control commands, while a range that is too long may result in a waste of time and space resources.

[0030]

[0031] In the formula, The length of the research route set when optimizing the trajectory of the convoy entering the signalized intersection. -d: Maximum deceleration a: Maximum acceleration C: Signal period duration, in seconds. According to formula (1), the control range xscope should be determined to ensure that: 1) the vehicle has sufficient space to stop before the stop line; 2) the vehicle has sufficient space to accelerate to the maximum speed limit; and 3) the time required for the vehicle to travel to the stop line at the minimum cruising speed should not exceed the cycle length under congestion-free conditions. The distance between any two vehicles should be less than 5 seconds.

[0032] Step 2: Congestion Determination. Based on the following prediction: the current speed of the formation will be blocked by downstream vehicles or signal control, this prediction should satisfy any of the following formulas:

[0033] Where x' is the current position of the nearest downstream vehicle; That is the initial speed of the first vehicle; This is the travel time of the vehicle leaving the intersection, which can be obtained from the downstream convoy by the system control; and TTR is the red light countdown time when the convoy enters the control range. This value is negative, and its absolute value is equal to the duration after the red light turns on, if the traffic light displays red at this time. If congestion is confirmed, the control logic will switch to the next component, i.e., convoy trajectory optimization; otherwise, the control logic will jump to the next component, i.e., state tracking. The initial headway between the leading vehicle and its nearest downstream vehicle; This represents the initial distance (in meters) between the stop line and the p-th vehicle. Yellow light interval; Red light intervals; This is a threshold based on the initial speed (usually corresponding to the reference value of safe headway); this formula is used to limit the spatiotemporal relationship of vehicles in traffic flow, ensuring that the comprehensive relationship between the leading vehicle and the downstream vehicles, which is "headway + spatial position - speed × time", does not exceed twice the initial speed, thus ensuring that vehicle travel meets the stability conditions of the traffic flow model.

[0034] Step 3: State Tracking. If no congestion occurs or trajectory optimization is complete, the system will continuously track the fleet status to detect any violations of state constraints. If a violation is detected, the control logic will backtrack to the congestion determination and re-execute subsequent steps until the fleet has completely left the intersection.

[0035] Model building If congestion is determined to exist, a trajectory optimization model based on the fleet is constructed.

[0036] ① Decision variables The decision variable set is the speed curve of each vehicle in the convoy, defined as follows: = The speed of vehicle p at second t (m / s).

[0037] ② Objective function The objectives of this model are: (a) to minimize the average travel time of vehicles in the convoy; (b) to minimize the average idling time while satisfying objective (a); and (c) to minimize the average speed fluctuation while satisfying objectives (b) and (c), which are given by the following objective function: Objective (a):

[0038] Objective (b):

[0039] Target (c):

[0040] in, Let p be the travel time of the p-th vehicle; The binary idle speed indicator for vehicle p at second t is given by the following formula:

[0041] and It is the binary indication of the speed fluctuation of vehicle p at second t, as shown in formula (8).

[0042]

[0043] ③Constraints Apart from the internal correlations between objective functions, the general form of model constraints is shown below.

[0044] The vehicle speed must not exceed the maximum speed limit, which is expressed as:

[0045] In addition, if the vehicle is in cruise control mode, its speed should exceed the minimum cruise speed, calculated as follows:

[0046] The vehicle's acceleration and deceleration rates should be within a reasonable range, as given by the following formula:

[0047] Vehicles should always maintain a safe following distance to avoid rear-end collisions. To linearly express this constraint, this paper adopts the "two-second rule," a rule of thumb that states drivers can maintain a safe following distance at any speed. It requires drivers to maintain an ideal following distance of at least two seconds from the vehicle in front (New York State Department of Motor Vehicles, 2011), calculated using the following formula:

[0048] In the formula: Let p be the speed of vehicle p at second t (in meters per second). Let p be the initial headway between vehicle p and vehicle (p-1) (p>1). Left side: Based on the initial headway (( )), cumulative speed change of the front workshop (( )), the cumulative change in the vehicle's speed (( To quantify the relative spatiotemporal relationship between the two vehicles; Right side: (2) This corresponds to the "two-second rule": twice the current vehicle speed, reflecting the constraint of "two-second following time"; In other words, the combined result of the relative distance between the two vehicles and the change in speed must be no less than twice the current vehicle speed to meet the requirements for safe following.

[0049] Formulas (12) and (13) ensure that all vehicles in the platoon maintain a safe distance, where v introduced in formula (13) represents the speed of the downstream vehicle. Running red lights can be completely avoided using the following formula, such as... Figure 3 As shown:

[0050] Regarding formula (14), the range of R is determined by the initial signal information TTR, which represents the red light indication time. If the signal shows a red light when the convoy enters the control range, then TTR takes a negative value, and its absolute value is equal to the duration after the red light is on. Therefore, the remaining red light duration in the current cycle can be estimated as [0, TTR + r]. Accordingly, the range of R in the z-th cycle can be expressed as:

[0051] The entire convoy eventually passed through the intersection, given the following conditions:

[0052] Solution Algorithm Three-phase algorithm This study proposes a three-stage algorithm for solving the vehicle trajectory optimization model. Its working mechanism is as follows: Figure 4 As shown: In the first stage, multi-stage nonlinear programming (NLP) is used to minimize the average driving time of the fleet; in the second stage, based on the driving time of each vehicle determined in the first stage, a mixed integer programming model is constructed to further minimize the average idle time; in the third stage, under the constraints of the results of the first and second stages, another mixed integer programming model is used to finally minimize the average speed fluctuation of the fleet.

[0053] Minimize average driving time Average driving time optimization -- a multi-stage decision-making process Travel time estimation is based on vehicle speed data, but vehicle speed itself fluctuates. Due to these fluctuations, it is difficult to optimize travel time using a single algorithm over a long period. Therefore, a time-rolling algorithm is more suitable. This algorithm can estimate travel time based on the feasible speed of the current stage and update it in stages. Accordingly, this study proposes a multi-stage optimization process: in each stage, nonlinear programming (NLP) is used to find the optimal speed for each vehicle in the fleet that minimizes the average travel time. Figure 5 ).

[0054] Regarding the time interval H between two consecutive stages, this time interval should be as short as possible, while ensuring that all vehicles have sufficient time to switch between idling and maximum speed driving states. Figure 4 As shown on the left, the multi-stage NLP process terminates when all vehicles in the convoy have left the intersection. Otherwise, it is assumed that vehicles that have already crossed the stop line are still involved in the optimization process.

[0055] State transition function a. Update speed Within the time interval H, the time indices of the s-th stage and the (s+1)-th stage are sH and sH+H, respectively. Therefore, the velocity per second from the s-th to the (s+1)-th stage can be estimated as:

[0056] in, Represented by the following formula

[0057] Formulas (18) and (19) illustrate the speed update process: the vehicle uses the maximum acceleration / deceleration rate when updating the speed, and maintains cruise mode if there is still time remaining to enter the next stage.

[0058] b. Update cumulative driving distance Considering the speed update process, the cumulative travel distance in stage s+1 can be updated using the following formula:

[0059] in, The formula for estimating the travel distance from stage s to s+1 at time t is as follows:

[0060] For acceleration and deceleration (m / s²) 2 ).

[0061] c. Update travel dates Based on multi-stage travel time estimation, such as Figure 5 As shown.

[0062]

[0063] Where y is the idle speed indicator, given by the following formula, if If the value is zero, then the travel time will be assigned an extremely large value.

[0064]

[0065] From formula (22), it can be seen that if the vehicle has already left the intersection in stage s, then Taking a negative value results in a travel time less than sH. Given the travel time for each stage, it can be updated in stage s+1 using the following formula:

[0066] in

[0067] Therefore, the update of the average travel time of the fleet is given by the following formula:

[0068] objective function The objective of multi-stage NLP is to minimize the average travel time stage by stage. In the (s+1)th stage, the objective function can be expressed as:

[0069] Essentially can be transformed into

[0070] in, It is the optimized cumulative travel distance in stage s, and It is an indicator value used to determine whether travel time should be allocated through the maximum value, and it is defined as:

[0071] Based on multi-stage nonlinear programming (NILP), the time is s when all vehicles leave the intersection. * Phase terminated. Final phase s * The following formula should be satisfied:

[0072] Constraints The model constraints (as shown in equations (9) to (17)) need to be converted into a stage-based form, as follows: The speed limit constraint is given by the following formula:

[0073] Cruise speed limit constraints (as shown in formula (10)) can eliminate "if" conditions, specifically as follows:

[0074] The acceleration and deceleration constraints can be relaxed here, since the speed update process has been determined.

[0075] Safety distance maintenance constraints (as shown in formulas (12) and (13)) Can be converted to:

[0076] As shown in formula (14), the red light violation prevention constraint should be subject to the condition that the constraint only takes effect if the vehicle has not crossed the stop line in the previous stage. Its expression is:

[0077] Here, the constraint on clearing intersections can be relaxed, as it is a condition for the termination of multi-stage nonlinear programming.

[0078] The technical effects of the present invention will be illustrated below through specific embodiments: Example 1: This section validates the proposed platoon trajectory optimization model through several examples. A platoon of ten vehicles is selected, and various TTR-related scenarios are established. Ten vehicles are chosen because a platoon of ten is considered to have an appropriate length. Two constraints need to be considered: an excessively long platoon may lead to delays exceeding two cycles; an excessively short platoon will not fully realize the benefits of speed control.

[0079] The parameter settings are summarized in Table 2. The initial speed and distance of each vehicle in the convoy are set to be the same.

[0080]

[0081] Travel time assessment The performance of the fleet was compared in three scenarios under controlled and uncontrolled environments. Figure 7 Here, "controlled environment" refers to speed control, while "non-controlled environment" refers to the absence of speed control. Since we are tracking the state of the entire convoy as it approaches the intersection, there are only three possible outcomes when speed control is required: (1) The entire convoy accelerates through the intersection and completes the passage before the red light turns on; (2) The entire convoy decelerates until the start of the next green light cycle and passes through the intersection; (3) The convoy splits into two sub-convoys, with the rear sub-convoy accelerating through the intersection and the front sub-convoy decelerating or even stopping until the next green light cycle.

[0082] Based on the above results, we designed three corresponding scenario solutions.

[0083] Scenario 1 shows a significant difference in travel time between the leading and second vehicles in a platoon approaching an intersection, under controlled and uncontrolled conditions. This difference stems from the fact that controlled vehicles, when following control instructions, can pass through the intersection unimpeded by red lights or vehicles behind them. However, in uncontrolled conditions, vehicles may experience cruising, deceleration, and idling, leading to a substantial increase in travel time. In Scenario 2, the second and third vehicles experience similar conditions to those in Scenario 1, while the difference in travel time for the leading vehicle is not significant; even in uncontrolled conditions, the leading vehicle can still pass through the intersection unimpeded. In conclusion, platoons employing controlled strategies have shorter average travel times than uncontrolled platoons.

[0084] Figure 8 The driving trajectory of each vehicle under controlled conditions is further demonstrated. In scenarios 1 and 2, the convoy is divided into sub-convoys: the leading sub-convoy accelerates through the intersection, while the following sub-convoys decelerate until the next green light cycle. In scenario 3, downstream vehicles maintain an idling speed, allowing the entire convoy to decelerate completely through the intersection and avoiding idling.

[0085] Idle time and speed fluctuation assessment Table 3 compares the idling time, speed fluctuation, and average values ​​of each vehicle in different scenarios under controlled and uncontrolled environments. Note that all values ​​are rounded to integers. The results show that the idling time and speed fluctuation of each vehicle are significantly improved under controlled conditions compared to the uncontrolled environment. Furthermore, the average idling time and speed fluctuation of the fleet under controlled conditions are also lower than those under uncontrolled conditions.

[0086] Table 3. Comparison of idling time and speed fluctuation under controlled and uncontrolled environments.

[0087] To further explore the benefits of reducing idling time and speed fluctuations, this study uses the VT-micro model to compare fuel consumption of a fleet under controlled and uncontrolled environments.

[0088] based on Figure 6 The comparison chart, combined with the content of Table 3, shows two unreasonable driving modes: The left side shows the trajectory of excessive idling time. Red curve: After the vehicle speed decreases, it maintains a low / zero speed state for an extended period. Green curve: Vehicle speed decreases and then quickly resumes driving. Comparing the idling time differences between the two trajectories reflects the efficiency issue of "stalling and waiting" while the vehicle is in motion.

[0089] The right side shows the trajectory with excessive speed fluctuations. Red curve: Vehicle speed fluctuates frequently and drastically. Green curve: Vehicle speed is relatively stable and changes gently. Comparing the speed stability of the two trajectories reflects the smoothness of vehicle operation.

[0090] Based on the comparison, it can be seen that the optimized (green trajectory) driving state is more efficient and smoother.

[0091] This study employs a microscopic fuel consumption and emission model, namely the VT-micro model (Ahn et al., 1999), which has been proven to be highly accurate and easy to calibrate. The model expression is as follows:

[0092] Wherein, MOE is the instantaneous fuel consumption rate; Speed ​​power and acceleration power LowerMOE e The model coefficients; v is the instantaneous velocity; a is the instantaneous acceleration rate. The results are as follows: Figure 9 and Figure 10 As shown.

[0093] like Figure 9 As shown, in Scenario 1, due to the significant difference in driving time, the fuel consumption of the first and last vehicles in the controlled environment is much lower than that in the uncontrolled environment. The second and third vehicles in Scenario 2 exhibit similar patterns. In the remaining scenarios, fuel consumption remains low under controlled conditions, thanks to optimal idling time and speed fluctuation control. Since the driving times in controlled and uncontrolled states are similar, the fuel consumption differences between these samples are smaller than in the previous example.

[0094] Figure 10 The fuel consumption rates of the lead vehicle in scenarios 1 and 3 are discussed in detail (scenario 2 is omitted here as it is similar to scenario 1). It can be observed that the fuel consumption trajectory of the controlled vehicle is smoother than that of the uncontrolled vehicle. In scenario 1, the fuel consumption curve of the controlled vehicle ends much earlier than that of the uncontrolled vehicle, thus achieving significant energy savings. In scenario 2, due to time loss, the uncontrolled curve ends slightly later than the controlled curve. Furthermore, the uncontrolled curve exhibits a peak at the end when the vehicle aggressively accelerates through an intersection.

[0095] Sensitivity analysis This section explores the impact of different initial convoy speeds (assuming all vehicles travel at the same speed) on average travel time through sensitivity analysis. By adjusting the speed before the convoy enters the control range, it is expected that control performance can be further improved. Figure 11 The average travel time is summarized for scenarios 1 and 3 as defined in Section 4.1, with initial velocities ranging from 6 m / s to 16 m / s (in increments of 1 m / s).

[0096] like Figure 11 As shown, when the traffic light initially displays green, the average platoon time decreases with increasing initial speed because TTR > 0. This is likely because a higher initial speed allows vehicles more flexibility to adjust their speed to avoid congestion caused by the traffic light. However, when TTR < 0, the initial speed appears to have little effect on the average platoon time due to the unavoidable congestion caused by the traffic light.

[0097] The above are merely preferred embodiments of the present invention and do not constitute any limitation on the present invention. Any equivalent substitutions or modifications made by those skilled in the art to the technical solutions and content disclosed in the present invention without departing from the scope of the present invention shall be deemed to have remained within the protection scope of the present invention.

Claims

1. A trajectory optimization model based on a fleet of vehicles, characterized in that, The decision variable of the model is the speed curve of each vehicle in the fleet; The objective functions of the model include: a) minimizing the average travel time of vehicles in the fleet; b) minimizing the average idling time while satisfying objective a; and c) minimizing the average speed fluctuation while satisfying objectives b and a. The constraints of the model include: the vehicle speed must not exceed the maximum speed limit; if the vehicle is in cruise mode, its speed should exceed the minimum cruise speed; the vehicle's acceleration and deceleration rates should be within a reasonable range; and a safe distance should always be maintained between vehicles to avoid rear-end collisions.

2. The trajectory optimization model based on a fleet of vehicles according to claim 1, characterized in that, Regarding the constraint that vehicles should always maintain a safe distance to avoid rear-end collisions, the "two-second rule" is adopted, requiring drivers to maintain an ideal following distance of at least two seconds from the vehicle in front.

3. The trajectory optimization model based on a fleet of vehicles according to claim 1, characterized in that, The trajectory optimization model is solved using a three-stage algorithm. The first stage uses multi-stage nonlinear programming to minimize the average driving time of the fleet. The second stage, based on the driving time of each vehicle determined in the first stage, constructs a mixed integer programming model to further minimize the average idle time. The third stage, under the constraints of the results of the first and second stages, uses another mixed integer programming model to finally minimize the average speed fluctuation of the fleet.

4. The trajectory optimization model based on a fleet of vehicles according to claim 3, characterized in that, The first stage employs a multi-stage decision-making process to optimize average travel time. Specifically, a time-rolling algorithm estimates travel time based on the feasible speed of the current stage, implementing phased updates. In each stage, nonlinear programming (NLP) is used to find the optimal speed for each vehicle in the platoon that minimizes the average travel time. The time interval H between two consecutive stages should be minimized while ensuring that all vehicles have sufficient time to switch between idling and maximum speed limits. The multi-stage NLP terminates when all vehicles in the platoon have left the intersection. Otherwise, vehicles that have already crossed the stop line are assumed to still participate in the optimization process.

5. The trajectory optimization model based on a fleet of vehicles according to claim 3, characterized in that, The state transition function of the multi-stage decision-making process includes updating speed, updating cumulative travel distance, and updating travel time; The update rate is as follows: within the time interval H, the time indices of the s-th stage and the (s+1)-th stage are sH and sH+H, respectively; therefore, the rate per second from the s-th to the (s+1)-th stage is estimated as follows: ； in, It can be expressed by the following formula: ； Based on the above formula, the speed update process is shown: when updating the speed, the vehicle uses the maximum acceleration / deceleration rate, and if there is still time remaining to enter the next stage, it maintains the cruise state. The updated cumulative driving distance: The cumulative driving distance in stage s+1 can be updated using the following formula: ； The updated travel time is given by the following formula: ； Where y is the idle speed indicator, given by the following formula, if If the value is zero, then the travel time will be assigned a very large value; ； From the formula It can be seen that if the vehicle has already left the intersection in stage s, then Taking a negative value results in a travel time less than sH; given the travel time for each stage, it can be updated in stage s+1 using the following formula: ； in: ; Therefore, the update of the average travel time of the fleet is given by the following formula: 。 6. The trajectory optimization model based on a fleet of vehicles according to claim 3, characterized in that, The objective function of the multi-stage decision-making process is to minimize the average travel time stage by stage. In the (s+1)th stage, the objective function can be expressed as: 。 7. The trajectory optimization model based on a fleet of vehicles according to claim 3, characterized in that, The constraints of the multi-stage decision-making process include speed limit constraints, cruise speed limit constraints, and safe distance maintenance constraints.

8. A method for optimizing convoy trajectories at signalized intersections, characterized in that, The signalized intersection platoon formation trajectory optimization method uses the platoon-based trajectory optimization model as described in any one of claims 1-7, and includes the following steps: S1: Fleet Detection: Activated when the convoy leader vehicle enters the control range. The control range is the initially determined range. If the range is too short, it will not provide enough space for the vehicle to change its state according to the control command, while if it is too long, it may cause a waste of time and space resources. S2: Congestion Determination: Based on the following prediction: the current speed of the formation will be blocked by downstream vehicles or signal control, and the prediction should satisfy any of the following formulas: ； ； In the formula, x' is the current position of the nearest downstream vehicle; t is the initial speed of the first vehicle; t is the travel time of the vehicle leaving the intersection, which can be obtained from the downstream convoy by the system control; TTR is the red light countdown time when the convoy enters the control range. This value is negative, and its absolute value is equal to the duration after the red light is on. If the traffic light is red at this moment; if congestion is confirmed, the control logic will switch to the trajectory optimization model to optimize the convoy trajectory; otherwise, the control logic will jump to the unused component, i.e., state tracking. S3: State Tracking: If no congestion occurs or the trajectory optimization is completed, the system will continuously track the fleet status to detect whether the state constraints are violated; if a violation is found, the control logic will backtrack to the congestion determination and re-execute the subsequent steps until the fleet has completely left the intersection.

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