CN115230706B

CN115230706B - Multi-vehicle collaborative lane change decision and control method based on game

Info

Publication number: CN115230706B
Application number: CN202210914698.2A
Authority: CN
Inventors: 林程; 汪博文; 吕沛原; 田雨; 梁晟
Original assignee: Beijing Institute of Technology BIT
Current assignee: Beijing Institute of Technology BIT
Priority date: 2022-08-01
Filing date: 2022-08-01
Publication date: 2024-06-14
Anticipated expiration: 2042-08-01
Also published as: CN115230706A

Abstract

The invention discloses a multi-vehicle collaborative lane change decision-making and control method based on a game, which comprises the steps of obtaining the state of each vehicle under a certain prediction domain based on a vehicle kinematic model, wherein the state comprises the speed, the acceleration, the steering angle and the position of the vehicle; based on the positions of the vehicles, obtaining interaction logic parameters between each vehicle; based on the speed, acceleration and interaction logic parameters of each vehicle, respectively obtaining an efficiency coefficient, a comfort coefficient and a safety coefficient of each vehicle, and constructing a vehicle game optimization function; based on the vehicle game optimization function, constructing a constraint equation by taking the minimum cost of the overall game function of all vehicles as a target, and obtaining a Nash equilibrium result of each vehicle; acquiring a planning path of each vehicle based on Nash equilibrium results and a vehicle kinematic model; tracking the planned path of each vehicle, establishing a path tracking optimization objective function, and obtaining the acceleration and steering angle of each vehicle; the invention realizes the multi-vehicle cooperative motion control which takes the driving requirements in multiple aspects into consideration.

Description

Multi-vehicle collaborative lane change decision and control method based on game

Technical Field

The invention relates to the technical field of intelligent transportation, in particular to a multi-vehicle collaborative lane change decision and control method based on game.

Background

Traffic accidents are often caused by irregular lane changes, especially when multiple vehicles must change lanes simultaneously or continuously (e.g., exit ramps), the risk of traffic accidents increases exponentially. Therefore, the establishment of the multi-vehicle collaborative lane change motion planning method, the reasonable organization of multi-vehicle lane change in a complex scene, is one of important technologies for ensuring the safety of automatic driving and reducing traffic jam in the future. In recent years, various solutions are adopted to solve the lane change decision problem, and the existing lane change decision and control methods include: three methods, rule-based, optimization-based, and learning-based. The method based on the rules is difficult to describe complex movement of multiple vehicles by using simple rules under difficult driving scenes (such as annular intersections, multiple vehicle road sections and the like), the control strategy under the rule judgment is easy to generate a frequently switched decision instruction, and the multiple vehicles are difficult to carry out high-efficiency cooperative control; the optimization-based method depends on the accuracy of the model and the solving mode and speed of the optimization problem, so that the method has higher requirements on the controller, and meanwhile, when the number of the controlled vehicles is increased, the complexity of the vehicle interaction model is gradually increased, and the calculation efficiency is seriously influenced; the learning-based method such as reinforcement learning and the like obtains a corresponding control strategy through offline or online training of a data set, can be well applied to bicycle intelligence under some complex scenes, has poor interpretation of calculation results, and the quality of performance depends on the quality of the data set and an algorithm. The game method also belongs to a special optimization method, combines the ideas of optimization and learning, expresses the demands of all aspects in the form of benefits, seeks the benefit maximization of all parties, and has the defect of high computational complexity when the number of game parties is gradually increased.

The invention patent with publication number CN111267846A discloses a game theory-based peripheral vehicle interactive behavior prediction method, and establishes a running benefit evaluation function to calculate benefits of the movement of a self-vehicle and the peripheral vehicle under different driving behaviors, and predicts the movement track of the vehicle in a future time period to predict the interactive behavior, so that the self-vehicle is safer and more reliable in decision planning.

The invention patent with publication number CN113920740A discloses a vehicle-road collaborative driving system and method combining the association degree of vehicles and a game theory, which screens vehicles with high association degree with vehicle lane changing, avoids other irrelevant vehicles from participating in collaborative driving calculation to increase the calculation complexity, and ensures that the speed and the safety benefit among the vehicles are highest by a multi-vehicle game method.

The invention patent with publication number CN110390839A discloses a vehicle lane changing method considering the overlapping area of a multi-vehicle interaction area, which defines the overlapping area between vehicles to judge whether lane changing is performed.

In the above patent, the vehicle interaction problem in the game process is well considered, but when a plurality of vehicles need to make collaborative decisions, the aspects of interaction target screening, future state prediction and the like need to be comprehensively considered, and meanwhile, the optimal decision quantity of each vehicle needs to be calculated. Based on the scheme, the collaborative lane change decision and control method for the multi-car game is provided.

Disclosure of Invention

Aiming at the defects existing in the problems, the invention provides a multi-car collaborative lane change decision and control method based on game.

In order to achieve the above purpose, the present invention provides a multi-car collaborative lane change decision and control method based on game, comprising:

Acquiring a state of each vehicle under a certain prediction domain based on a vehicle kinematic model, wherein the state comprises the speed, acceleration, steering angle and position of the vehicle;

based on the positions of the vehicles, obtaining interaction logic parameters between each vehicle;

Based on the speed, acceleration and interaction logic parameters of each vehicle, respectively obtaining an efficiency coefficient, a comfort coefficient and a safety coefficient of each vehicle;

Constructing a vehicle game optimization function based on the comfort coefficient, the efficiency coefficient and the safety coefficient of the vehicle;

based on the vehicle game optimization function, constructing a constraint equation with the minimum cost of the overall game function of all vehicles as a target, and obtaining a Nash equilibrium result of each vehicle;

acquiring a planning path of each vehicle based on the Nash equilibrium result and the vehicle kinematic model;

And tracking the planned path of each vehicle, and establishing a path tracking optimization objective function to obtain the acceleration and the steering angle of each vehicle.

Preferably, the vehicle kinematic model is:

Wherein: k|t is the kth predicted state at time t; is a course angle; x _i is a lateral displacement; y _i is longitudinal displacement; l _f,i and l _r,i are the distances of the centroid to the anterior and posterior axes, respectively; delta _f,i is the vehicle steering angle, a _i is the vehicle acceleration; v _i is vehicle speed; t represents a time step.

Preferably, based on the position of the vehicle, obtaining the interaction logic parameter between each vehicle includes:

defining a buffer area between lanes;

obtaining the position of the vehicle according to the lateral displacement predicted by the vehicle kinematic model;

through the interactive logic formula, the method comprises the following steps:

Wherein: lambda _ij and lambda _ji are interaction logic parameters of the vehicle i and the vehicle j in the prediction domain respectively; d _s is the relative safe distance between any two vehicles; sigma is a location identification parameter of the vehicle.

Preferably, based on the speed, acceleration and interaction logic parameters of each vehicle, respectively obtaining the efficiency coefficient, the comfort coefficient and the safety coefficient of each vehicle includes:

The safety coefficient The formula is:

The comfort coefficient The formula is:

The efficiency coefficient The formula is:

Wherein: s _i and s _j are the longitudinal displacements of vehicle i and vehicle j, respectively; Is the desired speed of the vehicle; Δa _i is the acceleration delta of the vehicle.

Preferably, the vehicle game optimization function J _i is:

Wherein: q ₁、Q₂、Q₃ is a weight matrix.

Preferably, the constraint equation is:

Wherein: a _min、a_max is a control quantity constraint;

Solving the constraint equation to obtain a Nash equilibrium result of each vehicle;

Wherein: and (3) a Nash equilibrium result predicted by the kth step of the vehicle i at the t moment.

Preferably, based on the nash equalization result and the vehicle kinematic model, each vehicle planning path is obtained by applying the nash equalization result to the vehicle kinematic model and planning by adopting a method of five-order polynomial interpolation, and the method comprises the following steps:

Firstly, calculating interpolation points in four sections, wherein the formula is as follows:

Wherein: x _ref,i、Y_ref,i is the abscissa and ordinate vectors of the vehicle i at the time t respectively;

interpolation point fitting based on the formula to obtain a fifth order polynomial The method comprises the following steps:

wherein: p ₁～p₅ is the fitting coefficient of the fifth order polynomial.

Preferably, the path tracking optimization objective function is:

Wherein: c= [0, 1]; c _R = [0,1] is the parameter extraction matrix; Δu _min and Δu _max are control increment constraints; u _min and u _max are control quantity constraints; q _c,R_a,R_δ,R_Δ is a weight matrix; u _i ^t is the optimal control amount obtained; ζ _i、u_i is the state vector and the control vector of the vehicle i in the prediction domain, respectively.

Preferably, the state vector and the control vector of the vehicle i under the prediction domain include:

Based on the vehicle kinematic model, the nominal state quantity and the control quantity of the vehicle are obtained, and the formula is as follows:

Wherein: The method comprises the steps of respectively obtaining a k-th nominal state quantity and a control quantity of a vehicle i at a time t; g is a vehicle kinematic model; initial nominal state quantity is/> Initial control amount is To adopt the calculated control quantity/>, at the previous momentLet/>, when k=n

Linearizing the vehicle kinematic model by using a taylor expansion to obtain a time-varying state matrix A _ctrl,i and a control matrix B _ctrl,i, wherein the formula is as follows:

Obtaining the time-varying state matrix A _ctrl,i and the control matrix B _ctrl,i based on linearization to obtain a linear discretized state increment, wherein the formula is as follows:

Wherein: to control the increment; /(I) Is an incremental discrete state matrix, wherein I is an identity matrix; /(I)Is an incremental discrete control matrix; Δζ _i is the k+1st step state increment of vehicle i at time t;

The state quantity ζ _i and the control quantity u _i of the k+1st step state of the vehicle i at the time t are:

compared with the prior art, the invention has the beneficial effects that:

according to the invention, interactive prediction is creatively embedded in the constructed game framework to evaluate lane change safety, an optimal scheme for avoiding potential collision of vehicles in a cooperative control area is provided, and the computational complexity of a multi-vehicle interactive model is reduced; in addition, the constructed multi-vehicle collaborative lane change game theory problem is solved through a time-varying model prediction algorithm, a multi-vehicle optimal action decision in a prediction domain is given, and multi-vehicle collaborative motion control considering various driving requirements is realized.

Drawings

FIG. 1 is a flow chart of a multi-car collaborative lane change decision and control method based on gaming of the present invention;

FIG. 2 is a diagram of a multi-car collaborative lane change decision and control framework based on gaming in accordance with the present invention;

fig. 3 is a diagram illustrating a three-lane scene in the present invention.

Detailed Description

For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.

The invention is described in further detail below with reference to fig. 1:

the invention provides a multi-vehicle collaborative lane change decision and control method based on game, which comprises the following steps:

based on a vehicle kinematic model, acquiring a state of each vehicle under a certain prediction domain, wherein the state comprises the speed, the acceleration, the steering angle and the position of the vehicle;

specifically, the vehicle kinematic model is:

specifically, a buffer area between lanes is defined;

Based on the speed, acceleration and interaction logic parameters of each vehicle, respectively acquiring an efficiency coefficient, a comfort coefficient and a safety coefficient of each vehicle;

In particular, the safety factor The formula is:

comfort coefficient The formula is:

Efficiency coefficient The formula is:

specifically, the vehicle game optimization function J _i is:

Wherein: q ₁、Q₂、Q₃ is a weight matrix.

Based on the vehicle game optimization function, constructing a constraint equation by taking the minimum cost of the overall game function of all vehicles as a target, and obtaining a Nash equilibrium result of each vehicle;

Specifically, the constraint equation is:

Wherein: a _min、a_max is a control quantity constraint;

Solving a constraint equation to obtain a Nash equilibrium result of each vehicle;

Acquiring a planning path of each vehicle based on Nash equilibrium results and a vehicle kinematic model;

Specifically, the Nash equilibrium result is applied to a vehicle kinematic model, and a vehicle planning path is planned by adopting a method of five-degree polynomial interpolation, comprising the following steps:

wherein: p ₁～p₅ is the fitting coefficient of the fifth order polynomial.

And tracking the planned path of each vehicle, and establishing a path tracking optimization objective function to obtain the acceleration and steering angle of each vehicle.

Specifically, the path tracking optimization objective function is:

Further, the state vector and the control vector of the vehicle i under the prediction domain include:

based on a vehicle kinematic model, a vehicle nominal state quantity and a control quantity are obtained, wherein the formula is as follows:

Linearizing the vehicle kinematic model by using a taylor expansion to obtain a time-varying state matrix A _ctr l, i and a control matrix B _ctrl_,i, wherein the formula is as follows:

Based on the obtained time-varying state matrix a _ctrl_,i and control matrix B _ctrl_,i, a linear discretized state increment is obtained, with the formula:

Referring to fig. 2, the present invention constructs a three-layer hierarchical decision control architecture, wherein the upper layer is a vehicle interaction layer, the middle layer is a game decision layer, and the lower layer is a planning control layer; and (3) calculating and optimizing a certain target parameter in different sub-control layers in a key way, and realizing balance among targets through mutual progressive between layers, so that the cooperative control effect capable of considering the requirements of multiple vehicles in multiple aspects is finally achieved. The vehicle interaction layer firstly determines a lane area where the vehicle is located, screens vehicles needing interaction through the position where the vehicle is located, and calculates to obtain interaction logic values between the controlled vehicle and other vehicles. The game decision layer establishes an evaluation function comprehensively considering three performances of safety, comfort and efficiency of the vehicle based on the information obtained by the vehicle interaction layer, and calculates and gives out an optimal Nash equilibrium decision value of each vehicle in a section of prediction domain through a time-varying model prediction algorithm, namely the expected acceleration of each vehicle. The planning control layer firstly generates a safe and continuous reference track based on an expected lane, adopts a multi-input multi-output linear time-varying model to predict and control, constructs an integral objective function, simultaneously tracks a planning path and a decision result, calculates and obtains a front wheel corner and control acceleration of bottom control, and finally realizes the motion process of multi-vehicle collaborative lane change.

In the present embodiment, the vehicle interaction layer: the vehicle interaction layer obtains the optimal interaction target of the own vehicle by means of mutual communication of relative position information among vehicles, and the output value is the interaction logic value of the own vehicle and the other vehicles.

Specifically, first, the buffer area width W _buffer between lanes is determined, and this width area between lanes is defined as B, as shown in fig. 3, giving an example of a three-lane scene.

W_buffer＝W_lane-W_veh；

Wherein: w _lane is the lane width; w _veh is the vehicle width.

The states of all vehicles under a certain prediction domain N are predicted based on a vehicle kinematic model. For example, for vehicle i, its vehicle state at the kth+1 step prediction is as follows:

And obtaining the position identification parameter of the vehicle according to the predicted transverse position. For vehicle i, the location identification parameter is σ _i = { lane 1, lane 2, l, buffer area B };

The interaction logic parameters lambda _ij and lambda _ji for vehicle i and vehicle j in the N-step prediction domain are calculated. When two vehicles are in the same lane or one vehicle is in the corresponding buffer area, if the relative distance is relatively close, the logic value is 1. The interaction logic parameters at the kth step at time t are expressed as follows:

Game decision layer: comprehensively considering safety, comfort and efficiency of the vehicle, constructing game problems and calculating to obtain Nash equilibrium solutions through a time-varying predictive control algorithm.

Specifically, the logic parameters are interacted, and the driving safety coefficient of each vehicle in the system is calculated. For example, for vehicle i, driving safety factorThe method comprises the following steps:

Where s _i and s _j represent the longitudinal displacement of vehicle i and vehicle j, respectively.

The efficiency coefficient of each vehicle is calculated. For example for vehicle i, efficiency coefficientThe method comprises the following steps:

In the middle of Indicating a desired speed of the vehicle.

A ride comfort factor is calculated for each vehicle within the system. For example for vehicle i, riding comfort factorThe method comprises the following steps:

Where Δa _i represents the acceleration increase of the vehicle.

And comprehensively considering the safety, comfort and efficiency of the vehicle, and constructing a vehicle game optimization function. For example, when the current time is t, for the vehicle i, the game optimization function J _i is as follows:

Wherein Q ₁,Q₂,Q₃ is a weight matrix;

Based on game optimization functions, the finite time domain constraint optimization problem of N vehicles under the N-step prediction domain is constructed in a centralized mode:

Wherein a _min、a_max represents a control amount constraint;

solving the optimization problem to obtain Nash equilibrium of each vehicle. Wherein for vehicle i is denoted:

In the middle of The nash equalization result of the kth step prediction of the vehicle i at the time t is shown.

Planning a control layer: based on Nash equilibrium reference values obtained by the decision layer, the planning control layer firstly generates a continuous feasible reference track, a linear time-varying model prediction controller is adopted to track the reference track and the Nash equilibrium values, and the expected control acceleration and steering angle of each vehicle are respectively calculated.

Specifically, a method based on quintic polynomial interpolation is adopted to plan and obtain a vehicle expected running path. Interpolation points are calculated first in four segments. For example, for vehicle i at time t, abscissa vector X _ref,i and ordinate vector Y _ref,i are obtained as follows:

In the middle of Obtained by the process of the calculation step of the vehicle kinematic model, Y _ref,i is the transverse offset of the center line of the expected lane,The transverse offset of the vehicle i at the moment t;

interpolation point fitting based on the formula to obtain a fifth order polynomial The following are listed below

Wherein p ₁：p₅ is a fitting coefficient of a fifth-order polynomial;

The nominal state quantity and the control quantity are calculated based on the vehicle kinematic model. For example, for vehicle i, at time t, the kth step is the nominal state quantity And control amountExpressed as:

Wherein g represents a vehicle kinematic model, and the initial nominal state quantity is The initial nominal control quantity is, The control quantity calculated at the previous moment is adoptedLet/>, when k=n

And linearizing the time-varying vehicle kinematic model function by using a Taylor expansion to obtain a time-varying state matrix and a control matrix. For example, for vehicle i, time-varying state matrix A _ctrl,i and control matrix B _ctrl,i are represented as:

A linear discretized representation of the state increment is obtained based on the above formula. For example, for vehicle i, the k+1st step state increment Δζ _i at time t is denoted as:

In the middle of To control the increment,In the form of an incremental discrete state matrix,Is an incremental discrete control matrix.

Based on the above formula, the vehicle state vector and the control vector in the N-step prediction domain are predicted and estimated. For example, for vehicle i, the (k+1) th step state vector ζ _i and control vector u _i at time t are as follows

The problem of tracking the calculated expected track is converted into a constraint optimization problem psi of an N-step prediction domain. For example, for vehicle i, construct ψ as follows:

Where c= [0,1], C _R = [0,1] represent parameter extraction matrices, Δu _min and Δu _max represent control increment constraints, u _min and u _max represent control quantity constraints, and Q _c,R_a,R_δ,R_Δ is a weight matrix. To obtain the optimal control vector. /(I)

Solving the optimization problem psi to obtain an optimal control vector, and applying the optimal control vector to the vehicle.

The invention is different from the existing lane change decision control method only considering the vehicle control and the current state, constructs a multi-vehicle motion planning algorithm comprising a three-layer framework based on game theory, and realizes multi-vehicle cooperative lane change comprehensively considering effective interaction targets and future state prediction. In the control architecture, different computing tasks are decomposed into different sub-control layers, wherein an upper vehicle interaction layer screens potential collision targets in a cooperative area for each vehicle for a future time; the middle-layer game decision layer considers driving safety, driving efficiency and riding comfort in a future time for each vehicle, and calculates and obtains Nash equilibrium decision results, and the lower-layer planning control layer accurately tracks the generated lane change track for each vehicle based on the decision results. The multi-vehicle high-efficiency and safe lane change motion control is realized through mutual progressive and cooperative among layers.

The above is only a preferred embodiment of the present invention, and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A multi-vehicle collaborative lane change decision and control method based on game is characterized by comprising the following steps:

tracking the planned path of each vehicle, and establishing a path tracking optimization objective function to obtain the acceleration and steering angle of each vehicle;

The vehicle kinematic model is as follows:

Wherein: k|t is the kth predicted state at time t; Is a course angle; x _i is a lateral displacement; y _i is longitudinal displacement; l _f,i and l _r,i are the distances of the centroid to the anterior and posterior axes, respectively; delta _f,i is the vehicle steering angle, a _i is the vehicle acceleration; v _i is vehicle speed; t represents a time step;

Based on the location of the vehicles, obtaining the interaction logic parameters between each of the vehicles includes:

defining a buffer area between lanes;

Wherein: lambda _ij and lambda _ji are interaction logic parameters of the vehicle i and the vehicle j in the prediction domain respectively; d _s is the relative safe distance between any two vehicles; sigma is a position identification parameter of the vehicle;

Based on the speed, acceleration and interaction logic parameters of each vehicle, respectively obtaining the efficiency coefficient, the comfort coefficient and the safety coefficient of each vehicle comprises the following steps:

The safety coefficient The formula is:

The comfort coefficient The formula is:

The efficiency coefficient The formula is:

2. The method for determining and controlling a lane change in cooperation with multiple vehicles based on a game according to claim 1, wherein the vehicle game optimization function J _i is:

Wherein: q ₁、Q₂、Q₃ is a weight matrix.

3. The multi-car collaborative lane change decision and control method based on gaming according to claim 2, wherein the constraint equation is:

Wherein: a _min、a_max is a control quantity constraint;

4. The game-based multi-car collaborative lane change decision-making and control method according to claim 3, wherein obtaining each vehicle planning path based on the nash equalization result and the vehicle kinematic model to apply the nash equalization result to the vehicle kinematic model and planning to obtain a vehicle planning path by adopting a method of five-degree polynomial interpolation comprises:

wherein: p ₁～p₅ is the fitting coefficient of the fifth order polynomial.

5. The method for determining and controlling a lane change in cooperation with multiple vehicles based on game according to claim 4, wherein the path tracking optimization objective function is:

Wherein: c= [0, 1]; c _R = [0,1] is the parameter extraction matrix; Δu _min and Δu _max are control increment constraints; u _min and u _max are control quantity constraints; q _c,R_a,R_δ,R_Δ is a weight matrix; to obtain the optimal control quantity; ζ _i、u_i is the state vector and the control vector of the vehicle i in the prediction domain, respectively.

6. The method for determining and controlling a lane change in cooperation with a plurality of vehicles based on a game according to claim 5, wherein the state vector and the control vector of the vehicle i in the prediction domain comprise:

Based on the time-varying state matrix A _ctrl,i and the control matrix B _ctrl,i, a linear discretized state increment is obtained, wherein the formula is as follows:

Wherein: to control the increment; /(I) The matrix is an incremental discrete state matrix, and I is an identity matrix; Is an incremental discrete control matrix; Δζ _i is the k+1st step state increment of vehicle i at time t;