Trajectory tracking and stability cooperative control method and system for four-wheel independent steering automobile

Abstract

The invention discloses a trajectory tracking and stability cooperative control method and system for a four-wheel independent steering vehicle. The method comprises the steps that firstly, a four-wheel independent steering vehicle dynamics model and a tire model are built according to vehicle parameter information; secondly, drawing a vehicle phase plane graph based on a kinetic model and a tire model to obtain a vehicle stability constraint relation and dividing a stability region; then a dual-mode adaptive model prediction controller is constructed based on the phase plane stability region and the vehicle state; and finally, constructing a system model for trajectory tracking and stability coordination control of the four-wheel independent steering automobile by combining a lower-layer corner torque distributor. The stability constraint relation and control parameters of the vehicle can be adjusted in real time according to the state parameters of the vehicle, and the trajectory tracking precision and stability of the four-wheel independent steering vehicle are comprehensively improved.

Description

Technical Field

[0001] The present invention relates to the field of automatic driving of automobiles, and in particular to a method and system for coordinated control of trajectory tracking and stability of a four-wheel independent steering automobile. Background Art

[0002] Thanks to the maturity of corner module technology and the development of drive-by-wire technology, four-wheel independent steering (FWS) vehicles, capable of flexibly distributing the steering angles across all four wheels, have emerged. This improves vehicle maneuverability at low speeds and enhances driving stability at high speeds. Trajectory tracking and stability control are two primary research objectives. However, the interference between these two control objectives, the volatile driving environment, and the real-time changes in vehicle parameters can affect the vehicle's path tracking accuracy and stability control. Therefore, designing a coordinated trajectory tracking and stability control method is crucial for improving vehicle tracking accuracy and stability.

[0003] Based on multiple constraints, multiple objectives, and inherent predictive properties, model predictive control algorithms are often used for coordinated control of trajectory tracking and stability. Current research primarily adjusts the weight coefficients of the objective function's outputs based on the vehicle's real-time state and environmental information to achieve better control. However, adjusting the weight coefficients can lead to shortcomings such as non-convergence, complex adjustment strategies, and conflicting constraint handling, resulting in poor solution results. These studies focus solely on adjusting the weight coefficients while ignoring the impact of the prediction horizon on control effectiveness. When the prediction horizon is too small, the controller attempts to complete the optimization solution in a relatively short period of time, which often causes violent vehicle motion and destabilization. When the prediction horizon is too large, the control algorithm's computational complexity increases, resulting in larger tracking errors and reduced trajectory tracking accuracy. Dynamically adjusting the prediction horizon can comprehensively ensure tracking accuracy and stability. Summary of the Invention

[0004] The purpose of the present invention is to propose a method and system for coordinated control of trajectory tracking and stability of a four-wheel independent steering vehicle, so as to enhance the stability and tracking accuracy of the four-wheel independent steering vehicle under different driving conditions.

[0005] To achieve the above object, the technical solution of the present invention is as follows:

[0006] The present invention proposes a method for coordinated control of trajectory tracking and stability of a four-wheel independent steering vehicle, comprising the following steps:

[0007] Step 1: construct a vehicle dynamics model and tire model based on vehicle parameter information, and preliminarily construct a system model for trajectory tracking and stability coordinated control based on the dynamics model and tire model;

[0008] Step 2: Draw a vehicle phase plane diagram based on the dynamic model and tire model, obtain the vehicle stability constraint relationship and divide the stability area;

[0009] Step 3: construct a parameter regulator based on the phase plane area and vehicle state parameters to dynamically adjust the controller parameters;

[0010] Step 4: Based on the dynamic model and tire model, and combined with dynamic parameters, a dual-mode adaptive model predictive controller DMA-MPC is established;

[0011] Step 5, optimizing the distribution of the four-wheel steering angles of the four-wheel independent steering vehicle based on the Ackerman steering model;

[0012] Step 6: Design an optimization objective function. Based on the expected additional yaw moment and the expected longitudinal vehicle speed, use the maximum stability margin strategy to solve the objective function, thereby optimizing the four-wheel torque distribution of the four-wheel independent steering vehicle.

[0013] Preferably, the step 1 is specifically as follows:

[0014] Step 1.1: Based on the vehicle parameter information, establish a four-wheel independent steering vehicle dynamics model. The vehicle dynamics equation is described as follows:

[0015]

[0016] Where m is the vehicle mass, I z is the yaw moment of inertia; l f and l r are the lengths from the center of mass to the front and rear axes; v x and v y are the longitudinal and lateral velocities of the car, respectively; and ω r are the heading angle and yaw rate of the car respectively; δ f and δ r are the front and rear wheel turning angles of the car respectively; X and Y are the horizontal and vertical axis positions of the car in the geodetic coordinate system respectively; F yf and F yr are the lateral forces of the front and rear wheels respectively; M z is the additional yaw moment;

[0017] Step 1.2: Construct a brush tire model to characterize the lateral force of the tire. The lateral force of the tire is calculated by the following formula:

[0018]

[0019] Where C α is the tire cornering stiffness; α is the tire slip angle; α sis the tire slip angle corresponding to the peak tire cornering force; μ is the road adhesion coefficient; F z is the vertical force on the tire;

[0020] Perform offline linearization on each slip angle:

[0021]

[0022] Where C f and C r is the equivalent tire cornering stiffness of the front and rear wheels in the linear region; α f and α r is the front and rear wheel slip angle;

[0023] The tracking model is constructed based on the kinematic relationship between the vehicle and the road and the vehicle dynamics relationship, specifically:

[0024]

[0025] Where, is the vehicle heading angle;

[0026] Combining formula (1) and formula (2), the nonlinear system model for trajectory tracking and stability coordinated control is obtained as follows:

[0027]

[0028] Where, is the state vector; u=[δ f δ r M z ] T is the control input; f(x,u) represents the transfer function;

[0029] Assuming that the system is highly differentiable at the operating point (x0, u0), expand the Taylor series at the operating point and ignore the high-order terms. Formula (5) can be expressed as the following linear state space form for controller design:

[0030]

[0031] Where,

[0032] A and B are the system matrix and input matrix; C is the output matrix; x(t) represents the state vector at time t; y(t) represents the output state vector at time t; u(t) represents the control input at time t; d(t) = f(x0,u0)-Ax0-Bu0; d(t) represents the additional matrix at time t; x0 and u0 are the initial state vector and initial control input, respectively;

[0033] Preferably, the step 2 is specifically as follows:

[0034] Step 2.1, according to the composite differential equation composed of formula (1) and (2), plot β-ω according to the predetermined longitudinal speed, front wheel steering angle, rear wheel steering angle and road friction coefficient. r Phase trajectory, then based on the phase trajectory bifurcation stability theory, the stable point and saddle point are calculated by searching for the equilibrium solution;

[0035] In step 2.2, based on the maximum and minimum rear wheel slip angles and the maximum and minimum steady-state yaw rates, the following vehicle dynamic envelope boundaries are obtained:

[0036]

[0037] Where, α s,r is the limit value of the rear wheel slip angle; g is the acceleration of gravity; ω r and β are the actual yaw rate and actual sideslip angle of the vehicle respectively;

[0038] In step 2.3, based on the stable point bifurcation phenomenon of the phase plane, the front and rear wheel angle constraint relationship of the vehicle at different vehicle speeds and adhesion coefficients is obtained. Through the parameter fitting method, the following linear front and rear wheel angle constraint relationship is obtained:

[0039] -ψ≤σδ f +ζδ r ≤ψ (8)

[0040] Where, σ, ζ, and Ψ are fitting parameters;

[0041] Based on the physical constraints of the actual steering system and the four-wheel independent steering system, the control input limits are set as follows:

[0042]

[0043] Where, δ max and δ min are the maximum and minimum front and rear wheel turning angles respectively; M z,max and M z,min are the maximum and minimum additional yaw moments, respectively;

[0044] In step 2.4, the stability region is divided based on the phase plane envelope constraint. The phase plane region within the envelope is defined as the stable region, and the entire phase plane region outside the envelope is defined as the unstable region.

[0045] Preferably, the step 3 is specifically as follows:

[0046] Step 3.1: Construct the prediction domain N for adjusting the DMA-MPC controller in the stable domain. p Fuzzy controller, the input of the fuzzy controller is the lateral error e and the stability index η, and the output is the predicted time domain increment ΔNp ;

[0047] For the lateral error e, it is obtained by the following formula:

[0048] e=|YY ref | (10)

[0049] Where, Y and Y ref are the actual lateral position and reference position of the vehicle in the geodetic coordinate system respectively;

[0050] The stability index η is obtained by the relationship between the center point of the envelope and the actual state point of the vehicle. Assume that the distance from the center point of the envelope to the left, right, up, and down directions of the envelope are D1, D2, D3, and D4, which can be expressed by the following formula:

[0051]

[0052] The distances from the actual state point of the vehicle to the envelope are d1, d2, d3, and d4, which are expressed by the following formula:

[0053]

[0054] Where, ω r and β are the actual yaw rate and actual sideslip angle of the vehicle respectively;

[0055] The stability index η is calculated by calculating the relative distance:

[0056]

[0057] Where, d min is the minimum value among d1, d2, d3 and d4;

[0058] Step 3.2, set corresponding fuzzy subsets for the input and output of fuzzy control, where the fuzzy subset of the lateral error e is {VS, S, SS, M, SL, L, VL}, denoted as {extremely small, small, slightly small, medium, slightly large, large, extremely large}; the fuzzy subset of the stability index η is {VS, S, M, L, VL}, denoted as {extremely small, small, medium, large, extremely large}; the time domain increment ΔN is predicted. p The fuzzy subsets are {NB, NM, NS, ZO, PS, PM, PB}, denoted as {negative large, negative medium, negative small, zero, positive small, positive medium, positive large}. The specific fuzzy rules are as follows:

[0059]

[0060] Step 3.3: Construct a weight coefficient adaptive controller in the instability domain. Let the distance from the actual state point of the vehicle to the center of the envelope be d aThe point closest to the vehicle state point among the intersections of the straight line formed by the line connecting the vehicle state point and the center of the envelope line and the envelope line is point c1, and the distance between the vehicle state point and point c1 is d b , thus obtaining the stability index η2 in the unstable region:

[0061] η2=d b / d a (14)

[0062] According to the stability index η2 in the unstable region, the weight adjustment coefficient q is obtained by the following formula:

[0063] q=log(1+39n2) / log(40) (15).

[0064] Preferably, the step 4 is specifically as follows:

[0065] Step 4.1: Discrete and linearize Equation (6) to obtain the following discrete state space form:

[0066]

[0067] Where A k =1+AT;B k =BT;d(k)=d(t)T;C k =C; T represents the sampling time; A k 、B k and C k represents the discretized system matrix, input matrix, and output matrix; x(k), u(k), y(k), and d(k) represent the state quantity, control quantity, output state quantity, and additional matrix of the kth time domain;

[0068] Define the new state quantity of the kth time domain as Δu(k)=u(k)-u(k-1); Δu(k) represents the control input increment in the kth time domain, and the discrete state space equation is transformed into the following augmented form:

[0069]

[0070] Where, and represents the augmented system matrix, input matrix and additional matrix; 0 3×5 is a zero matrix with 3 rows and 5 columns; I3 represents the third-order identity matrix; 0 3×1 represents a zero matrix of 3 rows and 1 column; η(k) represents the output state quantity of the kth time domain after augmentation; Represents the augmented output matrix; 0 4×3 represents a zero matrix with 4 rows and 3 columns;

[0071] In the prediction domain N p The system state output matrix Y(t) on is expressed as follows:

[0072] Y(t)=ψ t ξ0(t)+θ t ΔU(t)+τ t φ(t) (18)

[0073] Where: N p and N c are the prediction time domain and the control time domain respectively; ξ0(t) represents the initial state vector and control increment at time t, x0(k) and u0(k-1) represent the initial state quantity and initial control quantity at time t respectively; ΔU(t) represents the control increment sequence at time t; φ(t) represents the additional matrix sequence at time t; ψ t ,θ t , τ t Represents the transformation matrix obtained after sorting;

[0074] Step 4.2: Design the objective function for the state space equation to optimize the solution. Use a quadratic objective function to solve the optimal control input increment in each finite time domain. The designed objective function is as follows:

[0075]

[0076] Where ρ and ε are weight factors and relaxation factors, respectively. The first term of the objective function is to make the system state follow the desired vehicle state. The second term is the constraint on the control input increment, which makes the vehicle control input smoother. Q, P, and R represent the weight matrices of the objective function state input, total control output, and incremental control output, respectively. J1(t) is the objective function at time t. η(k+i / t), η ref (k+i / t), u(k+i / t) and Δu(k+i / t) are the output vector, reference output vector, total control input and control input increment of the k+ith time domain at time t, respectively;

[0077] Step 4.3, adjust the DMA-MPC controller parameters based on the parameter regulator, according to the predicted time domain N p The predicted time domain increment ΔN of the fuzzy controller output p , the real-time prediction time domain N is obtained by the following formula p :

[0078] N p =N p0 +round(ΔN p ) (20)

[0079] Where N p With N p0 They are real-time prediction time domain and initial prediction time domain respectively;

[0080] Based on the weight adjustment coefficient q output by the weight adaptive controller, the state input increment output weight matrix Q is adjusted by the following formula:

[0081]

[0082] Where W p1 、W p2 、W p3 、W p4 are the initial weights of lateral velocity error, heading angle error, yaw angular velocity error, and lateral displacement error, respectively; σ1, σ2, σ3, and σ4 are the gain coefficients of lateral velocity error, heading angle error, yaw angular velocity error, and lateral displacement error, respectively;

[0083] In step 4.4, the optimization problem of DMA-MPC is transformed into the following standard quadratic programming problem by combining equations (6), (7), (8), and (21):

[0084]

[0085] Where, U(t)=ΔU(t)+U0(t);H t and G t represents the normalized transformation matrix; e t represents the error matrix; U(t) represents the total control sequence at time t; where ΔU min , ΔU max 、U min and U max is the actuator constraint sequence; Y min and Y max is the state quantity constraint sequence; U0(t) is the initial control quantity matrix; η ref is the reference output vector sequence; M is the conversion matrix between the control amount and the increment; F = M T PM; F is the control total amount transformation matrix;

[0086] Step 4.5: The DMA-MPC controller is used to solve the front and rear wheel angles and the additional yaw moment. To maintain a constant vehicle speed, a PID controller is designed to output the ideal longitudinal force F. xd .

[0087] Preferably, the step 5 is specifically as follows:

[0088] Receive the front and rear wheel steering angles δ output by the DMA-MPC controllerf and δ r , based on the Ackerman steering model, the four-wheel steering angles of the four-wheel independent steering vehicle are solved:

[0089]

[0090] Where, δ fl , δ fr , δ rl and δ rr are the turning angles of the left front wheel, right front wheel, left rear wheel and right rear wheel of the vehicle respectively; B is the wheel spacing; k f and k r are the front axle steering judgment factor and the rear axle steering judgment factor respectively; the specific expressions are:

[0091]

[0092] Preferably, the step 6 is specifically as follows:

[0093] Step 6.1: Receive vehicle parameter information, consider the vertical load transfer of each wheel caused by longitudinal acceleration and lateral acceleration, and calculate the vertical load of each wheel based on the moment balance relationship:

[0094]

[0095] Where, F zfl 、F zfr 、F zrl and F zrr are the left front wheel load, right front wheel load, left rear wheel load and right rear wheel load respectively; a x and a y is the longitudinal acceleration and lateral acceleration of the vehicle; h g is the height of the vehicle's center of mass;

[0096] Step 6.2: Allocate wheel torque according to the maximum tire stability margin and design the following objective function:

[0097]

[0098] Where, is the driving force of each wheel of the car; r is the wheel radius; Indicates the torque of each wheel of the car;

[0099] In step 6.3, the additional yaw torque and ideal longitudinal force output by the DMA-MPC controller and the PID speed tracker are received, and the following constraints are obtained based on the force balance relationship:

[0100]

[0101] Where, F xd and M z are the ideal longitudinal force and the additional yaw torque, respectively;

[0102] Based on the actuator constraints and road adhesion conditions, the following constraints are designed:

[0103]

[0104] Where, T max is the maximum torque allowed for the wheel;

[0105] In step 6.4, the torque distribution optimization problem is transformed into a typical quadratic programming problem by combining the maximum tire stability margin objective function and the constraints:

[0106]

[0107] Where u e =[T fl T rl T rl T rr ] T ; v d =[F xd M z ] T ;

[0108] u e is the control input vector; W is the transformation matrix; v d and A e are the equality constraint target value and constraint matrix respectively; u min,e and u max,e are the maximum and minimum control input values, respectively.

[0109] The present invention also proposes a four-wheel independent steering vehicle trajectory tracking and stability collaborative control system, including a processor, a memory and a computer program stored on the memory. When the processor executes the computer program, it specifically executes any step in the above-mentioned four-wheel independent steering vehicle trajectory tracking and stability collaborative control method.

[0110] Compared with the prior art, the present invention has the following beneficial effects:

[0111] Compared with the traditional trajectory tracking and stability coordination method based on the front-wheel steering dynamic model, the vehicle dynamic model based on four-wheel independent steering in the present invention can have a more flexible angle distribution, and can better cope with various low-adhesion and high-speed harsh working conditions to improve the vehicle trajectory tracking angle and handling stability; the DMA-MPC controller based on the constraint relationship of the phase plane, the fuzzy control algorithm and the adaptive adjustment algorithm can enable the vehicle to adjust the control parameters and constraints under different driving conditions, effectively realizing the coordinated control of trajectory tracking and stability. BRIEF DESCRIPTION OF THE DRAWINGS

[0112] Figure 1 Schematic diagram of the trajectory tracking and stability coordinated control method for a four-wheel independent steering vehicle according to the present invention. DETAILED DESCRIPTION

[0113] The following is combined with Figure 1 , the technical solution of the present invention is described in detail.

[0114] The present invention can be implemented in many different forms and should not be considered to be limited to the embodiments described herein. On the contrary, these embodiments are provided to make this disclosure thorough and complete and will fully convey the scope of the invention to those skilled in the art. In the accompanying drawings, components are enlarged for clarity.

[0115] The present invention discloses a method for coordinated control of trajectory tracking and stability of a four-wheel independent steering vehicle, comprising the following steps:

[0116] Step 1: construct a vehicle dynamics model and tire model based on vehicle parameter information, and preliminarily construct a system model for trajectory tracking and stability coordinated control based on the dynamics model and tire model;

[0117] Step 2: Draw a vehicle phase plane diagram based on the dynamic model and tire model, obtain the vehicle stability constraint relationship and divide the stability area;

[0118] Step 3: construct a parameter regulator based on the phase plane area and vehicle state parameters to dynamically adjust the controller parameters;

[0119] Step 4: Based on the dynamic model and tire model, and combined with dynamic parameters, a dual-mode adaptive model predictive controller DMA-MPC is established;

[0120] Step 5, optimizing the distribution of the four-wheel steering angles of the four-wheel independent steering vehicle based on the Ackerman steering model;

[0121] Step 6: Design an optimization objective function. Based on the expected additional yaw moment and the expected longitudinal vehicle speed, use the maximum stability margin strategy to solve the objective function, thereby optimizing the four-wheel torque distribution of the four-wheel independent steering vehicle.

[0122] The specific steps of step 1 are as follows:

[0123] Step 1.1: Based on the vehicle parameter information, establish a four-wheel independent steering vehicle dynamics model. The vehicle dynamics equation is described as follows:

[0124]

[0125] Where m is the vehicle mass, I z is the yaw moment of inertia; l f and l r are the lengths from the center of mass to the front and rear axes; v x and v y are the longitudinal and lateral velocities of the car, respectively; and ω r are the heading angle and yaw rate of the car respectively; δ f and δ r are the front and rear wheel turning angles of the car respectively; X and Y are the horizontal and vertical axis positions of the car in the geodetic coordinate system respectively; F yf and F yr are the lateral forces of the front and rear wheels respectively; M z is the additional yaw moment;

[0126] Step 1.2: Construct a brush tire model to characterize the lateral force of the tire. The lateral force of the tire is calculated by the following formula:

[0127]

[0128] Where C α is the tire cornering stiffness; α is the tire slip angle; α s is the tire slip angle corresponding to the peak tire cornering force; μ is the road adhesion coefficient; F z is the vertical force on the tire;

[0129] Perform offline linearization on each slip angle:

[0130]

[0131] Where C f and C r is the equivalent tire cornering stiffness of the front and rear wheels in the linear region; α f and α r is the front and rear wheel slip angle;

[0132] The tracking model is constructed based on the kinematic relationship between the vehicle and the road and the vehicle dynamics relationship, specifically:

[0133]

[0134] Where, is the vehicle heading angle;

[0135] Combining formula (1) and formula (2), the nonlinear system model for trajectory tracking and stability coordinated control is obtained as follows:

[0136]

[0137] Where, is the state vector; u=[δ f δ r M z ] T is the control input; f(x,u) represents the transfer function;

[0138] Assuming that the system is highly differentiable at the operating point (x0, u0), expand the Taylor series at the operating point and ignore the high-order terms. Formula (5) can be expressed as the following linear state space form for controller design:

[0139]

[0140] Where,

[0141] A and B are the system matrix and input matrix; C is the output matrix; x(t) represents the state vector at time t; y(t) represents the output state vector at time t; u(t) represents the control input at time t; d(t) = f(x0,u0)-Ax0-Bu0; d(t) represents the additional matrix at time t; x0 and u0 are the initial state vector and initial control input, respectively;

[0142] The specific steps of step 2 are as follows:

[0143] Step 2.1, according to the composite differential equation composed of formula (1) and (2), plot β-ω according to the predetermined longitudinal speed, front wheel steering angle, rear wheel steering angle and road friction coefficient. r Phase trajectory, then based on the phase trajectory bifurcation stability theory, the stable point and saddle point are calculated by searching for the equilibrium solution;

[0144] In step 2.2, based on the maximum and minimum rear wheel slip angles and the maximum and minimum steady-state yaw rates, the following vehicle dynamic envelope boundaries are obtained:

[0145]

[0146] Where, α s,r is the limit value of the rear wheel slip angle; g is the acceleration of gravity; ω r and β are the actual yaw rate and actual sideslip angle of the vehicle respectively;

[0147] In step 2.3, based on the stable point bifurcation phenomenon of the phase plane, the front and rear wheel angle constraint relationship of the vehicle at different vehicle speeds and adhesion coefficients is obtained. Through the parameter fitting method, the following linear front and rear wheel angle constraint relationship is obtained:

[0148] -ψ≤σδ f +ζδ r ≤ψ (8)

[0149] Where, σ, ζ, and Ψ are fitting parameters;

[0150] Based on the physical constraints of the actual steering system and the four-wheel independent steering system, the control input limits are set as follows:

[0151]

[0152] Where, δ max and δ min are the maximum and minimum front and rear wheel turning angles respectively; M z,max and M z,min are the maximum and minimum additional yaw moments, respectively;

[0153] In step 2.4, the stability region is divided based on the phase plane envelope constraint. The phase plane region within the envelope is defined as the stable region, and the entire phase plane region outside the envelope is defined as the unstable region.

[0154] The specific steps of step 3 are as follows:

[0155] Step 3.1: Construct the prediction domain N for adjusting the DMA-MPC controller in the stable domain. p Fuzzy controller, the input of the fuzzy controller is the lateral error e and the stability index η, and the output is the predicted time domain increment ΔN p ;

[0156] For the lateral error e, it is obtained by the following formula:

[0157] e=|YY ref | (10)

[0158] Where, Y and Y ref are the actual lateral position and reference position of the vehicle in the geodetic coordinate system respectively;

[0159] The stability index η is obtained by the relationship between the center point of the envelope and the actual state point of the vehicle. Assume that the distance from the center point of the envelope to the left, right, up, and down directions of the envelope are D1, D2, D3, and D4, which can be expressed by the following formula:

[0160]

[0161] The distances from the actual state point of the vehicle to the envelope are d1, d2, d3, and d4, which are expressed by the following formula:

[0162]

[0163] Where, ω r and β are the actual yaw rate and actual sideslip angle of the vehicle respectively;

[0164] The stability index η is calculated by calculating the relative distance:

[0165]

[0166] Where, d min is the minimum value among d1, d2, d3 and d4;

[0167] Step 3.2, set corresponding fuzzy subsets for the input and output of fuzzy control, where the fuzzy subset of the lateral error e is {VS, S, SS, M, SL, L, VL}, denoted as {extremely small, small, slightly small, medium, slightly large, large, extremely large}; the fuzzy subset of the stability index η is {VS, S, M, L, VL}, denoted as {extremely small, small, medium, large, extremely large}; the time domain increment ΔN is predicted. p The fuzzy subsets are {NB, NM, NS, ZO, PS, PM, PB}, denoted as {negative large, negative medium, negative small, zero, positive small, positive medium, positive large}. The specific fuzzy rules are as follows:

[0168]

[0169] Step 3.3: Construct a weight coefficient adaptive controller in the instability domain. Let the distance from the actual state point of the vehicle to the center of the envelope be d a The point closest to the vehicle state point among the intersections of the straight line formed by the line connecting the vehicle state point and the center of the envelope line and the envelope line is point c1, and the distance between the vehicle state point and point c1 is d b , thus obtaining the stability index η2 in the unstable region:

[0170] η2=d b / d a (14)

[0171] According to the stability index η2 in the unstable region, the weight adjustment coefficient q is obtained by the following formula:

[0172] q=log(1+39n2) / log(40) (15).

[0173] The specific steps of step 4 are as follows:

[0174] Step 4.1: Discrete and linearize Equation (6) to obtain the following discrete state space form:

[0175]

[0176] Where A k =1+AT;B k =BT;d(k)=d(t)T;C k =C; T represents the sampling time; A k 、B k and C k represents the discretized system matrix, input matrix, and output matrix; x(k), u(k), y(k), and d(k) represent the state quantity, control quantity, output state quantity, and additional matrix of the kth time domain;

[0177] Define the new state quantity of the kth time domain as Δu(k)=u(k)-u(k-1); Δu(k) represents the control input increment in the kth time domain, and the discrete state space equation is transformed into the following augmented form:

[0178]

[0179] Where, and represents the augmented system matrix, input matrix and additional matrix; 0 3×5 is a zero matrix with 3 rows and 5 columns; I3 represents the third-order identity matrix; 0 3×1 represents a zero matrix of 3 rows and 1 column; η(k) represents the output state quantity of the kth time domain after augmentation; Represents the augmented output matrix; 0 4×3 represents a zero matrix with 4 rows and 3 columns;

[0180] In the prediction domain N p The system state output matrix Y(t) on is expressed as follows:

[0181] Y(t)=ψ t ξ0(t)+θ t ΔU(t)+τ t φ(t) (18)

[0182] Where: N p and N c are the prediction time domain and the control time domain respectively; ξ0(t) represents the initial state vector and control increment at time t, x0(k) and u0(k-1) represent the initial state quantity and initial control quantity at time t respectively; ΔU(t) represents the control increment sequence at time t; φ(t) represents the additional matrix sequence at time t; ψ t ,θt , τ t Represents the transformation matrix obtained after sorting;

[0183] Step 4.2: Design the objective function for the state space equation to optimize the solution. Use a quadratic objective function to solve the optimal control input increment in each finite time domain. The designed objective function is as follows:

[0184]

[0185] Where ρ and ε are weight factors and relaxation factors, respectively. The first term of the objective function is to make the system state follow the desired vehicle state. The second term is the constraint on the control input increment, which makes the vehicle control input smoother. Q, P, and R represent the weight matrices of the objective function state input, total control output, and incremental control output, respectively. J1(t) is the objective function at time t. η(k+i / t), η ref (k+i / t), u(k+i / t) and Δu(k+i / t) are the output vector, reference output vector, total control input and control input increment of the k+ith time domain at time t, respectively;

[0186] Step 4.3, adjust the DMA-MPC controller parameters based on the parameter regulator, according to the predicted time domain N p The predicted time domain increment ΔN of the fuzzy controller output p , the real-time prediction time domain N is obtained by the following formula p :

[0187] N p =N p0 +round(ΔN p ) (20)

[0188] Where N p With N p0 They are real-time prediction time domain and initial prediction time domain respectively;

[0189] Based on the weight adjustment coefficient q output by the weight adaptive controller, the state input increment output weight matrix Q is adjusted by the following formula:

[0190]

[0191] Where W p1 、W p2 、W p3 、W p4 are the initial weights of lateral velocity error, heading angle error, yaw angular velocity error, and lateral displacement error, respectively; σ1, σ2, σ3, and σ4 are the gain coefficients of lateral velocity error, heading angle error, yaw angular velocity error, and lateral displacement error, respectively;

[0192] In step 4.4, the optimization problem of DMA-MPC is transformed into the following standard quadratic programming problem by combining equations (6), (7), (8), and (21):

[0193]

[0194] Where, U(t)=ΔU(t)+U0(t);H t and G t represents the normalized transformation matrix; e t represents the error matrix; U(t) represents the total control sequence at time t; where ΔU min , ΔU max 、U min and U max is the actuator constraint sequence; Y min and Y max is the state quantity constraint sequence; U0(t) is the initial control quantity matrix; η ref is the reference output vector sequence; M is the conversion matrix between the control amount and the increment; F = M T PM; F is the control total amount transformation matrix;

[0195] Step 4.5: The DMA-MPC controller is used to solve the front and rear wheel angles and the additional yaw moment. To maintain a constant vehicle speed, a PID controller is designed to output the ideal longitudinal force F. xd .

[0196] The specific steps of step 5 are as follows:

[0197] Receive the front and rear wheel steering angles δ output by the DMA-MPC controller f and δ r , based on the Ackerman steering model, the four-wheel steering angles of the four-wheel independent steering vehicle are solved:

[0198]

[0199] Where, δ fl , δ fr , δ rl and δ rr are the turning angles of the left front wheel, right front wheel, left rear wheel and right rear wheel of the vehicle respectively; B is the wheel spacing; k f and k r are the front axle steering judgment factor and the rear axle steering judgment factor respectively; the specific expressions are:

[0200]

[0201] The specific steps of step 6 are as follows:

[0202] Step 6.1: Receive vehicle parameter information, consider the vertical load transfer of each wheel caused by longitudinal acceleration and lateral acceleration, and calculate the vertical load of each wheel based on the moment balance relationship:

[0203]

[0204] Where, F zfl 、F zfr 、F zrl and F zrr are the left front wheel load, right front wheel load, left rear wheel load and right rear wheel load respectively; a x and a y is the longitudinal acceleration and lateral acceleration of the vehicle; h g is the height of the vehicle's center of mass;

[0205] Step 6.2: Allocate wheel torque according to the maximum tire stability margin and design the following objective function:

[0206]

[0207] Where, is the driving force of each wheel of the car; r is the wheel radius; Indicates the torque of each wheel of the car;

[0208] In step 6.3, the additional yaw torque and ideal longitudinal force output by the DMA-MPC controller and the PID speed tracker are received, and the following constraints are obtained based on the force balance relationship:

[0209]

[0210] Where, F xd and M z are the ideal longitudinal force and the additional yaw torque, respectively;

[0211] Based on the actuator constraints and road adhesion conditions, the following constraints are designed:

[0212]

[0213] Where, T max is the maximum torque allowed for the wheel;

[0214] In step 6.4, the torque distribution optimization problem is transformed into a typical quadratic programming problem by combining the maximum tire stability margin objective function and the constraints:

[0215]

[0216] Where u e =[Tfl T rl T rl T rr ] T ; v d =[F xd M z ] T ;

[0217] u e is the control input vector; W is the transformation matrix; v d and A e are the equality constraint target value and constraint matrix respectively; u min,e and u max,e are the maximum and minimum control input values, respectively.

[0218] The present invention also proposes a four-wheel independent steering vehicle trajectory tracking and stability collaborative control system, including a processor, a memory and a computer program stored on the memory. When the processor executes the computer program, it specifically executes any step in the above-mentioned four-wheel independent steering vehicle trajectory tracking and stability collaborative control method.

[0219] It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by those skilled in the art in the art to which the present invention belongs. It should also be understood that terms such as those defined in common dictionaries should be understood to have meanings consistent with their meanings in the context of the prior art and, unless defined as such, will not be interpreted in an idealized or overly formal sense.

[0220] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for coordinated control of trajectory tracking and stability of a four-wheel independent steering vehicle, characterized in that: The following steps are involved: Step 1: construct a vehicle dynamics model and tire model based on vehicle parameter information, and preliminarily construct a system model for trajectory tracking and stability coordinated control based on the dynamics model and tire model; Step 2: Draw a vehicle phase plane diagram based on the dynamic model and tire model, obtain the vehicle stability constraint relationship and divide the stability area; Step 3: construct a parameter regulator based on the phase plane area and vehicle state parameters to dynamically adjust the controller parameters; Step 4: Based on the dynamic model and tire model, and combined with dynamic parameters, a dual-mode adaptive model predictive controller DMA-MPC is established; Step 5, optimizing the distribution of the four-wheel steering angles of the four-wheel independent steering vehicle based on the Ackerman steering model; Step 6: Design an optimization objective function. Based on the expected additional yaw moment and the expected longitudinal vehicle speed, use the maximum stability margin strategy to solve the objective function, thereby optimizing the four-wheel torque distribution of the four-wheel independent steering vehicle.

2. The method for coordinated control of trajectory tracking and stability of a four-wheel independent steering vehicle according to claim 1, characterized in that: The step 1 is specifically as follows: Step 1.1: Based on the vehicle parameter information, establish a four-wheel independent steering vehicle dynamics model. The vehicle dynamics equation is described as follows: Where m is the vehicle mass, I z is the yaw moment of inertia; l f and l r are the lengths from the center of mass to the front and rear axes; v x and v y are the longitudinal and lateral velocities of the car, respectively; and ω r are the heading angle and yaw rate of the car respectively; δ f and δ r are the front and rear wheel turning angles of the car respectively; X and Y are the horizontal and vertical axis positions of the car in the geodetic coordinate system respectively; F yf and F yr are the lateral forces of the front and rear wheels respectively; M z is the additional yaw moment; Step 1.2: Construct a brush tire model to characterize the lateral force of the tire. The lateral force of the tire is calculated by the following formula: Where C α is the tire cornering stiffness; α is the tire slip angle; α s is the tire slip angle corresponding to the peak tire cornering force; μ is the road adhesion coefficient; F z is the vertical force on the tire; Perform offline linearization on each slip angle: Where C f and C r is the equivalent tire cornering stiffness of the front and rear wheels in the linear region; α f and α r is the front and rear wheel slip angle; The tracking model is constructed based on the kinematic relationship between the vehicle and the road and the vehicle dynamics relationship, specifically: Where, is the vehicle heading angle; Combining formula (1) and formula (2), the nonlinear system model for trajectory tracking and stability coordinated control is obtained as follows: Where, is the state vector; u=[δ f δ r M z ] T is the control input; f(x,u) represents the transfer function; Assuming that the system is highly differentiable at the operating point (x0, u0), expand the Taylor series at the operating point and ignore the high-order terms. Formula (5) can be expressed as the following linear state space form for controller design: Where, A and B are the system matrix and input matrix; C is the output matrix; x(t) represents the state vector at time t; y(t) represents the output state vector at time t; u(t) represents the control input at time t; d(t) = f(x0,u0)-Ax0-Bu0; d(t) represents the additional matrix at time t; x0 and u0 are the initial state vector and initial control input, respectively.

3. The method for coordinated control of trajectory tracking and stability of a four-wheel independent steering vehicle according to claim 1, characterized in that: The step 2 is specifically as follows: Step 2.1, according to the composite differential equation composed of formula (1) and (2), plot β-ω according to the predetermined longitudinal speed, front wheel steering angle, rear wheel steering angle and road friction coefficient. r Phase trajectory, then based on the phase trajectory bifurcation stability theory, the stable point and saddle point are calculated by searching for the equilibrium solution; In step 2.2, based on the maximum and minimum rear wheel slip angles and the maximum and minimum steady-state yaw rates, the following vehicle dynamic envelope boundaries are obtained: Where, α s,r is the limit value of the rear wheel slip angle; g is the acceleration of gravity; ω r and β are the actual yaw rate and actual sideslip angle of the vehicle respectively; In step 2.3, based on the stable point bifurcation phenomenon of the phase plane, the front and rear wheel angle constraint relationship of the vehicle at different vehicle speeds and adhesion coefficients is obtained. Through the parameter fitting method, the following linear front and rear wheel angle constraint relationship is obtained: -ψ≤σδ f +ζδ r ≤ψ (8)In the formula, σ, ζ, and Ψ are fitting parameters; Based on the physical constraints of the actual steering system and the four-wheel independent steering system, the control input limits are set as follows: Where, δ max and δ min They are the maximum and minimum front and rear wheel turning angles respectively; M z,max and M z,min are the maximum and minimum additional yaw moments, respectively; In step 2.4, the stability region is divided based on the phase plane envelope constraint. The phase plane region within the envelope is defined as the stable region, and the entire phase plane region outside the envelope is defined as the unstable region.

4. The method for coordinated control of trajectory tracking and stability of a four-wheel independent steering vehicle according to claim 1, characterized in that: The step 3 is as follows: Step 3.1: Construct the prediction domain N for adjusting the DMA-MPC controller in the stable domain. p Fuzzy controller, the input of the fuzzy controller is the lateral error e and the stability index η, and the output is the predicted time domain increment ΔN p ; For the lateral error e, it is obtained by the following formula: e=|YY ref | (10) Where, Y and Y ref are the actual lateral position and reference position of the vehicle in the geodetic coordinate system respectively; The stability index η is obtained by the relationship between the center point of the envelope and the actual state point of the vehicle. Assume that the distance from the center point of the envelope to the left, right, up, and down directions of the envelope are D1, D2, D3, and D4, which can be expressed by the following formula: The distances from the actual state point of the vehicle to the envelope are d1, d2, d3, and d4, which are expressed by the following formula: Where, ω r and β are the actual yaw rate and actual sideslip angle of the vehicle respectively; The stability index η is calculated by calculating the relative distance: Where, d min is the minimum value among d1, d2, d3 and d4; Step 3.2, set corresponding fuzzy subsets for the input and output of fuzzy control, where the fuzzy subset of the lateral error e is {VS, S, SS, M, SL, L, VL}, denoted as {extremely small, small, slightly small, medium, slightly large, large, extremely large}; the fuzzy subset of the stability index η is {VS, S, M, L, VL}, denoted as {extremely small, small, medium, large, extremely large}; the time domain increment ΔN is predicted. p The fuzzy subsets are {NB, NM, NS, ZO, PS, PM, PB}, denoted as {negative large, negative medium, negative small, zero, positive small, positive medium, positive large}. The specific fuzzy rules are as follows: Step 3.3: Construct a weight coefficient adaptive controller in the instability domain. Let the distance from the actual state point of the vehicle to the center of the envelope be d a The point closest to the vehicle state point among the intersections of the straight line formed by the line connecting the vehicle state point and the center of the envelope line and the envelope line is point c1, and the distance between the vehicle state point and point c1 is d b , thus obtaining the stability index η2 in the unstable region: η2=d b / d a (14) According to the stability index η2 in the unstable region, the weight adjustment coefficient q is obtained by the following formula: q=log(1+39n2) / log(40) (15).

5. The method for coordinated control of trajectory tracking and stability of a four-wheel independent steering vehicle according to claim 1, characterized in that: The step 4 is as follows: Step 4.1: Discrete and linearize Equation (6) to obtain the following discrete state space form: Where A k =1+AT;B k =BT;d(k)=d(t)T;C k =C; T represents the sampling time; A k 、B k and C k represents the discretized system matrix, input matrix, and output matrix; x(k), u(k), y(k), and d(k) represent the state quantity, control quantity, output state quantity, and additional matrix of the kth time domain; Define the new state quantity of the kth time domain as Δu(k)=u(k)-u(k-1); Δu(k) represents the control input increment in the kth time domain, and the discrete state space equation is transformed into the following augmented form: Where, and represents the augmented system matrix, input matrix and additional matrix; 0 3×5 is a zero matrix with 3 rows and 5 columns; I3 represents the third-order identity matrix; 0 3×1 represents a zero matrix with 3 rows and 1 column; η(k) represents the output state quantity of the kth time domain after augmentation; Represents the augmented output matrix; 0 4×3 represents a zero matrix with 4 rows and 3 columns; In the prediction domain N p The system state output matrix Y(t) on is expressed as follows: Y(t)=ψ t ξ0(t)+θ t ΔU(t)+τ t φ(t) (18) Where: N p and N c are the prediction time domain and the control time domain respectively; ξ0(t) represents the initial state vector and control increment at time t, x0(k) and u0(k-1) represent the initial state quantity and initial control quantity at time t respectively; ΔU(t) represents the control increment sequence at time t; φ(t) represents the additional matrix sequence at time t; ψ t ,θ t , τ t Represents the transformation matrix obtained after sorting; Step 4.2: Design the objective function for the state space equation to optimize the solution. Use a quadratic objective function to solve the optimal control input increment in each finite time domain. The designed objective function is as follows: Where ρ and ε are weight factors and relaxation factors, respectively. The first term of the objective function is to make the system state follow the desired vehicle state. The second term is the constraint on the control input increment, which makes the vehicle control input smoother. Q, P, and R represent the weight matrices of the objective function state input, total control output, and incremental control output, respectively. J1(t) is the objective function at time t. η(k+i / t), η ref (k+i / t), u(k+i / t) and Δu(k+i / t) are the output vector, reference output vector, total control input and control input increment of the k+ith time domain at time t, respectively; Step 4.3, adjust the DMA-MPC controller parameters based on the parameter regulator, according to the predicted time domain N p The predicted time domain increment ΔN of the fuzzy controller output p , the real-time prediction time domain N is obtained by the following formula p : N p =N p0 +round(ΔN p ) (20) Where N p With N p0 They are real-time prediction time domain and initial prediction time domain respectively; Based on the weight adjustment coefficient q output by the weight adaptive controller, the state input increment output weight matrix Q is adjusted by the following formula: Where W p1 、W p2 、W p3 、W p4 are the initial weights of lateral velocity error, heading angle error, yaw angular velocity error, and lateral displacement error, respectively; σ1, σ2, σ3, and σ4 are the gain coefficients of lateral velocity error, heading angle error, yaw angular velocity error, and lateral displacement error, respectively; In step 4.4, the optimization problem of DMA-MPC is transformed into the following standard quadratic programming problem by combining equations (6), (7), (8), and (21): Where, U(t)=ΔU(t)+U0(t);H t and G t represents the normalized transformation matrix; e t represents the error matrix; U(t) represents the total control sequence at time t; where ΔU min , ΔU max 、U min and U max is the actuator constraint sequence; Y min and Y max is the state quantity constraint sequence; U0(t) is the initial control quantity matrix; η ref is the reference output vector sequence; M is the conversion matrix between the control amount and the increment; F = M T PM; F is the control total amount transformation matrix; Step 4.5: The DMA-MPC controller is used to solve the front and rear wheel angles and the additional yaw moment. To maintain a constant vehicle speed, a PID controller is designed to output the ideal longitudinal force F. xd .

6. The method for coordinated control of trajectory tracking and stability of a four-wheel independent steering vehicle according to claim 1, characterized in that: The step 5 is as follows: Receive the front and rear wheel steering angle δ output by the DMA-MPC controller f and δ r , based on the Ackerman steering model, the four-wheel steering angles of the four-wheel independent steering vehicle are solved: Where, δ fl , δ fr , δ rl and δ rr are the turning angles of the left front wheel, right front wheel, left rear wheel and right rear wheel of the vehicle respectively; B is the wheel spacing; k f and k r are the front axle steering judgment factor and the rear axle steering judgment factor respectively; the specific expressions are:

7. The method for coordinated control of trajectory tracking and stability of a four-wheel independent steering vehicle according to claim 1, characterized in that: The step 6 is as follows: Step 6.1: Receive vehicle parameter information, consider the vertical load transfer of each wheel caused by longitudinal acceleration and lateral acceleration, and calculate the vertical load of each wheel based on the moment balance relationship: Where, F zfl 、F zfr 、F zrl and F zrr are the left front wheel load, right front wheel load, left rear wheel load and right rear wheel load respectively; a x and a y is the longitudinal acceleration and lateral acceleration of the vehicle; h g is the height of the vehicle's center of mass; Step 6.2: Allocate wheel torque according to the maximum tire stability margin and design the following objective function: Where, is the driving force of each wheel of the car; r is the wheel radius; Indicates the torque of each wheel of the car; In step 6.3, the additional yaw torque and ideal longitudinal force output by the DMA-MPC controller and the PID speed tracker are received, and the following constraints are obtained based on the force balance relationship: Where, F xd and M z are the ideal longitudinal force and the additional yaw torque, respectively; Based on the actuator constraints and road adhesion conditions, the following constraints are designed: Where, T max is the maximum torque allowed for the wheel; In step 6.4, the torque distribution optimization problem is transformed into a typical quadratic programming problem by combining the maximum tire stability margin objective function and the constraints: Where u e =[T fl T rl T rl T rr ] T ; v d =[F xd M z ] T ; u e is the control input vector; W is the transformation matrix; v d and A e are the equality constraint target value and constraint matrix respectively; u min,e and u max,e are the maximum and minimum control input values, respectively.

8. A four-wheel independent steering vehicle trajectory tracking and stability coordinated control system, characterized in that: The invention comprises a processor, a memory and a computer program stored in the memory. When the processor executes the computer program, the method for coordinated control of trajectory tracking and stability of a four-wheel independent steering vehicle as described in any one of claims 1 to 7 is specifically performed.

Images