Path planning method for racing game of multiple unmanned vehicles

Abstract

The invention discloses a path planning method for a racing game of multiple unmanned vehicles, and relates to the technical field of path planning. The method has the beneficial effects that the speed and defensive performance of the vehicle are optimized under the winner eating rule, and the racing problem of the racing vehicle is modeled and analyzed by introducing the Nash-Stackelberg nested game theory framework; meanwhile, possible trajectories of opponents are calculated through an interactive enhanced iterative optimal response algorithm, so that the optimal trajectory of the opponents is determined, and finally an approximate Nash equilibrium solution in a competitive environment is found. When the vehicle is in the defense stage, the curvature of the racing track and the distance between the vehicle and the hostile vehicle must be considered to calculate the self-adaptive blocking weight, so that the balance between the blocking effect and the competition progress is realized, and finally, in the simulation experiment environment, compared with a traditional game theory algorithm or a many-for-one game theory algorithm, the method has certain advantages, and the method is suitable for popularization and application. And the defense vehicle can obtain final wins in most cases.

Description

Technical Field

[0001] The present invention relates to the technical field of path planning, and in particular to a path planning method for a multi-unmanned vehicle racing game. Background Art

[0002] Autonomous driving has made significant progress in both academia and industry. Most previous research has focused on scenarios and control mechanisms in urban environments, including daily driving on streets and highways. However, autonomous racing has both similarities and differences compared to urban environments. In autonomous racing, the focus is still on four-wheeled vehicles, and the main goal is to reach the finish line as quickly as possible. Although the topics and problem descriptions in racing may have some overlap with urban environments, racing emphasizes interactive behaviors between participants, similar to those in daily urban driving.

[0003] Since the introduction of the DARPA Urban Challenge, the problem of safe path planning on public roads in close proximity with unpredictable vehicles has been well addressed. In racing, vehicles must consider their own safety while driving at high speeds, which poses a significant challenge to safety. Previous work on autonomous racing has generally ignored collision avoidance entirely, or has only considered avoiding static obstacles. Although racing is more structured than city driving - with designated tracks and simpler rules (no lane markings or crosswalks), racing is more competitive and aggressive, with all vehicles typically moving towards the same goal. Despite the safety-based rules, collisions still occur relatively frequently in real racing, a split-second decision error by a driver or team can lead to an accident, and the core motivation of racing games is to explore the limits of performance, and some games even require teamwork and competition. Summary of the invention

[0004] The purpose of the present invention is to provide a path planning method for multi-unmanned vehicle racing game in view of the shortcomings and defects in the prior art, optimize the speed and defense performance of the vehicle under the winner-takes-all rule, introduce the Nash-Stackberg nested game theory framework to model and analyze the racing problem, and use an interactively enhanced iterative best response algorithm to calculate the opponent's possible trajectory to determine its own optimal trajectory, and finally find the approximate Nash equilibrium solution in the competitive environment. When the vehicle is in the defensive stage, the curvature of the track and the distance from the hostile vehicle must be considered to calculate the adaptive blocking weight, so as to achieve a balance between the blocking effect and the progress of the game. Finally, in the simulation experimental environment, this method has certain advantages over the traditional game theory algorithm or the many-to-one game theory algorithm, and in most cases the defensive vehicle can obtain the final victory.

[0005] To achieve the above purpose, the present invention adopts the following technical solution: it includes a vehicle kinematics model, a track model and a Nash-Stackelberg nested game model: the vehicle kinematics model is specifically: the dynamic equation of the unmanned vehicle is modeled as: The vehicle state X is determined by its vehicle position and vehicle speed Definition, the acceleration of the vehicle As the input U of the system, Indicates the discretization fixed time step, the bracket k in the upper right corner is {1,…,H p} represents each discrete moment, H p Represents a limited range of discrete moments; in the vehicle kinematic model, the maximum lateral and longitudinal accelerations of the tire are related to the speed, and this relationship is summarized as a mapping relationship between two semi-ellipses: Convert it to linear constraints that satisfy quadratic programming:

[0007]

[0008] The track model specifically uses a discrete track model: a discrete track model is characterized by the existence of a centerline reference trajectory C:[0,S]→T, where Indicates the effective range of the track area. Represents the length of the center line; contains the normal vector n of each discrete point i and the tangent vector f i , and set the track width to a fixed size The anti-collision constraints of the track can be set by solving the component of the vehicle position in the direction of the normal vector at each discrete point, as shown below: Through the defensive blocking behavior of the team multi-unmanned vehicle racing game, the behavior state of the defensive vehicle can be divided into the blocking competition state and the free driving state; a Nash-Stackelberg nested game model, which includes the internal Stackelberg game and the external Nash game. For the competitive behavior between teams, the concept of Nash game is adopted, and the Stackelberg game is used within the team. At the same time, the external Nash game and hierarchical blocking strategy can block the enemy leader as efficiently as possible; in the same team, vehicles can naturally be sorted according to their progress on the track:

[0009] Assume there are three vehicles in the first team and two vehicles in the second team. At this time, they can be sorted according to the progress as P 1,R ,P 2,R and P 1,B ,P 2,B ,P 3,BIn addition, there will be a Nash game between the competing teams. The defending vehicle will play the Nash game with the matching enemy vehicle through an activation function. They will enter the competitive game behavior of overtaking / blocking. The activation function is defined as: The activation function determines the state of each vehicle at any time. Each ordered defense vehicle has its own defense range based on the order. If any pair of vehicles wants to completely surpass the vehicles of the other team, they need to break through layer by layer. The vehicles in each defense layer will give priority to the vehicles of the other team that are at the front of the layer, thereby blocking the leader of the other team in layers, while maximizing the protection of the leading position of the leader of the team as much as possible. By establishing sequential quadratic programming and using model predictive control to solve the local trajectory generation and tracking problems, there is the following quadratic programming problem for any vehicle: in, represents the blocking component of the vehicle to the enemy vehicle, α ij Denotes the blocking weight, and describes the blocking weight as a Gaussian distribution function related to the track curvature and the distance between vehicles:

[0010] Furthermore, the blocking competition state and free driving state are as follows: when the vehicle is in the free driving state, the vehicle will focus on moving forward and avoid collision with other vehicles. When the vehicle is in the blocking state, the enemy vehicle enters its perception range, and the vehicle's main goal is to block the enemy vehicle from overtaking.

[0011] Furthermore, the Nash game is specifically as follows: for the competitive behavior between teams, the concept of Nash game is adopted. In the Nash game, neither party has more information advantage than the opponent. Specifically, the vehicle cannot obtain the planned trajectory of the competing vehicle through the communication network.

[0012] Furthermore, the use of Stackelberg game is specifically: using Stackelberg game within the team, the leader's benefits do not depend on the actions of the followers. In a team, team members are ranked according to their progress, and the leading vehicle chooses the best driving trajectory without considering the rear team members, and then transmits the trajectory to the rear members through communication. The following vehicles will choose their own best response accordingly, and such behavioral decisions can be continued from the front vehicle to the rear vehicle.

[0013] After adopting the above technical solution, the beneficial effects of the present invention are as follows: the speed and defense performance of the vehicle are optimized under the winner-takes-all rule, the racing problem is modeled and analyzed by introducing the Nash-Stackberg nested game theory framework, and the possible trajectory of the opponent is calculated by an interactively enhanced iterative best response algorithm to determine the best trajectory of the opponent, and finally find the approximate Nash equilibrium solution in the competitive environment. When the vehicle is in the defensive stage, the curvature of the track and the distance from the hostile vehicle must be considered to calculate the adaptive blocking weight, so as to achieve a balance between the blocking effect and the progress of the game. Finally, in the simulation experimental environment, this method has certain advantages over the traditional game theory algorithm or the many-to-one game theory algorithm, and in most cases the defensive vehicle can obtain the final victory. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0015] Figure 1 It is a schematic diagram of the track model in the present invention.

[0016] Figure 2 It is a schematic diagram of vehicle state conversion in the present invention.

[0017] Figure 3 It is a Nash-Stackberg game framework diagram in the present invention.

[0018] Figure 4 It is a progress sorting diagram in the present invention.

[0019] Figure 5 It is a schematic diagram of a simulation scene snapshot in the present invention.

[0020] Figure 6 It is a statistical chart of the winning rate of the defensive vehicle in the present invention.

[0021] Figure 7 It is a schematic diagram of the average lead distance of the many-to-one game theory planning algorithm in the present invention.

[0022] Figure 8 Schematic diagram of the average lead distance of the present invention. (The dots represent the average lead distance, and the vertical bars represent the corresponding variance). DETAILED DESCRIPTION

[0023] The technical solution adopted in this specific implementation is: it includes a vehicle kinematics model, a track model and a Nash-Stackelberg nested game model:

[0024] 1) The vehicle kinematic model is as follows: The dynamic equation of the unmanned vehicle is modeled as:

[0025]

[0026] The vehicle state X is determined by its vehicle position and vehicle speed Definition, the acceleration of the vehicle As the input U of the system, Indicates the discretization fixed time step, the bracket k in the upper right corner is {1,…,H p} represents each discrete moment, H p Represents a finite range of discrete moments;

[0027] In the vehicle kinematic model, the maximum lateral and longitudinal acceleration of the tire is related to the speed, and this relationship is summarized as the mapping relationship of two semi-ellipses:

[0028]

[0029] Convert it to linear constraints that satisfy quadratic programming:

[0030]

[0031] 2) The track model specifically uses a discrete track model:

[0032] A discrete track model is characterized by the existence of a centerline reference trajectory C:[0,S]→T, where Indicates the effective range of the track area. Indicates the length of the center line; see Figure 1 shown.

[0033] Contains the normal vector n for each discrete point i and the tangent vector f i , and set the track width to a fixed size The anti-collision constraints of the track can be set by solving the component of the vehicle position in the direction of the normal vector at each discrete point, as shown below:

[0034]

[0035] Through the defensive blocking behavior of the team multi-unmanned vehicle racing game, the behavior state of the defensive vehicle can be divided into the blocking competition state and the free driving state. When the vehicle is in the free driving state, the vehicle will focus on moving forward and avoid collision with other vehicles. When the vehicle is in the blocking state, the enemy vehicle enters its own perception range, and the vehicle's main goal is to block the enemy vehicle from overtaking. Figure 2 shown.

[0036] 3) See Figure 3 As shown in the figure, a Nash-Stackelberg nested game model includes internal Stackelberg games and external Nash games. For the competitive behavior between teams, the concept of Nash game is adopted. In the Nash game, neither party has more information advantage than the opponent. Specifically, the vehicle cannot obtain the planned trajectory of the competing vehicle through the communication network. Within the team, the vehicles will naturally be sorted according to the progress on the track. There are leaders and followers, and the teams can transmit their respective planned trajectories through the communication network. Under the winner-takes-all rule, the competition between the teams can be summarized as a zero-sum game between the team leaders. The use of Stackelberg game within the team can protect the leading position of the team leader as much as possible. At the same time, the external Nash game and layered blocking strategy can block the enemy leader as efficiently as possible.

[0037] In the same team, cars can naturally be sorted according to their progress on the track:

[0038]

[0039] See also Figure 4 As shown, assuming there are three vehicles in the first team and two vehicles in the second team, they can be sorted according to the progress as P 1,R ,P 2,R and P 1,B ,P 2,B ,P 3,B .

[0040] Using Stackelberg game within the team, the leader's payoff does not depend on the actions of the followers. Within a team, team members are ranked according to their progress. The leading vehicle chooses the best driving trajectory without considering the team members behind it, and then communicates the trajectory to the rear members. The following vehicles will choose their own best response based on this. This behavior decision can be continued from the front vehicle to the rear vehicle.

[0041] In addition, there will be a Nash game between the competing teams. The defending vehicle will play the Nash game with the matching enemy vehicle through an activation function. They will enter the competitive game behavior of overtaking / blocking. The activation function is defined as:

[0042]

[0043] The activation function determines the state of each vehicle at any time, and each ordered defense vehicle has its own order-based defense range. If any pair of vehicles wants to completely surpass the other team's vehicles, they need to break through layer by layer. The vehicles in each defense layer will give priority to the other team's vehicle that is at the front of the layer, thereby blocking the leader of the other team in layers, while maximizing the protection of the leader's leading position as much as possible.

[0044] By establishing sequential quadratic programming and using model predictive control to solve the local trajectory generation and tracking problem, for any vehicle, there is the following quadratic programming problem:

[0045]

[0046] in, represents the blocking component of the vehicle to the enemy vehicle, α ij Denotes the blocking weight, and describes the blocking weight as a Gaussian distribution function related to the track curvature and the distance between vehicles:

[0047]

[0048] The following are the relevant experiments and verifications of the present invention

[0049] Solve the quadratic programming problem through a finite number of iterations to approximate the original problem and obtain a local approximate optimal solution. Figure 5 As shown in the figure, the simulation demonstrates how a team of defensive vehicles can complete the game and win through reasonable layered blocking.

[0050] In addition, the proposed method is compared with many-to-one game theory planning methods and traditional free-race MPC methods. Figure 6As shown in the figure, by repeating the simulation experiment 100 times, under the same maximum speed, the average winning rate of the first team using our method and the traditional unblocked MPC algorithm is 100%. This is because under the same maximum speed, the vehicles are homogeneous. Without external interference, the rear vehicle cannot surpass the front vehicle. In contrast, the many-to-one game theory planning algorithm focuses on a single opponent, causing the team's attention to be focused on one vehicle, which will allow the other second team vehicle to slip away and finish the race first, resulting in the failure of the first team. In addition, under different maximum speeds, this method still achieves the highest average winning rate among the three methods. As the speed gap increases, the average winning rate of this method decreases the least.

[0051] The progress gap between the vehicles at the end of the race is also compared. Figure 7 and 8 As shown in the figure, the lead distance of the first vehicle to finish the race is 0, and the lead distances of other vehicles are negative. The dots represent the average lead distance, and the vertical bars represent the corresponding variance. Figure 7 In the figure, it shows the leading distance when a team of vehicles chooses the many-to-one game theory planning algorithm. The defending team of vehicles only chooses one team of vehicles as the blocking target, which is R2, which is initially in the front. This allows R1 to surpass all the vehicles in front and finish the race first, resulting in R1's average leading distance being close to 0 and having a small variance, while R2 and the other team of vehicles have a closer average leading distance and a larger equation.

[0052] And in Figure 8 In the example, the proposed method can better enable the defending team of vehicles to block the second team of vehicles in layers, so as to keep the leading position of the leader of the team as much as possible. The average leading distance from B1 to B3 gradually increases, while the variance gradually decreases, which is consistent with the initial progress sorting (B3>B2>B1). The average leading distance of B3 is closest to 0, indicating that in most cases, this method can enable the slower defending team of vehicles to win the game through the layered blocking method. From the comparative experiment, it can be seen that the lagging team of vehicles prioritizes the second team of vehicles as the blocking target, thereby sacrificing its own progress to protect the advantage of the leading team of vehicles. This layered blocking strategy effectively enables the weaker vehicles to outperform their opponents in heterogeneous vehicle competitions.

[0053] The above description is only used to illustrate the technical solution of the present invention rather than to limit it. Other modifications or equivalent substitutions made to the technical solution of the present invention by ordinary technicians in this field should be included in the scope of the claims of the present invention as long as they do not depart from the spirit and scope of the technical solution of the present invention.

Claims

1. A path planning method for a multi-unmanned vehicle racing game, characterized by: It includes a vehicle kinematics model, a track model, and a Nash-Stackelberg nested game model: 1) The vehicle kinematic model is as follows: The dynamic equation of the unmanned vehicle is modeled as: The state X of the vehicle is given by its vehicle position p = (p x ,p y ) T and vehicle speed v = (v x ,v y ) T Definition: The acceleration of the vehicle is a = (a x ,a y ) T As the input U of the system, Indicates the discretization fixed time step, the bracket k in the upper right corner is {1,…,H p } represents each discrete moment, H p Represents a finite range of discrete moments; In the vehicle kinematic model, the maximum lateral and longitudinal acceleration of the tire is related to the speed, and this relationship is summarized as the mapping relationship of two semi-ellipses: Convert it to linear constraints that satisfy quadratic programming: 2) The track model specifically uses a discrete track model: A discrete track model is characterized by the existence of a centerline reference trajectory C:[0,S]→T, where Indicates the effective range of the track area. Indicates the length of the center line; Contains the normal vector n for each discrete point i and the tangent vector f i , and set the track width to a fixed size The anti-collision constraints of the track can be set by solving the component of the vehicle position in the direction of the normal vector at each discrete point, as shown below: Through the defensive blocking behavior of the team-based multi-unmanned vehicle racing game, the behavior state of the defensive vehicle can be divided into the blocking competition state and the free driving state; 3) A Nash-Stackelberg nested game model, which includes an internal Stackelberg game and an external Nash game. For the competitive behavior between teams, the concept of Nash game is adopted. Stackelberg game is used within the team, while the external Nash game and hierarchical blocking strategy can block the enemy leader as efficiently as possible; In the same team, cars can naturally be sorted according to their progress on the track: Among them, three vehicles in the first team and two vehicles in the second team can be sorted into P according to the progress. 1,R ,P 2,R and P 1,B ,P 2,B ,P 3,B In addition, there will be a Nash game between the competing teams. The defending vehicle will play the Nash game with the matching enemy vehicle through an activation function. They will enter the competitive game behavior of overtaking / blocking. The activation function is defined as: The activation function determines the state of each vehicle at any time. Each ordered defense vehicle has its own defense range based on the order. If any pair of vehicles want to completely surpass the vehicles of the other team, they need to break through layer by layer. The vehicles in each defense layer will give priority to the frontmost vehicle of the other team in that layer, thereby blocking the leader of the other team in layers, while maximizing the protection of the leading position of the leader of the own team as much as possible. By establishing sequential quadratic programming and using model predictive control to solve the local trajectory generation and tracking problem, for any vehicle, there is the following quadratic programming problem: in, represents the blocking component of the vehicle to the enemy vehicle, α ij Denotes the blocking weight, and describes the blocking weight as a Gaussian distribution function related to the track curvature and the distance between vehicles:

2. A path planning method for a multi-unmanned vehicle racing game according to claim 1, characterized in that: The blocking competition state and free driving state are specifically as follows: when the vehicle is in the free driving state, the vehicle will focus on moving forward and avoid collision with other vehicles, and when the vehicle is in the blocking state, the enemy vehicle enters its own perception range, and the vehicle's main goal is to block the enemy vehicle from overtaking.

3. A path planning method for a multi-unmanned vehicle racing game according to claim 1, characterized in that: The Nash game is specifically as follows: for the competitive behavior between teams, the concept of Nash game is adopted. In the Nash game, neither party has more information advantage than the opponent. Specifically, the vehicle cannot obtain the planned trajectory of the competing vehicle through the communication network.

4. The path planning method for a multi-unmanned vehicle racing game according to claim 1, characterized in that: The use of Stackelberg game is specifically as follows: Stackelberg game is used within the team, the leader's benefits do not depend on the actions of the followers. Within a team, team members are ranked according to their progress, and the leading vehicle chooses the best driving trajectory without considering the rear team members, and then transmits the trajectory to the rear members through communication. The subsequent vehicles will choose their own best response accordingly, and such behavioral decisions can be continued from the head vehicle to the tail vehicle.

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