A frenet coordinate system-based lateral and longitudinal coupling vehicle platoon cooperative control method

Abstract

The application discloses a kind of transverse and longitudinal coupling car team cooperative control method based on Frenet coordinate system.In the present application, each vehicle in the car team is given an initial state, and the state of other vehicles is transmitted and received according to the communication topology, so that the vehicles in the whole car team follow the target state, ensuring the consistency of the vehicles in the car team and the safety of the car team under non-constant straight road conditions. First, a three-degree-of-freedom dynamic model of the vehicle is introduced, then a Frenet coordinate system is introduced, and the control model of a single vehicle in the car team is derived by combining the two. Each vehicle in the car team is optimized and solved at each time by DMPC algorithm, so that the car team maintains good car team cooperative performance under non-constant straight road conditions, and better results are obtained in simulation, verifying the effectiveness of the transverse and longitudinal coupling distributed model predictive control method under the Frenet coordinate system.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of intelligent networked vehicle cooperative control, and particularly relates to a vehicle platoon cooperative control method and system based on a Frenet coordinate system and a longitudinal-lateral coupling distributed model predictive control. BACKGROUND

[0002] Intelligent networked vehicle cooperative control has important social and economic values in energy saving and emission reduction and energy consumption reduction for autonomous vehicles. Vehicle platoon control of intelligent networked vehicles has important research significance in improving traffic capacity, reducing traffic accidents and reducing driver fatigue. Previous vehicle platoon researches are mostly concentrated in one-dimensional, i.e. longitudinal, control, while in recent years, two-dimensional, i.e. longitudinal and lateral, control has become a current hot issue because comprehensive longitudinal and lateral control can make the vehicle platoon cope with more complex road conditions. Many current longitudinal and lateral comprehensive control methods based on a single vehicle are decoupled, which simplifies control system design and implementation, facilitates development and debugging, and reduces computational burden. However, when the problem perspective is shifted to vehicle platoon control, the decoupled longitudinal and lateral control exposes a series of problems such as poor coordination and decreased comprehensive performance of the vehicle platoon. Longitudinal and lateral coupling control of the vehicle platoon can greatly improve the overall coordination and safety of the vehicle platoon form and better handle complex road conditions.

[0003] The Frenet coordinate system is widely used in the field of autonomous driving, especially in the path planning system of autonomous vehicles in urban and highway traffic environments. The Frenet coordinate system uses the center line of the road as the Base frame and uses the tangent and normal vectors of the reference line to establish the coordinate system.

[0004] At present, a large number of control methods for vehicle platoon control have been verified by scholars for their feasibility, such as PID control, sliding mode control (SMC), model predictive control (MPC), etc. Among them, MPC is one of the mainstream control methods currently applied in vehicle platoon control. Compared with PID and SMC, MPC has obvious advantages in handling multivariable coupling problems, while PID and SMC will greatly increase the complexity of the controller design when facing problems of multiple input and output systems. At the same time, in handling constraint problems, MPC can explicitly handle the constraints of system input, state and output. In each control period, the control action is ensured within the constraint range by solving the optimization problem. This is very important in actual vehicle platoon control because actual vehicle platoon systems usually have physical or safety constraints, such as wheel steering angle.

[0005] At present, vehicle platoon control schemes mainly include the following two categories:

[0006] 1. Centralized control scheme: The centralized control scheme relies on a central controller that collects the state information (such as position, speed, acceleration, etc.) of all vehicles in the entire fleet, performs global optimization calculation, and then sends control instructions to each vehicle to ensure the coordination and optimization of the overall behavior of the fleet. Since all information and calculations are centralized in the central controller, a globally optimal control strategy can be achieved to ensure the overall coordination and optimization of the fleet, and the central controller can make unified decisions to avoid suboptimal decisions due to incomplete local information.

[0007] 2. Distributed control scheme: The distributed control scheme distributes control tasks to each vehicle or multiple subsystems in the fleet, each local controller independently performs local optimization, and coordinates through vehicle-to-vehicle (V2V) communication. Each vehicle makes local control decisions based on its own state and information from other vehicles to achieve overall optimization. Compared with the centralized control scheme, the distributed control scheme can effectively reduce the computational burden. With the development of V2V communication technology, the reliability of information transmission between vehicles has also been greatly improved, which further promotes the development of distributed control scheme. The combination of model predictive control and distributed control scheme forms a distributed model predictive control (DMPC) which has good effect in solving constraint problems, reducing computational burden and handling multi-objective optimization problems, and has strong reliability, so it can achieve consistency and stability between fleets.

[0008] In summary, the research on a vehicle fleet cooperative control method based on Frenet coordinate system horizontal and vertical coupling distributed model predictive control not only has theoretical significance, but also has engineering significance. SUMMARY

[0009] The purpose of the present application is to overcome the shortcomings of the current horizontal and vertical coupling distributed model predictive control vehicle fleet cooperative control method, and to propose a vehicle fleet cooperative control method based on Frenet coordinate system horizontal and vertical coupling distributed model predictive control, which combines distributed model predictive control, three-degree-of-freedom vehicle dynamics model and vehicle coordinates in Frenet coordinate system. Considering the real vehicle dynamics constraints, the horizontal and vertical directions of the fleet are controlled to ensure the consistency and safety of the fleet, and the feasibility and safety of the method are verified through simulation.

[0010] The purpose of the present application is achieved by the following technical solutions:

[0011] I. A vehicle fleet cooperative control method based on Frenet coordinate system horizontal and vertical coupling

[0012] S1: Combine Frenet coordinate system, and use three-degree-of-freedom bicycle dynamics model of vehicle to construct horizontal and vertical coupling control model of vehicle fleet;

[0013] S2: obtaining a discrete nonlinear model of each follower vehicle after discretizing the lateral and longitudinal coupled control model of the vehicle platoon using Euler forward difference method;

[0014] S3: constructing a communication topology of the vehicle platoon;

[0015] S4: according to the communication topology of the vehicle platoon and the discrete nonlinear model of each follower vehicle, solving the state of each follower vehicle in the vehicle platoon by using a distributed model predictive control method to realize the control of the vehicle platoon.

[0016] In the S1, the lateral and longitudinal coupled control model of the vehicle platoon satisfies the following formula:

[0017]

[0018] wherein, and are the differential of the longitudinal speed and the lateral speed of the follower vehicle i respectively, is the longitudinal acceleration of the follower vehicle i in the body coordinate system, m i represents the mass of the follower vehicle i, i∈1, 2, …, N, and N represents the number of follower vehicles in the vehicle platoon; represents the yaw rate of the follower vehicle i, is the derivative of the arc length s i of the follower vehicle i with respect to time, is the differential of the distance d i between the center of mass of the follower vehicle i and the projection point of the center of mass of the follower vehicle i on the reference line, and represent the cornering stiffness of the front wheel and the rear wheel of the follower vehicle i respectively, δ i is the front wheel steering angle of the follower vehicle i, γ i is the yaw rate of the follower vehicle i, a i and b i are the distances from the front wheel and the rear wheel steering axis to the center of mass of the follower vehicle i respectively, is the moment of inertia of the follower vehicle i, represents the yaw angle of the follower vehicle i, is the included angle between the tangent of the projection point of the follower vehicle i on the reference line and the X axis, k i is the corresponding road curvature at the projection point of the center of mass of the follower vehicle i on the reference line.

[0019] The discrete nonlinear model of each follower vehicle satisfies the following formula:

[0020]

[0021] wherein, X i (t+1) and X i(t) is the state sequence at time t+1 and time t, respectively, U i (t) is the control input at time t, y i (t) is the control output at time t, φ i (·) is the lateral-longitudinal coupling control model of the following vehicle i, T s is the sampling time, is the yaw angle of the following vehicle i at time t.

[0022] In the S3, the communication topology of the vehicle platoon is a directed graph containing a directed spanning tree, taking the lead vehicle of the vehicle platoon as the root node and the following vehicles as other nodes in the directed spanning tree, and the root node and the other nodes are connected.

[0023] The S4 is specifically:

[0024] S4.1: Construct an optimization problem for each following vehicle, and the formula is as follows:

[0025]

[0026] Wherein, is the predicted input sequence of the following vehicle i, J i (·) is the cost function, is the predicted state sequence of the following vehicle i, is the predicted output sequence of the following vehicle i, is the assumed output sequence of the following vehicle i, is the assumed output sequence of the vehicle j, is the predicted position sequence of the following vehicle i, s0(:|t) is the position sequence of the lead vehicle, is the state at time t+c predicted at time t, represents an unknown input variable to be optimized, X i (t) is the state of the following vehicle i at time t, φ i (·) is a nonlinear expression of the single-vehicle lateral-longitudinal coupling model, and are the lower and upper bounds of the input acceleration constraint, respectively, δ i,min and δ i,max are the lower and upper bounds of the input steering angle, respectively, is the input acceleration, is the input steering angle, |·| is the absolute value, N p is the prediction horizon, X i,des (c|t) is the ideal state sequence of the following vehicle i, Q i is the first positive definite weight matrix, s0(c|t) is the position sequence of the lead vehicle, G i is a second positive definite weight matrix, is a predicted output sequence of the following vehicle i, is a hypothetical output sequence of the following vehicle i, i is a third positive definite weight matrix, is an adjacency matrix of the following vehicle i, i is a fourth positive definite weight matrix, i is a fifth positive definite weight matrix; diag() is a matrix diagonalization operation;

[0027] S4.2: According to the communication topology of the vehicle platoon and the discrete nonlinear model of the following vehicle, the optimization problem of each following vehicle is optimized and solved by using a distributed model predictive control method, so as to control each following vehicle, all the optimization problems of the following vehicles in the vehicle platoon are iteratively optimized and solved, so as to control all the following vehicles, and then the control of the vehicle platoon is realized.

[0028] In S4.2, the optimization problem of each following vehicle is optimized and solved by using a distributed model predictive control method, so as to control each following vehicle, and the specific process is as follows:

[0029] Step 1: At t=0, the parameters are initialized:

[0030] Specifically, at t=0, the hypothetical control input sequence and the hypothetical state sequence X i of each following vehicle i are initialized; the hypothetical output sequence of each following vehicle i is initialized; i is a lateral and longitudinal coupling control model of the following vehicle i;

[0031] Step 2: After the optimization problem of each following vehicle i is optimized and solved according to S4.1, the optimal control input sequence is obtained, and the hypothetical output sequence of the following vehicle is transmitted to the adjacent following vehicle j according to the communication topology of the vehicle platoon, and the hypothetical output sequences of the preceding vehicle and the head vehicle are accepted;

[0032] Step 3: The hypothetical control input sequence, the hypothetical state sequence and the hypothetical output sequence of the next time are calculated according to the current optimal control input sequence, and the calculation formula is as follows:

[0033]

[0034] wherein, is the hypothetical control input sequence of the i-th following vehicle, is the hypothetical output sequence of the i-th following vehicle, and φt+cand φt+c+1are the hypothetical state sequences of the t+cth and t+c+1th time step respectively predicted at time t, φ i (·) is the lateral-longitudinal coupled control model of the ith follower vehicle, φt+cis the optimal control input sequence of the t+cth time step predicted by the follower i at time t-1, φt+N-2is the optimal control input sequence of the t+N-2th time step predicted by the follower i at time t-1, p and φtand φtare the hypothetical state sequence of the follower i and the optimal state sequence of the follower i respectively;

[0035] Step4: apply the first value of the current optimal control input sequence of each follower vehicle to the follower i as the real control amount of the follower i at present, to control the acceleration and front wheel steering angle of the follower i;

[0036] Step5: at the next time step, repeat Step2-Step4 to start the rolling optimization solution again based on the current hypothetical control input sequence, the hypothetical state sequence and the hypothetical output sequence of other vehicles, so as to continuously control the follower i.

[0037] II. A vehicle platoon cooperative control system based on lateral-longitudinal coupling of Frenet coordinate system

[0038] a vehicle platoon control model construction module, configured to construct a lateral-longitudinal coupled control model of the vehicle platoon by using a three-degree-of-freedom bicycle dynamics model in combination with the Frenet coordinate system;

[0039] a follower discrete nonlinear model construction module, configured to obtain a discrete nonlinear model of each follower vehicle by discretizing the lateral-longitudinal coupled control model of the vehicle platoon using Euler forward difference method;

[0040] a vehicle platoon communication topology generation module, configured to generate a communication topology of the vehicle platoon;

[0041] a vehicle platoon controller, configured to optimize and solve the states of each follower vehicle in the vehicle platoon by using a distributed model predictive control method according to the communication topology of the vehicle platoon and the discrete nonlinear model of the follower vehicle, to control all the follower vehicles in real time.

[0042] III. A computer device

[0043] The device comprises a memory and a processor, the memory stores a computer program, and the processor implements the steps of the lateral-longitudinal coupled vehicle platoon cooperative control method based on the Frenet coordinate system when executing the computer program.

[0044] IV. A computer readable storage medium ​

[0045] The medium has stored a computer program, the computer program is implemented when the processor executes the step of the Frenet coordinate system based on the lateral and longitudinal coupling vehicle team cooperative control method.

[0046] Five, a computer program product

[0047] The product includes computer program / instruction, which is implemented when the processor executes the step of the Frenet coordinate system based on the lateral and longitudinal coupling vehicle team cooperative control method.

[0048] The beneficial effects of the present application are as follows:

[0049] 1, the three-degree-of-freedom vehicle dynamics model is introduced, which is used for the control of the vehicle, compared with the high-degree-of-freedom model, the calculation burden is greatly reduced while ensuring that the model has a certain precision.

[0050] 2, the Frenet coordinate system of the vehicle is introduced, and it is combined with the three-degree-of-freedom vehicle dynamics model to form a vehicle team control model, which ensures that the vehicle team can maintain good consistency and safety of the vehicle team on non-constant straight road conditions.

[0051] 3, compared with the traditional PID control and SMC, the DMPC control algorithm is adopted, which is simpler in design, and can effectively constrain the state of the vehicle, and compared with the centralized MPC control algorithm, the solving speed is faster.

[0052] 4, for the change of the road curvature in reality, the above-mentioned lateral and longitudinal coupling vehicle team control method is tested and good experimental results are obtained, which proves the effectiveness of the above-mentioned vehicle team control method. BRIEF DESCRIPTION OF DRAWINGS

[0053] Figure 1 The vehicle team schematic diagram provided for the embodiment of the present application.

[0054] Figure 2 The three-degree-of-freedom vehicle dynamics model schematic diagram provided for the embodiment of the present application.

[0055] Figure 3 The coordinate schematic diagram of the vehicle in the Frenet coordinate system provided for the embodiment of the present application.

[0056] Figure 4 The PLF vehicle communication topology structure schematic diagram provided for the embodiment of the present application.

[0057] Figure 5 The reference trajectory schematic diagram provided for the embodiment of the present application.

[0058] Figure 6An experimental simulation effect diagram of a platoon provided by the embodiment of the application and running on a reference track by using a transverse-longitudinal coupling distributed model predictive control.

[0059] Figure 7 A carsim simulation scene diagram provided by the embodiment of the application.

[0060] Figure 8 A method flowchart of the application. DETAILED DESCRIPTION

[0061] The application will be further described below in conjunction with the drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to illustrate and explain the application, and are not used to limit the application.

[0062] As shown in Figure 8 and Figure 1 , the embodiment provides a transverse-longitudinal coupling platoon cooperative control method based on a Frenet coordinate system, comprising the following steps:

[0063] S1: combining the Frenet coordinate system, a transverse-longitudinal coupling control model of the platoon is constructed by using a three-degree-of-freedom bicycle dynamics model of the vehicle;

[0064] S1 specifically is:

[0065] S1.1: as shown in Figure 2 , a three-degree-of-freedom bicycle dynamics model of the vehicle is given, and the formula is as follows:

[0066]

[0067] wherein, m i represents the mass of the following vehicle i, i∈1,2,…,N, is the moment of inertia of the following vehicle i, a i and b i are the distances from the front wheel and rear wheel rotation axes to the center of mass of the following vehicle i, and respectively represent the longitudinal resultant forces received by the front and rear tires of the i-th vehicle; and respectively represent the lateral forces received by the front and rear tires of the i-th following vehicle; the three degrees of freedom of the vehicle are respectively the longitudinal velocity of the vehicle, the lateral velocity of the vehicle, and the yaw rate and are respectively the differentials of the longitudinal velocity of the vehicle and the lateral velocity of the vehicle.

[0068] Assuming that the side slip angles of the front and rear tires are within a small range, the tire model is linear, and the lateral forces of the front and rear tires are respectively:

[0069]

[0070] where, and denote the side slip stiffness of the front and rear wheels of the following vehicle i, respectively, and i is the front wheel steering angle of the following vehicle i.

[0071] Define the state x i and control input u i of the following vehicle i, which satisfy T denotes transpose, is the longitudinal acceleration of the following vehicle i in the body coordinate system. Rewrite the three-degree-of-freedom bicycle dynamics model of the vehicle:

[0072]

[0073] where, denotes the derivative of the yaw rate of the following vehicle i.

[0074] S1.2: As shown in Figure 3 , give the coordinates of the vehicle in the Frenet coordinate system:

[0075]

[0076] where s i is the arc length of the following vehicle i, i.e., the distance traveled by the vehicle i on the reference line from the starting point, is the derivative of s i with respect to time. is the derivative of the distance d i between the center of mass of the following vehicle i and the projection point of the center of mass of the following vehicle i on the reference line. denotes the yaw angle of the following vehicle i. k i is the road curvature corresponding to the projection point of the center of mass of the following vehicle i on the reference line, is the angle between the tangent of the projection point of the following vehicle i on the reference line and the X-axis. Since the actual road is mostly small curvature, 1-k i d i ≠ 0.

[0077] S1.3: Combine the above three-degree-of-freedom bicycle dynamics model of the vehicle and the coordinates of the vehicle in the Frenet coordinate system to obtain the lateral and longitudinal coupling control model. The lateral and longitudinal coupling control model of the vehicle satisfies the following formula:

[0078]

[0079] where, and are the longitudinal velocity of the follower vehicle i is the lateral velocity of the follower vehicle i is the derivative of is the longitudinal acceleration of the follower vehicle i in the body frame, m i denotes the mass of the follower vehicle i, i∈1, 2, …, N, N represents the number of follower vehicles in the platoon; denotes the yaw rate of the follower vehicle i, is the arc length s i of the follower vehicle i with respect to time, is the derivative of the distance d i between the projection of the center of mass of the follower vehicle i on the reference line and the center of mass of the vehicle, and denote the cornering stiffness of the front and rear wheels of the follower vehicle i, δ i is the front wheel steering angle of the follower vehicle i, γ i is the yaw rate of the follower vehicle i, a i and b i are the distances of the front and rear wheel steering axes from the center of mass of the follower vehicle i, is the moment of inertia of the follower vehicle i, denotes the yaw angle of the follower vehicle i, is the angle between the tangent of the projection of the follower vehicle i on the reference line and the X-axis, k i is the road curvature corresponding to the projection of the center of mass of the follower vehicle i on the reference line.

[0080] S2: After discretizing the lateral-longitudinal coupled control model of the platoon using the Euler forward difference method, a discrete nonlinear model of each follower vehicle is obtained for application in subsequent DMPC optimization solving;

[0081] S2 is specifically:

[0082] S2.1: At the discrete time t, the model is discretized using the Euler forward difference method:

[0083]

[0084] where T s is the sampling time;

[0085] The system state is defined as:

[0086]

[0087] The system input is:

[0088]

[0089] The system output is:

[0090] y i (t) = diag(1, 0, 0, 0, 1, 0)X i (t)

[0091] S2.2: The discrete nonlinear model of each follower vehicle satisfies the following formula:

[0092]

[0093]

[0094] where the function X i (t+1) and X i (t) are the state sequences at time t+1 and time t, respectively, U i (t) is the control input at time t, T is the transpose, y i (t) is the control output at time t, φ i (·) is the nonlinear expression of the lateral and longitudinal coupled control model of the follower vehicle i, T s is the sampling time, is the yaw angle of the follower vehicle i at time t.

[0095] S3: Construct the communication topology structure of the vehicle platoon for determining the information exchange strategy in the subsequent vehicle platoon;

[0096] S3 is specifically:

[0097] Suppose a vehicle platoon consisting of N+1 vehicles, whose indices are i∈{0, 1,…,N}, are driving on a non-constant straight road. 0 represents the leading vehicle, and the indices of the follower vehicles are from 1 to N. The vehicles in the vehicle platoon exchange information according to the topology structure.

[0098] The communication topology structure of the vehicle platoon is represented by a directed graph , the node set The edge set The adjacency matrix represents that there is a directed edge from node j to node i, i.e., vehicle i can receive information from node j. The adjacency coefficient a ij is defined as follows:

[0099] When a ij =1, it represents that vehicle i can receive information from vehicle j, i.e., vehicle j is a neighbor of vehicle i, so the neighbor set of vehicle i can be represented as follows:

[0100]

[0101] A directed graph G is said to contain a directed spanning tree if there is a root node such that any other node of the directed graph G is reachable by at least one path from the root node. Figure 4 As shown in the following table, the present application adopts a front vehicle-leader-following (PLF) topology.

[0102] S4: According to the communication topology of the vehicle platoon and the discrete nonlinear model of the following vehicle, the state of each following vehicle in the vehicle platoon is optimized and solved by using a distributed model predictive control method, so as to realize the control of the vehicle platoon.

[0103] It is assumed that the leader vehicle is not controlled and the leader vehicle always travels according to the target state, so the other states of the leader vehicle are always ideal values, but the vehicle speed will change over time. The position and speed information of the leader vehicle are defined as s0 and v0.

[0104] Based on the communication topology, each following vehicle receives the leader vehicle information and the front vehicle information, optimizes and solves at time t by using DMPC, and transmits the state information to the rear vehicle, so as to realize the consistency control of the vehicle platoon. In the experiment of the present application, the number of following vehicles is 2, that is, the vehicle platoon has 3 vehicles in total.

[0105] The ideal state X i,des (k) of each vehicle is defined.

[0106]

[0107] wherein, s i,des (t) is the ideal lateral speed, ideal longitudinal speed, ideal yaw rate, ideal yaw angle and ideal distance of the following vehicle i from the reference line. i,des (t) respectively. That is, each following vehicle follows the speed of the leader vehicle. That is, the lateral speed of the vehicle is equal to 0, so that the vehicle will not shake excessively. s i,des (t) = s0(t) - i*dis, dis represents the distance, which is a constant, and in the present application, the constant value is 15. i,des (t) = 0. s0 is the arc length of the leader vehicle.

[0108] For each following vehicle, its control input sequence U i (:|k), state sequence X i (:|k) and output sequence Y

[0109] U i (:|t) = {U i (0|t), Ui (1|t),…,U i (N p -1|t)}

[0110] X i (:|t)={X i (0|t),X i (1|t),…,X i (N p |t)}

[0111] Among them, U i (0|t),U i (1|t),U i (N p -1|t) represent the 0th, 1st, and Nth time points in the prediction time domain at time t, respectively. p The control input value at time -1, X i (0|t),X i (1|t),X i (N p |t) represent the 0th, 1st, and Nth time points in the prediction time domain at time t, respectively. p Vehicle state value at time -1. p This is a prediction of the time domain; in this invention, N is set... p =6.

[0112]

[0113] Among them, the road curvature k i (c|t) and the angle between the tangent at the projection point and the X-axis It is a quantity that is known in advance. Define the output sequence y. i (c|t):

[0114] y i (c|t)=diag(1,0,0,0,1,0)X i (c|t), c = 0, 1, ..., N p

[0115] S4 specifically refers to:

[0116] S4.1: Construct the optimization problem for each following vehicle, with the following formula:

[0117]

[0118]

[0119] in, For the prediction input sequence of car i, J i (·) represents the cost function. the predicted state sequence of the follower vehicle i, the predicted output sequence of the follower vehicle i, the assumed output sequence of the follower vehicle i, the assumed output sequence of the vehicle j, the predicted position sequence of the follower vehicle i, s0(:|t) is the position sequence of the leader vehicle, the state at time t+c predicted at time t, represents the unknown input variable to be optimized, X i (t) is the state of the follower vehicle i at time t, φ i (·) is the nonlinear expression of the single-vehicle lateral and longitudinal coupling model, and are the lower and upper bounds of the input acceleration constraint, respectively, 8m / s 2 and -5m / s 2 , δ i,min and δ i,max are the lower and upper bounds of the input steering angle, respectively, 1 rad and -1 rad, is the input acceleration, is the input steering angle, |·| is the absolute value, N p is the prediction horizon, X i,des (c|t) is the ideal state sequence of the follower vehicle i, Q i is the first positive definite weight matrix, dis=15 is the ideal distance between the two vehicles, s0(c|t) is the position sequence of the leader vehicle, is the predicted position sequence of the follower vehicle i, G i is the second positive definite weight matrix, is the predicted output sequence of the follower vehicle i, is the assumed output sequence of the follower vehicle i, F i is the third positive definite weight matrix, is the adjacency matrix of the follower vehicle i, M i is the fourth positive definite weight matrix, R i is the fifth positive definite weight matrix; diag() is the matrix diagonalization operation; and δ i,min ≤ δ i (j|k) ≤ δ i,max are input constraints. is the terminal constraint.

[0120] In the prediction horizon [0, N p -1], there are three control input sequences and state sequences.

[0121] predicted input; Assumed control input; Optimal control input.

[0122] Predicted state; Assumed state; Optimal state.

[0123] S4.2: According to the communication topology of the vehicle platoon and the discrete nonlinear model of the following vehicle, the optimization problem of each following vehicle is solved by using a distributed model predictive control method, so as to control each following vehicle, and all the optimization problems of the following vehicles in the vehicle platoon are solved by iteration, so as to control all the following vehicles, and then the control of the vehicle platoon is realized.

[0124] In S4.2, the optimization problem of each following vehicle is solved by using a distributed model predictive control method, and the state of each following vehicle is obtained, which is specifically:

[0125] Step 1: At t=0, the parameters are initialized:

[0126] Specifically, at t=0, the parameters N p , T s , Q i , G i , F i , M i , R i are initialized, and the assumed control input sequence and the assumed state sequence of each following vehicle i are initialized. X i (t) is the initial state of each vehicle preset; the assumed output sequence

[0127] φ i () is the lateral and longitudinal coupling control model of the following vehicle i;

[0128] Step 2: After the optimization problem of each following vehicle i is solved according to S4.1, the optimal control input sequence is obtained, and the assumed output sequence of itself is transmitted to the adjacent following vehicle j, i.e., the rear vehicle, according to the communication topology of the vehicle platoon, and the assumed output sequences of the front and head vehicles are accepted;

[0129] Step 3: The assumed control input sequence, the assumed state sequence and the assumed output sequence at the next time are calculated according to the current optimal control input sequence, and the calculation formula is as follows:

[0130]

[0131] wherein, a hypothetical control input sequence for the ith follower vehicle, a hypothetical output sequence for the ith follower vehicle, and are respectively the hypothetical state sequences of the ith follower vehicle at time t+c and t+c+1 predicted at time t, φ i (·) is a lateral-longitudinal coupling control model of the ith follower vehicle, is an optimal control input sequence of the ith follower vehicle at time t+c predicted at time t-1, is an optimal control input sequence of the ith follower vehicle at time t+N p -2 predicted at time t-1, and are respectively a hypothetical state sequence of the ith follower vehicle and an optimal state sequence of the ith follower vehicle;

[0132] Step 4: the first value of the current optimal control input sequence of each follower vehicle is applied to the ith follower vehicle as the real control quantity of the ith follower vehicle at present, to control the acceleration and front wheel steering angle of the ith follower vehicle;

[0133] Step 5: at the next time, based on the current hypothetical control input sequence, the hypothetical state sequence and the hypothetical output sequence of other vehicles, Steps 2-4 are repeated to start the rolling optimization solution again, so as to continuously control the ith follower vehicle.

[0134] The application further provides a vehicle platoon cooperative control system based on Frenet coordinate system lateral-longitudinal coupling distributed model predictive control, comprising:

[0135] a vehicle platoon control model construction module, configured to combine the Frenet coordinate system and use a three-degree-of-freedom bicycle dynamics model to construct a lateral-longitudinal coupling control model of the vehicle platoon;

[0136] a follower discrete nonlinear model construction module, configured to use Euler forward difference method to discretize the lateral-longitudinal coupling control model of the vehicle platoon, and obtain a discrete nonlinear model of each follower vehicle;

[0137] a vehicle platoon communication topology structure generation module, configured to generate a communication topology structure of the vehicle platoon;

[0138] a vehicle platoon controller, configured to use a distributed model predictive control method to optimize and solve the states of each follower vehicle in the vehicle platoon according to the communication topology structure of the vehicle platoon and the discrete nonlinear model of the follower vehicle, and control all follower vehicles in real time.

[0139] The simulation of the embodiment is combined simulation of matlab and carsim, and a carsim simulation scene diagram is shown in Figure 7 The simulation results are shown in Figure 6 Figure 6 ​(a) of FIG. 1, Figure 6 (b) of FIG. 1, Figure 6 (c) of FIG. 1, Figure 6 (d) of FIG. 1, Figure 6 (e) of FIG. 1, Figure 6 (f) of FIG. 1, and Figure 6 (g) of FIG. 1 are respectively a simulation graph of vehicle speed changing with time, a simulation graph of vehicle spacing error changing with time, a simulation graph of vehicle lateral error changing with time, a simulation graph of vehicle lateral speed changing with time, a simulation graph of vehicle position changing with time, a simulation graph of vehicle yaw rate changing with time, and a simulation graph of vehicle yaw angle changing with time. As can be seen from the graphs, the following vehicles in the vehicle platoon can all follow the speed of the leading vehicle well, and the spacing error of each following vehicle from the leading vehicle is within a very small range, proving the safety of the vehicle platoon, and the distance of each vehicle from the center of the reference line is very small, proving that the vehicles are on the reference trajectory.

[0140] According to the above experimental results, it can be found that:

[0141] 1. A three-degree-of-freedom vehicle dynamics model is introduced for vehicle control, which greatly reduces the computational burden while ensuring a certain accuracy of the model compared to high-degree-of-freedom models.

[0142] 2. The Frenet coordinate system of the vehicle is introduced, and it is combined with the three-degree-of-freedom vehicle dynamics model to form a vehicle platoon control model, which ensures that the vehicles in the vehicle platoon can maintain good consistency and safety of the vehicle platoon on non-constant straight road conditions.

[0143] 3. The DMPC control algorithm is used, which is simpler to design than traditional PID control and SMC, and can effectively constrain the state of the vehicle, and is faster to solve than centralized MPC control algorithm.

[0144] 4. The above-mentioned lateral and longitudinal coupling vehicle platoon control method is tested for the change of road curvature in reality and good experimental results are obtained, proving the effectiveness of the above-mentioned vehicle platoon control method.

[0145] The above only describes the preferred embodiments of the present application, although the present application has been disclosed as above with the preferred embodiments, however, it is not intended to limit the present application. Any person skilled in the art, without departing from the scope of the technical scheme of the present application, can make many possible changes and modifications to the technical scheme of the present application by using the above disclosed methods and technical contents, or modify equivalent embodiments. Therefore, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present application, without departing from the content of the technical scheme of the present application, all still belong to the scope of protection of the technical scheme of the present application.

Claims

1. A method for lateral and longitudinal coupled platoon cooperative control based on Frenet coordinate system, characterized in that, The method comprises the following steps: S1: combining the Frenet coordinate system, a three-degree-of-freedom bicycle dynamics model of a vehicle is used to construct a lateral-longitudinal coupling control model of the vehicle platoon; S2: after the lateral-longitudinal coupling control model of the vehicle platoon is discretized using the Euler forward difference method, a discrete nonlinear model of each follower vehicle is obtained; S3: a communication topology structure of the vehicle platoon is constructed; S4: according to the communication topology structure of the vehicle platoon and the discrete nonlinear model of the follower vehicle, a distributed model predictive control method is used to optimize and solve the state of each follower vehicle in the vehicle platoon, so as to realize the control of the vehicle platoon; The S4 is specifically: S4.1: constructing an optimization problem of each follower vehicle, the formula is as follows: wherein, is a predicted input sequence of the follower vehicle i, is a cost function, is a predicted state sequence of the follower vehicle i, is a predicted output sequence of the follower vehicle i, is a hypothetical output sequence of the follower vehicle i, is a hypothetical output sequence of the vehicle j, is a predicted position sequence of the follower vehicle i, is a position sequence of the leader vehicle, is a state of the t+c time predicted at the t time, represents unknown input variables to be optimized, is a state of the follower vehicle i at the t time, is a nonlinear expression of the single-vehicle lateral and longitudinal coupling control model, and are a lower bound and an upper bound of the input acceleration constraint, respectively, and are a lower bound and an upper bound of the input steering angle, respectively, is an input acceleration, is an input steering angle, is an absolute value, is a prediction time domain, is an ideal state sequence of the follower vehicle i, is a first positive definite weight matrix, is a position sequence of the leader vehicle, is a predicted position sequence of the follower vehicle i, is a second positive definite weight matrix, is a predicted output sequence of the follower vehicle i, is a hypothetical output sequence of the follower vehicle i, is a third positive definite weight matrix, is an adjacency matrix of the follower vehicle i, is a fourth positive definite weight matrix, is a fifth positive definite weight matrix; is a matrix diagonalization operation; is an ideal distance between the two vehicles;​​​ S4.2: according to the communication topology structure of the vehicle platoon and the discrete nonlinear model of the follower vehicle, the optimization problem of each follower vehicle is optimized and solved by using the distributed model predictive control method, so as to control each follower vehicle, and the optimization problem of all follower vehicles in the vehicle platoon is iteratively optimized and solved, so as to control all follower vehicles, and then the control of the vehicle platoon is realized. 2.The Frenet frame based lateral and longitudinal coupled vehicle platoon cooperative control method of claim 1, wherein, In the S1, the lateral-longitudinal coupling control model of the vehicle platoon satisfies the following formula: where and are the longitudinal velocity , the derivative of the vehicle lateral velocity of the following vehicle i, is the longitudinal acceleration of the following vehicle i in the body coordinate system, denotes the mass of the following vehicle i, , denotes the number of following vehicles in the platoon; denotes the yaw rate of the following vehicle i, is the derivative of the arc length of the following vehicle i with respect to time, is the derivative of the distance between the center of mass of the following vehicle i and the projection of the center of mass of the following vehicle i on the reference line, and denote the cornering stiffness of the front and rear wheels of the following vehicle i, respectively, is the front wheel steering angle of the following vehicle i, is the yaw rate of the following vehicle i, and are the distances of the front and rear wheel rotation axes from the center of mass of the following vehicle i, is the moment of inertia of the following vehicle i, denotes the yaw angle of the following vehicle i, is the angle between the tangent of the projection of the following vehicle i on the reference line and the x-axis, is the corresponding road curvature at the projection of the center of mass of the following vehicle i on the reference line.

3. The Frenet frame based lateral and longitudinal coupled vehicle platoon control method of claim 2, wherein, The discrete nonlinear model of each follower vehicle satisfies the following formula: wherein, and are the state sequence at time t+1 and time t, respectively, is the control input at time t, is the control output at time t, is the sampling time, is the yaw angle of the following vehicle i.

4. The Frenet frame based lateral and longitudinal coupled vehicle platoon control method of claim 1, wherein, In the S3, the communication topology structure of the vehicle platoon is a directed graph containing a directed spanning tree, the leading vehicle of the vehicle platoon is taken as a root node, the follower vehicles are taken as other nodes in the directed spanning tree, and the root node and the other nodes are connected.

5. The Frenet frame based lateral and longitudinal coupled vehicle platoon control method of claim 1, wherein, In the S4.2, the optimization problem of each follower vehicle is optimized and solved by using the distributed model predictive control method, so as to control each follower vehicle, specifically: Step 1: at t=0, the parameters are initialized: In particular, at time t = 0, initialize the assumed control input sequence for each follower vehicle i and the assumed state sequence : , is the pre-specified initial state for each vehicle; the assumed output sequence : , ; Step 2: At time t>0, each follower i solves the optimization problem described in S4.1 to obtain the optimal control input sequence and passes its assumed output sequence to its neighboring followers according to the communication topology of the platoon and accepts the assumed output sequences of the predecessor and the leader. Step 3: according to the current optimal control input sequence, the hypothetical control input sequence, the hypothetical state sequence and the hypothetical output sequence at the next moment are calculated, and the calculation formula is as follows: wherein, is a hypothetical control input sequence for the ith follower vehicle, is a hypothetical output sequence for the ith follower vehicle, and are hypothetical state sequences predicted at time t for times t + c and t + c + 1, respectively, is an optimal control input sequence for the follower vehicle i predicted at time t - 1 for time t + c, is an optimal control input sequence for the follower vehicle i predicted at time t - 1 for time t + c + 1, is an optimal control input sequence for the follower vehicle i predicted at time t - 1 for time t + c + 1, are a hypothetical state sequence for the follower vehicle i and an optimal state sequence for the follower vehicle i, respectively;​ Step 4: the first value of the current optimal control input sequence of each follower vehicle is applied to the follower vehicle i as the real control amount of the follower vehicle i, so as to control the acceleration and the front wheel steering angle of the follower vehicle i; Step 5: at the next moment, based on the current hypothetical control input sequence, the hypothetical state sequence and the hypothetical output sequence of other vehicles, Step 2-Step 4 are repeated to start the rolling optimization solution again, so as to continuously control the follower vehicle i.

6. A Frenet frame based longitudinal-lateral coupled platoon cooperative control system for implementing the method of claim 1, characterized in that, It comprises: A vehicle platoon control model construction module is configured to combine the Frenet coordinate system and use a three-degree-of-freedom bicycle dynamics model of a vehicle to construct a lateral-longitudinal coupling control model of the vehicle platoon; A follower vehicle discrete nonlinear model construction module is configured to use the Euler forward difference method to discretize the lateral-longitudinal coupling control model of the vehicle platoon, and obtain a discrete nonlinear model of each follower vehicle; A vehicle platoon communication topology structure generation module is configured to generate a communication topology structure of the vehicle platoon; A vehicle platoon controller is configured to use a distributed model predictive control method to optimize and solve the state of each follower vehicle in the vehicle platoon according to the communication topology structure of the vehicle platoon and the discrete nonlinear model of the follower vehicle, and control all follower vehicles in real time. 7.A computer device, comprising a memory and a processor, wherein the memory stores a computer program, and the computer device is configured to perform the method according to any one of claims 1-6 when the computer program is executed by the processor. The processor executes the computer program to realize the steps of the method in any one of claims 1 to 5. The processor executes the computer program to realize the steps of the method in any one of claims 1 to 5.

8. A computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program, which when executed by the processor, implements the steps of the method of any one of claims 1 to 5.

9. A computer program product comprising computer programs / instructions, characterized in that, The computer program / instructions, which when executed by the processor, implement the steps of the method of any one of claims 1 to 5.

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