Path tracking preset performance fault-tolerant control method considering automobile steering fault

Abstract

The invention relates to an automobile finite time path tracking fault-tolerant control method considering steering actuator faults. The method comprises the following steps: firstly, establishing a vehicle dynamics model and a steering execution mechanism dynamics model, designing a path tracking control strategy by applying a model prediction control method, and establishing an upper-layer path tracking controller; then, on the basis of a differential driving auxiliary steering principle, a preset performance control method of finite time convergence and a nonsingular fast terminal sliding mode control theory are combined, and a steering actuator fault-tolerant controller is established; and finally, designing a torque distribution controller by adopting an optimal control theory, and solving an optimal four-wheel driving torque control quantity through quadratic programming. According to the method, the influence caused by the failure of the steering actuator can be effectively compensated, the safety and the stability of the vehicle are remarkably improved, and a feasible solution is provided for the fault-tolerant control of the steering actuator in a future intelligent vehicle path tracking scene.

Description

Technical Field

[0001] This invention belongs to the field of intelligent vehicle technology, specifically a path tracking preset performance fault-tolerant control method that takes into account vehicle steering failure. Background Technology

[0002] Currently, intelligent vehicles and autonomous driving technologies have become the core driving force for the transformation and upgrading of the global automotive industry, and are profoundly reshaping the future transportation ecosystem. Path tracking control, as a key component of autonomous driving technology, determines whether autonomous vehicles can drive safely and stably due to its robustness and tracking accuracy.

[0003] However, due to the complexity of vehicle steering actuators and the driving environment, steering actuator failures may occur during path tracking, which will seriously affect the path tracking effect and threaten vehicle driving safety. Therefore, fault-tolerant control of the vehicle steering system is a core technical link to ensure the reliability of intelligent driving functions and driving safety, and has important research value and practical significance.

[0004] Fault-tolerant control methods for actuator failures can be divided into passive fault-tolerant control and active fault-tolerant control. Passive fault-tolerant control utilizes the robustness and redundancy of the control system itself to replace the faulty actuator and achieve functionality, but its control effect is not ideal when the failure is severe. Active fault-tolerant control, on the other hand, establishes a completely new fault-tolerant controller. When an actuator fails, it reconstructs the control law and redistributes various vehicle control parameters to achieve the ideal control objective. It has stronger control capabilities and can adapt to various fault types.

[0005] While related fault-tolerant control methods have shown promising results, most have not focused on the impact of the transient performance of the fault-tolerant controller. In path-following driving scenarios, the instantaneous response accuracy and speed of fault-tolerant control directly determine the vehicle's ability to compensate for faults. If the convergence error is too large or the convergence time is too long, the vehicle will be unable to quickly and effectively handle the fault, causing it to deviate from the expected path and potentially leading to a serious accident. Summary of the Invention

[0006] To address the aforementioned issues, this invention provides a fault-tolerant control method for finite-time path tracking of automobiles that considers steering actuator failure. This method effectively compensates for the impact of steering actuator failure, significantly improves vehicle safety and stability, and provides a feasible solution for fault-tolerant control of steering actuators in future intelligent vehicle path tracking scenarios.

[0007] The technical solution of this invention is described below in conjunction with the accompanying drawings:

[0008] This invention provides a fault-tolerant control method for finite-time path tracking of automobiles that considers steering actuator failure, comprising the following steps:

[0009] Step 1: Establish vehicle dynamics model and steering actuator dynamics model, and apply model predictive control method to design path tracking control strategy and establish upper-level path tracking controller;

[0010] Step 2: Based on the differential drive assisted steering principle, combined with the preset performance control method and non-singular fast terminal sliding mode control theory, establish a fault-tolerant controller for the steering actuator, and set the desired front wheel steering angle δ. f Converted to additional yaw moment M f And ensure that the control error converges to the preset boundary within a finite time;

[0011] Step 3: Design a torque distribution controller using optimal control theory, and solve for the optimal four-wheel drive torque control quantity through quadratic programming.

[0012] Furthermore, the specific method for step one is as follows:

[0013] 11) Establish a vehicle dynamics model for the establishment of a path tracking controller;

[0014] Assuming the vehicle's left and right sides are dynamically symmetrical, and neglecting vertical, pitch, and roll motions, a 3-DOF vehicle dynamics model is established. Combined with the small-angle assumption, it is expressed as follows:

[0015]

[0016] In the formula, m is the total vehicle mass; and These represent the vehicle's longitudinal and lateral speeds, respectively; ψ is the yaw angle; F yf and F yr These represent the total lateral forces of the front and rear axle tires, respectively; I z The yaw moment of inertia of the vehicle; f and l r These are the distances from the vehicle's center of gravity to the front and rear axles, respectively; ΔM z To add yaw moment;

[0017] In the vehicle dynamics model, the longitudinal lateral forces of the tires are represented as follows:

[0018] F ci =C ci α i (i=f,r) (4)

[0019] In the formula, C ci For tire lateral stiffness, α i This refers to the tire slip angle;

[0020] Based on the small angle assumption, the tire slip angle is expressed as:

[0021]

[0022] In the formula, v x and v y For longitudinal and lateral vehicle speeds; The yaw rate is l. f and l r δ represents the distance from the vehicle's center of gravity to the front and rear axles. f The steering angle of the front wheels;

[0023] Finally, the state-space equation expression of the vehicle dynamics system is obtained as follows:

[0024]

[0025] In the formula, For system state variables; u = (δ f ) represents the system control variable, where δ f When steering fails, it represents the desired front wheel steering angle, which is a virtual control quantity; This is the system output quantity;

[0026] 12) Perform dynamic modeling of the steering actuator;

[0027] When a vehicle is steering, the forces acting on the steering actuator include the total self-centering torque, the steering torque, and the frictional resistance torque of the steering actuator. Furthermore, if the inertia and damping of the vehicle's steering actuator are all equated to the steering wheel, the steering actuator simplifies to a second-order system with one degree of freedom, and its dynamic model can be expressed as:

[0028]

[0029] In the formula, δ f J is the front wheel steering angle; eff and b eff These represent the equivalent moment of inertia and equivalent damping of the steering actuator on the steering wheel, respectively; T eq τ is the wheel drive torque. f The frictional resistance torque of the steering actuator; τ a It is the sum of the restoring torques of the left and right front wheels around their respective kingpins;

[0030] For a single wheel, the restoring torque around the kingpin can be considered to consist of three parts:

[0031] τ sz =F z ×cosγsinσsinδ f cosσ(r σ+rtanσ) (8)

[0032] τ sy =F y ×rsinγcosσ (9)

[0033] τ zz =M z ×cosγcosσ (10)

[0034] In the formula, τ sz The restoring torque τ is caused by the weight of the front axle. sy The restoring torque τ is caused by the lateral force between the tire and the ground. zz F is the component of the tire's self-aligning torque about its kingpin direction. z For the vertical load on the wheel; F y M is the lateral force of the wheel; z The self-aligning torque of the tire; γ is the caster angle; σ is the inclination angle; δ f The front wheel steering angle; r σ The kingpin offset is r; the wheel radius is r.

[0035] 13) Design a path tracking control strategy;

[0036] For the established state-space equations of the vehicle system at any point (ξ) r ,u r Perform a Taylor series expansion at () and retain only the first-order terms of the expanded equation, ignoring the higher-order terms, to obtain an approximately linearized model, as shown below:

[0037]

[0038] In the formula, ξ is the vehicle system state variable; ξ is the derivative of the system state variable; u is the system control variable; ξ is the derivative of the system state variable. r This is the reference value for the system state variables; u r f(ξ) is the reference value for system control input; r ,u r ) is in reference state ξ r and reference control input u r The system dynamic function under;

[0039] Combine the above formula with The difference, expressed in incremental form, is the error model for path tracking control:

[0040]

[0041] In the formula, The derivative of the system state error; This refers to the error in the system state variables; Let A be the system control error; let B be the Jacobian matrix of f with respect to ξ; let C be the Jacobian matrix of f with respect to u.

[0042]

[0043] In the formula, The derivative of the system state error; The derivative of the system state variables; This serves as a reference value for the differential of the system state variables; ξ is the system state variable error; ξ is the system state variable; r This serves as a reference value for system state variables; U is the system control error; u is the system control quantity; u r This is a reference value for system control variables;

[0044] The forward Euler method, a technique used in approximate discretization, replaces the differential in the state-space equations with a first-order difference quotient, i.e.:

[0045]

[0046] In the formula, The derivative of the system state error at time step k; The error in the system state at time step k+1; The error of the system state quantity at time step k is T, where T is the sampling time.

[0047] The state-space expression for the discrete vehicle dynamics model is then:

[0048]

[0049] In the formula, A(k) = I + TA(t), B(k) = TB(t), I is the identity matrix, let

[0050]

[0051] In the formula, x(k|t) is the extended state vector composed of state quantity error and control quantity error at time step k predicted at time t; The error of the state quantity at time step k when predicted at time t; The control error at time step k-1 predicted at time t;

[0052] The updated state-space equations of the vehicle dynamics system are then expressed as:

[0053]

[0054] In the formula, x(k+1|t) is the extended state vector predicted at time step k at time k+1; x(k|t) is the extended state vector predicted at time step k at time t; Δu(k|t) is the control increment predicted at time step k at time t; and η(k|t) is the output quantity predicted at time step k at time t. The state matrix; To control the increment matrix; The output matrix is ​​shown below:

[0055]

[0056] Let the prediction time domain be N. p The control time domain is N c And there are N p ≤N c The predicted output of the vehicle dynamics system in the prediction time domain is expressed as:

[0057]

[0058] In the formula, η(k+N) p |k) represents the predicted time step k+N at time step k. p Output quantity at time; Δu(k+N) c -1) represents time step k+N c The system control increment at -1;

[0059] The predicted output of the vehicle dynamics system described in equation (19) can be expressed in matrix form:

[0060] Y(k)=ψ(k)x(k)+θ(k)ΔU(k) ​​(20)

[0061] Furthermore, based on the quadratic programming method, the objective function of the path tracking model predictive control is defined as follows:

[0062]

[0063] In the objective function J, the first term reflects the control objective of the controller to ensure that the vehicle system tracks the target path efficiently and with high precision; its value is N in the prediction time domain. p The first term represents the deviation between the system's predicted output and the reference output; the second term reflects the controller's control objective of maintaining vehicle stability, and its value is N in the control time domain. c Within, the system controls the magnitude of the increment;

[0064] In the formula, η(t+i|t) is the actual output vector, η ref (t+i|t) is the reference output vector, as shown in the following equation: Δu(t+i|t) is the control increment, Q∈R 3×3The weight matrix for tracking accuracy is used to adjust the emphasis placed on path tracking performance during the solution process, R∈R 2×2 The weight matrix for controlling the increments has values ​​related to the smoothness of changes in each control variable:

[0065]

[0066] In the formula, For reference yaw rate; ψ ref (t+i|t) is the reference yaw angle; Y ref (t+i|t) is the reference lateral displacement;

[0067] A relaxation factor ε is introduced into the objective function, where ε>0, so that when there is no optimal solution, the system will use the obtained suboptimal solution as a substitute, and ρ is the weighting coefficient of ε.

[0068] The objective function of the path tracing control program can be expressed in standard quadratic form as follows:

[0069] minJ(ξ(t),u(t-1),ΔU(t))=min[ΔU(t) T ,ε]H t [ΔU(t) T ,ε] T +G t [ΔU(t) T ,ε](23)

[0070] In the formula, ξ(t) is the state variable; u(t-1) is the control variable at the previous time step; ΔU(t) is the control variable increment;

[0071]

[0072] Due to limitations in the vehicle's mechanical structure and motion constraints, the following constraints need to be applied to the control variables and some state variables:

[0073]

[0074] Equation (25) represents the constraints for the control increment, control quantity, output quantity, and the sideslip angle and lateral acceleration of the center of mass, respectively.

[0075] By combining the objective function and constraints, the optimal vehicle control increment sequence, i.e., the front wheel steering angle, in the control time domain is solved:

[0076] ΔU t =[Δu(t),Δu(t+1),…,Δu(t+N c -1)] T (26)

[0077] Take the first term as the control increment, which is applied to the vehicle system, i.e.

[0078]

[0079] Furthermore, the specific method for step two is as follows:

[0080] 21) Establish a dynamic model of the steering actuator;

[0081] The torques generated around the kingpin by the driving forces of the left and right wheels are as follows:

[0082]

[0083] In the formula, F tfl and F tfr These represent the longitudinal driving forces of the left and right wheels on the front axle, respectively; r σ Kingpin offset; γ is kingpin caster angle; σ is kingpin inclination angle.

[0084] The difference between the torques generated by the left and right wheels around their respective kingpins gives the front axle differential torque M. f 'as follows:

[0085] M f ′=τ dsr -τ dsl =(F tfr -F tfl )r σ cosγcosσ (29)

[0086] To achieve differential drive assisted steering, the differential torque M needs to be set... f Wheel drive torque T in the alternative steering actuator dynamics model eq Once control is achieved, the dynamic model of the steering actuator can be expressed in the following form:

[0087]

[0088] In the formula, δ f J is the front wheel steering angle; eff and b eff These represent the equivalent moment of inertia and equivalent damping of the steering actuator on the steering wheel, respectively; M f ′ represents the differential torque; τ f The frictional resistance torque of the steering actuator; τ a It is the sum of the restoring torques of the left and right front wheels around their respective kingpins;

[0089] 22) Design fault-tolerant control laws;

[0090] Define the control error of the steering actuator as:

[0091] e = δ fd -δ f = x 1d -x1 (31)

[0092] where e is the front wheel steering angle error; δ fd is the desired front wheel steering angle; δ f is the actual front wheel steering angle; x 1d and x1 are codes taken for easy representation;

[0093] Select a positive definite and monotonically decreasing exponential decay smooth function as the preset performance function:

[0094]

[0095] where μ0 > μ ∞ > 0, κ > 0 are both constants, μ0 = μ(0) ≥ |e(0)|;

[0096] According to this preset performance function, the tracking error of the front wheel steering angle is constrained within the required boundary, and the constraint relationship is specifically expressed as:

[0097]

[0098] where δ1 and δ2 are both overshoot exponential constants greater than 0;

[0099] Introduce a strictly monotonically increasing logarithmic barrier function as the error transformation function τ(z1):

[0100]

[0101] where z1 is the transformed error; through equation (34), the constrained tracking error is converted into an unconstrained transformed error z1 ∈ R, and satisfies the following conditions:

[0102]

[0103] According to the properties of τ(z1), the constraint conditions are transformed into the following equivalent conditions:

[0104] e(t) = μ(t)τ(z1) (36)

[0105] Then for any initial error e(0), select appropriate parameters δ1, δ2 and μ0 such that -δ1μ0 < e(0) < δ2μ0 holds, and control the transformed error z1 to be bounded, that is, ensure that the constraint conditions are satisfied;

[0106] Furthermore, since the error transformation function τ(z1) is a strictly monotonically increasing function, and the preset performance function μ(t) > 0. Therefore, the transformed error z1 is expressed as:

[0107]

[0108] Differentiating z1, we get:

[0109]

[0110] Furthermore, regarding By differentiation, we obtain:

[0111]

[0112] In the formula, e represents the front wheel steering angle error; The derivative of the front wheel steering angle error is given by μ; μ is the preset performance function. The derivative of the preset performance function; δ f J is the front wheel steering angle; eff and b eff These represent the equivalent moment of inertia and equivalent damping of the steering actuator on the steering wheel, respectively; τ f The frictional resistance torque of the steering actuator; τ a It is the sum of the restoring torques of the left and right front wheels around their respective kingpins;

[0113] Using non-singular fast terminal sliding mode control, the established sliding surface is as follows:

[0114]

[0115] In the formula, z1 is the transformation error; α1, α2, γ1, and γ2 are all control parameters to be adjusted; α1>0, α2>0, γ1>γ2, 1<γ2<2, and we have:

[0116]

[0117] In the formula, q1, q2, p1, and p2 are positive odd numbers;

[0118] Take the derivative with respect to the sliding surface s, and then calculate the second derivative of z1. Substituting the values, we get:

[0119]

[0120] make Equivalent control law u eq Its function is to maintain the system's motion on the sliding surface:

[0121]

[0122] The fast terminal sliding mode convergence law is designed as follows:

[0123]

[0124] In the formula, β1, β2 and ρ are adjustable control parameters, β1>0, β2>0, 0<ρ<1;

[0125] Based on this approach law, the switching control law u can be obtained. sw for:

[0126]

[0127] Switch control law u sw With equivalent control law u eq Combining these, we obtain the overall control law u of the steering fault-tolerant sliding mode controller:

[0128] u = u eq +u sw (49)

[0129] Furthermore, the specific method for step three is as follows:

[0130] 31) Taking the minimum overall adhesion utilization rate of the four wheels and tires as the optimization objective, the optimization objective function is designed as follows:

[0131]

[0132] In the formula, c ij F represents the weighting coefficient corresponding to each wheel. lij and F cij These are the longitudinal and lateral forces of the four wheels, respectively; F zij For the vertical load of the four wheels; μ ij The road surface adhesion coefficient;

[0133] 32) The optimization objective is simplified to:

[0134]

[0135] 33) While satisfying the driving force distribution requirements of the other controllers, considering the limitations on the maximum output torque of the hub motor and the road surface adhesion conditions, the final constraint conditions are as follows:

[0136]

[0137] In the formula, F t_exp Total driving force requirement; ΔM z To add yaw moment; M f ′ represents the differential torque; F tij B represents the magnitude of the driving force on the four wheels. f B is the front axle track width; r Rear axle track width; δ f Front wheel steering angle; l f and l r F represents the distance from the vehicle's center of gravity to the front and rear axles.zij T represents the vertical load on the wheel. ij_max γ is the maximum driving torque of the motor; σ is the kingpin backcurve angle; δ is the kingpin inclination angle; f The front wheel steering angle; r σ Master pin offset; μ ij r is the road surface adhesion coefficient; r is the wheel radius;

[0138] 34) The optimization problem can be expressed in L2 norm form as follows:

[0139]

[0140] In the formula, minimizing the first part increases the vehicle's stability margin, while the second part is used to meet the torque requirements of the remaining controllers; W u W v is a diagonal weighted matrix; γ is the weight coefficient, whose value determines the relative importance of the two optimization objectives;

[0141] 35) The diagonal weighted matrix is ​​represented as:

[0142]

[0143] In the formula, c ij The value of W affects u The weight distribution between the longitudinal forces of the wheels is set; W v This is used to allocate the weights between the control torques of each target;

[0144] 36) Boundary conditions for control variables are expressed in the following form:

[0145]

[0146] In the formula, u max The upper bound of the variable; u min F is the lower bound of the variable; tij,max This is the maximum driving force of the wheels;

[0147] 37) Apply the effective set method to solve the convex quadratic programming problem, obtain the optimal driving force of the four wheels, and then obtain the driving torque of the four wheels.

[0148] The beneficial effects of this invention are as follows:

[0149] 1. This invention uses a model predictive control algorithm to establish a path tracking controller, comprehensively considering the vehicle's mechanical structure and motion conditions as multiple constraints to ensure that the vehicle has good environmental adaptability. At the same time, it uses multi-dimensional state variables to participate in model predictive control to improve the path tracking control accuracy of the vehicle.

[0150] 2. This invention establishes a dynamic model of the steering actuator, fully considering the effects of return torque and frictional resistance torque, ensuring the simulation accuracy of the model, and designs a control strategy based on the differential drive assisted steering principle to ensure that the steering control can be carried out normally when the vehicle steering actuator fails, i.e. there is no steering wheel hand force input, thereby ensuring that the vehicle can complete the path tracking fault-tolerant driving task.

[0151] 3. This invention employs a non-singular fast terminal sliding mode control method to establish a steering fault-tolerant controller, which significantly improves the fault-tolerant control performance and avoids singular phenomena. At the same time, it designs preset performance functions and error transformation functions to optimize the transient performance of the fault-tolerant controller, such as convergence speed and convergence error, thereby improving the response speed and control effect of vehicle fault-tolerant control. Attached Figure Description

[0152] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0153] Figure 1 A diagram of a finite-time path tracking fault-tolerant control architecture that takes into account steering actuator failure;

[0154] Figure 2 This is a schematic diagram of a three-degree-of-freedom vehicle dynamics model;

[0155] Figure 3 A schematic diagram illustrating the principle of differential drive-assisted steering;

[0156] Figure 4a This is a schematic diagram of the lateral position results in a simulation experiment of a single lane-changing condition.

[0157] Figure 4b A schematic diagram showing the longitudinal vehicle speed results in a single lane change simulation experiment.

[0158] Figure 4c This is a schematic diagram of the yaw angle results from a simulation experiment of a single lane change condition.

[0159] Figure 4d This is a schematic diagram of the yaw rate results from a simulation experiment of a single lane change condition. Detailed Implementation

[0160] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, the accompanying drawings show only the parts relevant to the present invention, and not all of the structures.

[0161] Example 1

[0162] See Figure 1 This embodiment provides a fault-tolerant control method for finite-time path tracking of automobiles that considers steering actuator failure, including the following steps:

[0163] Step 1: Establish the vehicle dynamics model and the steering actuator dynamics model, and design the path tracking control strategy using model predictive control methods to establish the upper-level path tracking controller. The path tracking controller based on model predictive control takes vehicle state variables as inputs, including longitudinal position x, lateral position y, yaw angle ψ, and longitudinal speed v. x Lateral speed v y and yaw rate ω r After linearizing and discretizing the model, a prediction equation is constructed, and the desired front wheel steering angle δ is solved using a quadratic programming method. f The details are as follows:

[0164] 11) Establish a vehicle dynamics model for the establishment of a path tracking controller;

[0165] Assuming the vehicle's left and right sides are dynamically symmetrical, and neglecting vertical, pitch, and roll motions, we establish the following... Figure 2 The 3-DOF vehicle dynamics model shown, combined with the small-angle assumption, is expressed as follows:

[0166]

[0167] In the formula, m is the total vehicle mass; and These represent the vehicle's longitudinal and lateral speeds, respectively; ψ is the yaw angle; F yf and F yr These represent the total lateral forces of the front and rear axle tires, respectively; I z The yaw moment of inertia of the vehicle; f and l r These are the distances from the vehicle's center of gravity to the front and rear axles, respectively; ΔM z To add yaw moment;

[0168] In the vehicle dynamics model, the longitudinal lateral forces of the tires are represented as follows:

[0169] F ci =C ci α i (i=f,r) (4)

[0170] In the formula, C ci For tire lateral stiffness, α i This refers to the tire slip angle;

[0171] Based on the small angle assumption, the tire slip angle is expressed as:

[0172]

[0173] In the formula, v x and v y For longitudinal and lateral vehicle speeds; The yaw rate is l. f and l r δ represents the distance from the vehicle's center of gravity to the front and rear axles. f The steering angle of the front wheels;

[0174] Finally, the state-space equation expression of the vehicle dynamics system is obtained as follows:

[0175]

[0176] In the formula, For system state variables; u = (δ f ) represents the system control variable, where δ f When steering fails, it represents the desired front wheel steering angle, which is a virtual control quantity; This is the system output quantity;

[0177] 12) Perform dynamic modeling of the steering actuator;

[0178] When a vehicle is steering, the forces acting on the steering actuator include the total self-centering torque, the steering torque, and the frictional resistance torque of the steering actuator. Furthermore, if the inertia and damping of the vehicle's steering actuator are all equated to the steering wheel, the steering actuator simplifies to a second-order system with one degree of freedom, and its dynamic model can be expressed as:

[0179]

[0180] In the formula, δ f J is the front wheel steering angle; eff and b eff These represent the equivalent moment of inertia and equivalent damping of the steering actuator on the steering wheel, respectively; T eq τ is the wheel drive torque. f The frictional resistance torque of the steering actuator; τ a It is the sum of the restoring torques of the left and right front wheels around their respective kingpins;

[0181] For a single wheel, the restoring torque around the kingpin can be considered to consist of three parts:

[0182] τ sz =F z ×cosγsinσsinδ f cosσ(r σ +rtanσ) (8)

[0183] τ sy =F y ×rsinγcosσ (9)

[0184] τ zz =M z ×cosγcosσ (10)

[0185] In the formula, τ sz The restoring torque τ is caused by the weight of the front axle. sy The restoring torque τ is caused by the lateral force between the tire and the ground. zz F is the component of the tire's self-aligning torque about its kingpin direction. z For the vertical load on the wheel; F y M is the lateral force of the wheel; z The self-aligning torque of the tire; γ is the caster angle; σ is the inclination angle; δ f The front wheel steering angle; r σ The kingpin offset is r; the wheel radius is r.

[0186] 13) Design a path tracking control strategy;

[0187] For the established state-space equations of the vehicle system at any point (ξ) r ,u r Perform a Taylor series expansion at () and retain only the first-order terms of the expanded equation, ignoring the higher-order terms, to obtain an approximately linearized model, as shown below:

[0188]

[0189] In the formula, ξ is the vehicle system state variable; ξ is the derivative of the system state variable; u is the system control variable; ξ is the derivative of the system state variable. r This is the reference value for the system state variables; u r f(ξ) is the reference value for system control input; r ,u r ) is in reference state ξ r and reference control input u r The system dynamic function under;

[0190] Combine the above formula with The difference, expressed in incremental form, is the error model for path tracking control:

[0191]

[0192] In the formula, The derivative of the system state variable error; This refers to the error in the system state variables; Let A be the system control error; let B be the Jacobian matrix of f with respect to ξ; let C be the Jacobian matrix of f with respect to u.

[0193]

[0194] In the formula, The derivative of the system state variable error; The derivative of the system state variables; This serves as a reference value for the differential of the system state variables; ξ is the system state variable error; ξ is the system state variable; r This serves as a reference value for system state variables. U is the system control error; u is the system control quantity; u r This is a reference value for system control variables;

[0195] The forward Euler method, a technique used in approximate discretization, replaces the differential in the state-space equations with a first-order difference quotient, i.e.:

[0196]

[0197] In the formula, The derivative of the system state error at time step k; The error in the system state at time step k+1; Let T be the system state error at time step k, and T be the sampling time.

[0198] The state-space expression for the discrete vehicle dynamics model is then:

[0199]

[0200] In the formula, A(k) = I + TA(t), B(k) = TB(t), I is the identity matrix, let

[0201]

[0202] In the formula, x(k|t) is the extended state vector composed of state quantity error and control quantity error at time step k predicted at time t; The error of the state quantity at time step k when predicted at time t; The control error at time step k-1 predicted at time t;

[0203] The updated state-space equations of the vehicle dynamics system are then expressed as:

[0204]

[0205] In the formula, x(k+1|t) is the extended state vector predicted at time step k at time k+1; x(k|t) is the extended state vector predicted at time step k at time t; Δu(k|t) is the control increment predicted at time step k at time t; and η(k|t) is the output quantity predicted at time step k at time t. The state matrix; To control the increment matrix; The output matrix is ​​shown below:

[0206]

[0207] Let the prediction time domain be N. p The control time domain is N c And there are N p ≤N c The predicted output of the vehicle dynamics system in the prediction time domain is expressed as:

[0208]

[0209] In the formula, η(k+N) p |k) represents the predicted time step k+N at time step k. p Output quantity at time; Δu(k+N) c -1) represents time step k+N c The system control increment at -1;

[0210] The predicted output of the vehicle dynamics system described in equation (19) can be expressed in matrix form:

[0211] Y(k)=ψ(k)x(k)+θ(k)ΔU(k) ​​(20)

[0212] Furthermore, based on the quadratic programming method, the objective function of the path tracking model predictive control is defined as follows:

[0213]

[0214] In the objective function J, the first term reflects the control objective of the controller to ensure that the vehicle system tracks the target path efficiently and with high precision; its value is N in the prediction time domain. p The first term represents the deviation between the system's predicted output and the reference output; the second term reflects the controller's control objective of maintaining vehicle stability, and its value is N in the control time domain. c Within, the system controls the magnitude of the increment;

[0215] In the formula, η(t+i|t) is the actual output vector, η ref (t+i|t) is the reference output vector, as shown in the following equation: Δu(t+i|t) is the control increment, q∈R 3×3The weight matrix for tracking accuracy is used to adjust the emphasis placed on path tracking performance during the solution process, R∈R 2×2 The weight matrix for controlling the increments has values ​​related to the smoothness of changes in each control variable:

[0216]

[0217] In the formula, For reference yaw rate; ψ ref (t+i|t) is the reference yaw angle; Y ref (t+i|t) is the reference lateral displacement;

[0218] Meanwhile, in order to avoid the situation where the control system has no feasible solution, a relaxation factor ε is introduced into the objective function, ε>0, so that when there is no optimal solution, the system will use the obtained suboptimal solution as a substitute, and ρ is the weight coefficient of ε.

[0219] The objective function of the path tracing control program can be expressed in standard quadratic form as follows:

[0220] minJ(ξ(t),u(t-1),ΔU(t))=min[ΔU(t) T ,ε]H t [ΔU(t) T ,ε] T +G t [ΔU(t) T ,ε](23)

[0221] In the formula, ξ(t) is the state variable; u(t-1) is the control variable at the previous time step; ΔU(t) is the control variable increment;

[0222]

[0223] Due to limitations in the vehicle's mechanical structure and motion constraints, the following constraints need to be applied to the control variables and some state variables:

[0224]

[0225] Equation (25) represents the constraints for the control increment, control quantity, output quantity, and the sideslip angle and lateral acceleration of the center of mass, respectively.

[0226] By combining the objective function and constraints, the optimal vehicle control increment sequence in the control time domain is obtained:

[0227] ΔU t =[Δu(t),Δu(t+1),…,Δu(t+N c -1)] T (26)

[0228] Take the first term as the control increment, which is applied to the vehicle system, i.e.

[0229]

[0230] Step 2: Based on the differential drive assisted steering principle, combined with the preset performance control method and non-singular fast terminal sliding mode control theory, establish a fault-tolerant controller for the steering actuator, and set the desired front wheel steering angle δ. f Converted to additional yaw moment M f And ensure that the control error converges to the preset boundary within a finite time, as follows:

[0231] 21) Establish a dynamic model of the steering actuator;

[0232] In distributed drive electric vehicles, the four-wheel hub motors can independently control the driving torque of each wheel, ensuring that the driving torques of the left and right wheels are different. This results in a significant difference in the torque generated around the kingpin by each wheel. This difference can be used to overcome the wheel's self-centering torque and steering system friction torque, enabling the wheels to steer without manual steering input. Figure 3 As shown.

[0233] The torques generated around the kingpin by the driving forces of the left and right wheels are as follows:

[0234]

[0235] In the formula, F tfl and F tfr These represent the longitudinal driving forces of the left and right wheels on the front axle, respectively; r σ Kingpin offset; γ is kingpin caster angle; σ is kingpin inclination angle.

[0236] The difference between the torques generated by the left and right wheels around their respective kingpins gives the front axle differential torque M. f 'as follows:

[0237] M f ′=τ dsr -τ dsl =(F tfr -F tfl )r σ cosγcosσ (29)

[0238] Therefore, in order to achieve differential drive assisted steering, the differential torque M needs to be set... f Wheel drive torque T in the alternative steering actuator dynamics model eq Once control is achieved, the dynamic model of the steering actuator can be expressed in the following form:

[0239]

[0240] In the formula, δ f J is the front wheel steering angle; eff and b eff These represent the equivalent moment of inertia and equivalent damping of the steering actuator on the steering wheel, respectively; M f ′ represents the differential torque; τ f The frictional resistance torque of the steering actuator; τ a It is the sum of the restoring torques of the left and right front wheels around their respective kingpins;

[0241] 22) Design fault-tolerant control laws;

[0242] Define the control error of the steering actuator as:

[0243] e = δ fd -δ f =x 1d -x1 (31)

[0244] In the formula, e is the front wheel steering angle error; δ fd δ is the desired front wheel steering angle. f x is the actual front wheel steering angle; 1d x1 and x1 are chosen as symbols for ease of representation;

[0245] To match the requirements of the steering fault-tolerant controller in terms of transient convergence speed, overshoot, and steady-state accuracy, a positive definite and monotonically decreasing exponentially decaying smooth function is selected as the preset performance function:

[0246]

[0247] In the formula, μ0>μ ∞ >0, κ>0 are both constants, μ0=μ(0)≥|e(0)|;

[0248] Based on the preset performance function, the tracking error of the front wheel steering angle is constrained within the required boundary. The constraint relationship is specifically expressed as follows:

[0249]

[0250] In the formula, δ1 and δ2 are both overshoot exponential constants greater than 0;

[0251] The direct constraint on the tracking error makes controller design difficult. Therefore, a strictly monotonically increasing logarithmic barrier function is introduced as the error transformation function τ(z1):

[0252]

[0253] where \(z_1\) is the transformation error; the constrained tracking error is converted into an unconstrained transformation error \(z_1\in R\) through Equation (34), and the following conditions are satisfied:

[0254]

[0255] According to the properties of \(\tau(z_1)\), the constraint conditions are transformed into the following equivalent conditions:

[0256] \(e(t)=\mu(t)\tau(z_1)\ (36)\)

[0257] Then, for any initial error \(e(0)\), appropriate parameters \(\delta_1\), \(\delta_2\) and \(\mu_0\) are selected such that \(-\delta_1\mu_0 < e(0) < \delta_2\mu_0\) holds, and the control transformation error \(z_1\) is bounded, that is, the constraint conditions are guaranteed to be satisfied;

[0258] Furthermore, since the error transformation function \(\tau(z_1)\) is a strictly monotonically increasing function and the preset performance function \(\mu(t)>0\). Therefore, the transformation error \(z_1\) is expressed as:

[0259]

[0260] Differentiating \(z_1\) gives:

[0261]

[0262] Furthermore, differentiating gives:

[0263]

[0264] where \(e\) is the front wheel steering angle error; is the derivative of the front wheel steering angle error; \(\mu\) is the preset performance function; is the derivative of the preset performance function; \(\delta\) f is the front wheel steering angle; \(J\) eff and \(b\) eff are the equivalent moment of inertia and equivalent damping of the steering actuator on the steering wheel respectively; \(\tau\) f is the frictional torque of the steering actuator; \(\tau\) a is the sum of the return torques of the left front wheel and the right front wheel around their respective kingpins;

[0265] In order to improve the control performance of the steering fault-tolerant controller and avoid singularity phenomena, non-singular fast terminal sliding mode control is adopted, and the established sliding mode surface is as follows:

[0266]

[0267] In the formula, z1 is the transformation error; α1, α2, γ1, and γ2 are all control parameters to be adjusted; α1>0, α2>0, γ1>γ2, 1<γ2<2, and we have:

[0268]

[0269] In the formula, q1, q2, p1, and p2 are positive odd numbers;

[0270] Take the derivative with respect to the sliding surface s, and then calculate the second derivative of z1. Substituting the values, we get:

[0271]

[0272] make Equivalent control law u eq Its function is to maintain the system's motion on the sliding surface:

[0273]

[0274] To ensure that the system can quickly approach the sliding surface when deviating from it, a fast terminal sliding surface approach law is designed as follows:

[0275]

[0276] In the formula, β1, β2 and ρ are adjustable control parameters, β1>0, β2>0, 0<ρ<1;

[0277] Based on this approach law, the switching control law u can be obtained. sw for:

[0278]

[0279] Switch control law u sw With equivalent control law u eq Combining these, we obtain the overall control law u of the steering fault-tolerant sliding mode controller:

[0280] u = u eq +u sw (49)

[0281] Step 3: Design a torque distribution controller using optimal control theory, and solve for the optimal four-wheel drive torque control quantity using quadratic programming, as detailed below:

[0282] The outputs of the upper-level path tracking controller and steering fault-tolerant controller include information on the additional yaw moment ΔM. z Differential torque demand M f ′, Total vertical demand driver F x The torque distribution controller employs an optimal control method to integrate the above constraints and complete the four-wheel drive force distribution control.

[0283] 31) To ensure vehicle stability, the optimization objective is to minimize the overall adhesion utilization rate of the four tires. The optimization objective function is designed as follows:

[0284]

[0285] In the formula, c ij F represents the weighting coefficient corresponding to each wheel. lij and F cij These are the longitudinal and lateral forces of the four wheels, respectively; F zij For the vertical load of the four wheels; μ ij The road surface adhesion coefficient;

[0286] 32) Under certain extreme conditions, since the longitudinal and lateral forces of the tire are coupled, the stability margin of its lateral forces can be indirectly improved by reducing the longitudinal force of the tire. Therefore, the optimization objective can be simplified to:

[0287]

[0288] 33) While satisfying the driving force distribution requirements of the other controllers, considering the limitations on the maximum output torque of the hub motor and the road surface adhesion conditions, the final constraint conditions are as follows:

[0289]

[0290] In the formula, F t_exp Total driving force requirement; ΔM z To add yaw moment; M f ′ represents the differential torque; F tij B represents the magnitude of the driving force on the four wheels. f B is the front axle track width; r Rear axle track width; δ f Front wheel steering angle; l f and l r F represents the distance from the vehicle's center of gravity to the front and rear axles. zij T represents the vertical load on the wheel. ij_max γ is the maximum driving torque of the motor; σ is the kingpin backcurve angle; δ is the kingpin inclination angle; f The front wheel steering angle; r σ Master pin offset; μ ij r is the road surface adhesion coefficient; r is the wheel radius;

[0291] 34) The optimization problem can be expressed in L2 norm form as follows:

[0292]

[0293] In the formula, minimizing the first part increases the vehicle's stability margin, while the second part is used to meet the torque requirements of the remaining controllers; W u W v is a diagonal weighted matrix; γ is the weight coefficient, whose value determines the relative importance of the two optimization objectives;

[0294] 35) The diagonal weighted matrix is ​​represented as:

[0295]

[0296] In the formula, c ij The value of W affects u The weight distribution between the longitudinal forces of the wheels is set; W v This is used to allocate the weights between the control torques of each target;

[0297] 36) Boundary conditions for control variables are expressed in the following form:

[0298]

[0299] In the formula, u max The upper bound of the variable; u min F is the lower bound of the variable; tij,max This is the maximum driving force of the wheels;

[0300] 37) Finally, the effective set method is applied to solve the convex quadratic programming problem to obtain the optimal driving force of the four wheels, and then the driving torque of the four wheels is obtained.

[0301] Example 2

[0302] To verify the effectiveness of the path tracking fault-tolerant control strategy designed in this invention, a simulation experiment was conducted under a single lane-change condition. A control group was set up to compare and analyze whether the strategy has significant fault-tolerant control functionality. The operating condition was set as follows: the target vehicle speed was 54 km / h, and three types of test vehicles were used: a fault-free vehicle A (blue), a faulty vehicle B (red) without fault-tolerant control, and a faulty vehicle C (green) with a fault-tolerant control system. The experimental results are as follows: Figure 4a , Figure 4b , Figure 4c and Figure 4d As shown, the target path is represented by a black dashed line.

[0303] Depend on Figure 4aAs can be seen, when the test vehicle was traveling at a speed of 54 km / h on a road surface with good adhesion and following a single lane change path, the vehicle C equipped with the path tracking fault-tolerant control system could still track the target path with high path tracking accuracy during the tracking process. Moreover, the error was small compared with the path of the fault-free vehicle A, and the two curves almost overlapped. The maximum longitudinal error was about 0.004m, indicating that the fault-tolerant control strategy had a good effect on controlling the path tracking accuracy.

[0304] At the same time, by Figure 4b It can be seen that although the longitudinal speed of the fault-tolerant vehicle fluctuates to some extent during driving, its value is always maintained within 1 km / h above and below the target speed, indicating that the vehicle's dynamics are not significantly affected during the fault-tolerant control process.

[0305] Depend on Figure 4c , 4d It can be seen that when the vehicle is equipped with fault-tolerant control, the changes in its yaw angle and yaw rate are the same as those under fault-free conditions, and the curves fit closely, indicating that the fault-tolerant control has a significant effect on controlling the vehicle's yaw motion.

[0306] In summary, through simulation verification and comparative analysis, the distributed drive electric vehicle path tracking fault-tolerant control strategy designed in this invention, which considers the failure of the drive actuator, has good control performance under typical operating conditions. When the drive actuator fails, it can ensure the path tracking accuracy and driving stability of the vehicle through fault-tolerant control, and under this premise, it hardly loses power, thus meeting the control requirements.

[0307] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A path tracking preset performance fault-tolerant control method considering vehicle steering failure, characterized in that, Includes the following steps: Step 1: Establish vehicle dynamics model and steering actuator dynamics model, and apply model predictive control method to design path tracking control strategy and establish upper-level path tracking controller; Step 2: Based on the differential drive assisted steering principle, combined with the preset performance control method and non-singular fast terminal sliding mode control theory, establish a fault-tolerant controller for the steering actuator, and set the desired front wheel steering angle δ. f Converted to additional yaw moment M f And ensure that the control error converges to the preset boundary within a finite time; Step 3: Design a torque distribution controller using optimal control theory, and solve for the optimal four-wheel drive torque control quantity through quadratic programming.

2. The path tracking preset performance fault-tolerant control method considering vehicle steering failure as described in claim 1, characterized in that, The specific method for step one is as follows: 11) Establish a vehicle dynamics model for the establishment of a path tracking controller; Assuming the vehicle's left and right sides are dynamically symmetrical, and neglecting vertical, pitch, and roll motions, a 3-DOF vehicle dynamics model is established. Combined with the small-angle assumption, it is expressed as follows: In the formula, m is the total vehicle mass; and These represent the vehicle's longitudinal and lateral speeds, respectively; ψ is the yaw angle; F yf and F yr These represent the total lateral forces of the front and rear axle tires, respectively; I z The yaw moment of inertia of the vehicle; f and l r These are the distances from the vehicle's center of gravity to the front and rear axles, respectively; ΔM z To add yaw moment; In the vehicle dynamics model, the longitudinal lateral forces of the tires are represented as follows: F ci =C ci α i ,(i=f,r) (4) In the formula, C ci For tire lateral stiffness, α i This refers to the tire slip angle; Based on the small angle assumption, the tire slip angle is expressed as: In the formula, v x and v y For longitudinal and lateral vehicle speeds; The yaw rate; l f and l r δ represents the distance from the vehicle's center of gravity to the front and rear axles. f The steering angle of the front wheels; Finally, the state-space equation expression of the vehicle dynamics system is obtained as follows: In the formula, For system state variables; u = (δ f ) represents the system control variable, where δ f When steering fails, it represents the desired front wheel steering angle, which is a virtual control quantity; This is the system output quantity; 12) Perform dynamic modeling of the steering actuator; When a vehicle is steering, the forces acting on the steering actuator include the total self-centering torque, the steering torque, and the frictional resistance torque of the steering actuator. Furthermore, if the inertia and damping of the vehicle's steering actuator are all equated to the steering wheel, the steering actuator simplifies to a second-order system with one degree of freedom, and its dynamic model can be expressed as: In the formula, δ f J is the front wheel steering angle; eff and b eff These represent the equivalent moment of inertia and equivalent damping of the steering actuator on the steering wheel, respectively; T eq τ is the wheel drive torque. f The frictional resistance torque of the steering actuator; τ a It is the sum of the restoring torques of the left and right front wheels around their respective kingpins; For a single wheel, the restoring torque around the kingpin can be considered to consist of three parts: t sz =F z ×cosγsinσsinδ f cosσ(r σ +rtanσ) (8) t sy =F y ×rsinγcosσ (9) t zz =M z ×cosγcosσ (10) In the formula, τ sz The restoring torque τ is caused by the weight of the front axle. sy The restoring torque τ is caused by the lateral force between the tire and the ground. zz F is the component of the tire's self-aligning torque about its kingpin direction. z For the vertical load on the wheel; F y M is the lateral force of the wheel; z The self-aligning torque of the tire; γ is the caster angle; σ is the inclination angle; δ f The front wheel steering angle; r σ The kingpin offset is r; the wheel radius is r. 13) Design a path tracking control strategy; For the established state-space equations of the vehicle system at any point (ξ) r ,u r Perform a Taylor series expansion at () and retain only the first-order terms of the expanded equation, ignoring the higher-order terms, to obtain an approximately linearized model, as shown below: In the formula, ξ is the vehicle system state variable; ξ is the derivative of the system state variable; u is the system control variable; ξ is the derivative of the system state variable. r This is the reference value for the system state variables; u r f(ξ) is the reference value for system control input; r ,u r ) is in reference state ξ r and reference control input u r The system dynamic function under; Combine the above formula with The difference, expressed in incremental form, is the error model for path tracking control: In the formula, The derivative of the system state variable error; This refers to the error in the system state variables; Let A be the system control error; let B be the Jacobian matrix of f with respect to ξ; let C be the Jacobian matrix of f with respect to u. In the formula, The derivative of the system state variable error; The derivative of the system state variables; This serves as a reference value for the differential of the system state variables; ξ is the system state variable error; ξ is the system state variable; r This serves as a reference value for system state variables. U is the system control error; u is the system control quantity; u r This is a reference value for system control variables; The forward Euler method, a technique used in approximate discretization, replaces the differential in the state-space equations with a first-order difference quotient, i.e.: In the formula, The derivative of the system state error at time step k; The error in the system state at time step k+1; Let T be the system state error at time step k, and T be the sampling time. The state-space expression for the discrete vehicle dynamics model is then: In the formula, A(k) = I + TA(t), B(k) = TB(t), I is the identity matrix, let In the formula, x(k|t) is the extended state vector composed of state quantity error and control quantity error at time step k predicted at time t; The error of the state quantity at time step k when predicted at time t; The control error at time step k-1 predicted at time t; The updated state-space equations of the vehicle dynamics system are then expressed as: In the formula, x(k+1|t) is the extended state vector predicted at time step k at time k+1; x(k|t) is the extended state vector predicted at time step k at time t; Δu(k|t) is the control increment predicted at time step k at time t; and η(k|t) is the output quantity predicted at time step k at time t. The state matrix; To control the increment matrix; The output matrix is ​​shown below: Let the prediction time domain be N. p The control time domain is N c And there are N p ≤N c The predicted output of the vehicle dynamics system in the prediction time domain is expressed as: In the formula, η(k+N) p |k) represents the predicted time step k+N at time step k. p Output quantity at time; Δu(k+N) c -1) represents time step k+N c The system control increment at -1; The predicted output of the vehicle dynamics system described in equation (19) can be expressed in matrix form: Y(k)=ψ(k)x(k)+θ(k)ΔU(k) ​​(20) Furthermore, based on the quadratic programming method, the objective function of the predictive control of the path tracking model is defined. The number is: In the objective function J, the first term reflects the control objective of the controller to ensure that the vehicle system tracks the target path efficiently and with high precision; its value is N in the prediction time domain. p The first term represents the deviation between the system's predicted output and the reference output; the second term reflects the controller's control objective of maintaining vehicle stability, and its value is N in the control time domain. c Within, the system controls the magnitude of the increment; In the formula, η(t+i|t) is the actual output vector, η ref (t+i|t) is the reference output vector, as shown in the following equation: Δu(t+i|t) is the control increment, Q∈R 3×3 The weight matrix for tracking accuracy is used to adjust the emphasis placed on path tracking performance during the solution process, R∈R 2×2 The weight matrix for controlling the increments has values ​​related to the smoothness of changes in each control variable: In the formula, For reference yaw rate; ψ ref (t+i|t) is the reference yaw angle; Y ref (t+i|t) is the reference lateral displacement; A relaxation factor ε is introduced into the objective function, where ε>0, so that when there is no optimal solution, the system will use the obtained suboptimal solution as a substitute, and ρ is the weighting coefficient of ε. The objective function of the path tracing control program can be expressed in standard quadratic form as follows: minJ(ξ(t),u(t-1),ΔU(t))=min[ΔU(t) T ,e]H t [ΔU(t) T ,e] T +G t [ΔU(t) T ,e](23) In the formula, ξ(t) is the state variable; u(t-1) is the control variable at the previous time step; ΔU(t) is the control variable increment; G t =[2E(t) T Qθ t ];E(t)=-Y ref (t)(24) Due to limitations in the vehicle's mechanical structure and motion constraints, the following constraints need to be applied to the control variables and some state variables: Equation (25) represents the constraints for the control increment, control quantity, output quantity, and the sideslip angle and lateral acceleration of the center of mass, respectively. By combining the objective function and constraints, the optimal vehicle control increment sequence in the control time domain is obtained: D.U. t =[Δu(t),Δu(t+1),…,Δu(t+N c -1)] T (26) Take the first term as the control increment, which is applied to the vehicle system, i.e.

3. The path tracking preset performance fault-tolerant control method considering vehicle steering failure as described in claim 1, characterized in that, The specific method for step two is as follows: 21) Establish a dynamic model of the steering actuator; The torques generated around the kingpin by the driving forces of the left and right wheels are as follows: In the formula, F tfl and F tfr These represent the longitudinal driving forces of the left and right wheels on the front axle, respectively; r σ Kingpin offset; γ is kingpin caster angle; σ is kingpin inclination angle. The difference between the torques generated by the left and right wheels around their respective kingpins gives the front axle differential torque M. f 'as follows: M f ′=τ dsr -t dsl =(F tfr -F tfl )r σ cosγcosσ (29) To achieve differential drive assisted steering, the differential torque M needs to be set... f Wheel drive torque T in the alternative steering actuator dynamics model eq Once control is achieved, the dynamic model of the steering actuator can be expressed in the following form: In the formula, δ f J is the front wheel steering angle; eff and b eff These represent the equivalent moment of inertia and equivalent damping of the steering actuator on the steering wheel, respectively; M f ′ represents the differential torque; τ f The frictional resistance torque of the steering actuator; τ a It is the sum of the restoring torques of the left and right front wheels around their respective kingpins; 22) Design fault-tolerant control laws; Define the control error of the steering actuator as: e=δ fd -d f =x 1d -x1 (31) In the formula, e is the front wheel steering angle error; δ fd δ is the desired front wheel steering angle. f x is the actual front wheel steering angle; 1d x1 and x1 are chosen as symbols for ease of representation; We select a positive definite and monotonically decreasing exponentially decaying smooth function as the preset performance function: In the formula, μ0>μ ∞ >0, κ>0 are both constants, μ0=μ(0)≥|e(0)|; According to the preset performance function, the tracking error of the front wheel steering angle is constrained within the required boundary, and the constraint relationship is specifically expressed as: In the formula, both δ1 and δ2 are overshoot index constants greater than 0; Introduce a strictly monotonically increasing logarithmic barrier function as the error transformation function τ(z1): In the formula, z1 is the transformed error; through formula (34), the constrained tracking error is converted into an unconstrained transformed error z1∈R, and the following conditions are satisfied: According to the properties of τ(z1), the constraint conditions are transformed into the following equivalent conditions: e(t) = μ(t)τ(z1) (36) Then for any initial error e(0), select appropriate parameters δ1, δ2 and μ0 such that -δ1μ0 < e(0) < δ2μ0 holds, and control the transformed error z1 to be bounded, that is, ensure that the constraint conditions are satisfied; Furthermore, since the error transformation function τ(z1) is a strictly monotonically increasing function, and the preset performance function μ(t) > 0. Therefore, the transformed error z1 is expressed as: Differentiate z1 to obtain: Furthermore, regarding By differentiation, we obtain: In the formula, e represents the front wheel steering angle error; The derivative of the front wheel steering angle error is given by μ; μ is the preset performance function. The derivative of the preset performance function; δ f J is the front wheel steering angle; eff and b eff These represent the equivalent moment of inertia and equivalent damping of the steering actuator on the steering wheel, respectively; τ f The frictional resistance torque of the steering actuator; τ a It is the sum of the restoring torques of the left and right front wheels around their respective kingpins; Adopt non-singular fast terminal sliding mode control, and the established sliding mode surface is as follows: In the formula, z1 is the transformed error; α1, α2, γ1, γ2 are all control parameters to be adjusted; α1 > 0, α2 > 0, γ1 > γ2, 1 < γ2 < 2, and there is: In the formula, q1, q2, p1, p2 are positive odd numbers; Take the derivative with respect to the sliding surface s, and then calculate the second derivative of z1. Substituting the values, we get: make Equivalent control law u eq Its function is to maintain the system's motion on the sliding surface: Design the fast terminal sliding mode reaching law as shown below: In the formula, β1, β2 and ρ are adjustable control parameters, β1 > 0, β2 > 0, 0 < ρ < 1; Based on this approach law, the switching control law u can be obtained. sw for: Switch control law u sw With equivalent control law u eq Combining these, we obtain the overall control law u of the steering fault-tolerant sliding mode controller: in=in eq +in sw (49).

4. The path tracking preset performance fault-tolerant control method considering vehicle steering failure as described in claim 1, characterized in that, The specific method of step three is as follows: 31) Take the minimum comprehensive adhesion utilization rate of the four-wheel tires as the optimization objective, and design the form of the optimization objective function as follows: In the formula, c ij F represents the weighting coefficient corresponding to each wheel. lij and F cij These are the longitudinal and lateral forces of the four wheels, respectively; F zij For the vertical load of the four wheels; μ ij The road surface adhesion coefficient; 32) Simplify the optimization objective to: 33) While meeting the driving force distribution requirements of the rest of the controller, consider the limitations of the maximum output torque of the hub motor and the road surface adhesion conditions, then the final constraint conditions obtained are: In the formula, F t_exp Total driving force requirement; ΔM z To add yaw moment; M f ′ represents the differential torque; F tij B represents the magnitude of the driving force on the four wheels. f B is the front axle track width; r Rear axle track width; δ f Front wheel steering angle; l f and l r F represents the distance from the vehicle's center of gravity to the front and rear axles. zij T represents the vertical load on the wheel. ij_max γ is the maximum driving torque of the motor; σ is the kingpin backcurve angle; δ is the kingpin inclination angle; f The front wheel steering angle; r σ Master pin offset; μ ij r is the road surface adhesion coefficient; r is the wheel radius; 34) Express the optimization problem in the form of the L2 norm as follows: In the formula, minimizing the first part increases the vehicle's stability margin, while the second part is used to meet the torque requirements of the remaining controllers; W u W v is a diagonal weighted matrix; γ is the weight coefficient, whose value determines the relative importance of the two optimization objectives; 35) The diagonal weighting matrix is expressed as: In the formula, c ij The value of W affects u The weight distribution between the longitudinal forces of the wheels is set; W v This is used to allocate the weights between the control torques of each target; 36) The boundary conditions of the control variables are expressed in the following form: In the formula, u max The upper bound of the variable; u min F is the lower bound of the variable; tij,max This is the maximum driving force of the wheels; 37) Apply the active set method, that is, solve the convex quadratic programming problem, obtain the optimal driving force of the four wheels, and then calculate the driving torque of the four wheels.

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