A vehicle tracking control method based on immersion and invariant manifold

Abstract

The invention discloses a vehicle tracking control method based on immersion and invariant manifold, including: design of immersion and invariant manifold parameter estimator; design of immersion and invariant manifold lateral tracking controller; training of RBF neural network; RBF neural network compensation of additional front wheel turning angle; summing the front wheel turning angle and the additional front wheel turning angle to obtain the front wheel turning angle control instruction to control the vehicle. The method of the invention adopts the immersion and invariant manifold estimation method to estimate the target acceleration, and designs the control law to reduce the system error when the vehicle is modeled, and compensates the front wheel turning angle through the RBF neural network to reduce the steady-state error of the designed controller, thereby further improving the accuracy of trajectory tracking.

Description

Technical Field

[0001] The present invention belongs to the technical field of vehicle trajectory tracking control, and specifically refers to a vehicle tracking control method based on immersion and invariant manifold. Background Art

[0002] Vehicle trajectory tracking control technology is a key link in realizing unmanned driving, which requires stable tracking of the pre-trajectory to ensure driving safety. The tasks of trajectory tracking control include longitudinal control and lateral control. Lateral control is to automatically control the vehicle to track the reference trajectory through the steering wheel. Considering the high nonlinearity of vehicle dynamics itself, and its uncertainty and interference in practical applications, the control robustness in the trajectory tracking process becomes a key issue.

[0003] In the process of trajectory tracking control, current research has adopted the driver's optimal preview lateral acceleration and optimal curvature model method based on the preview-follow theory, and its control algorithms include transfer function method, PID control, sliding mode control, linear quadratic regulator, etc. In addition, because MPC can handle multi-objective optimization problems under complex constraints, it is also widely used in vehicle motion control.

[0004] To design a controller, we must first analyze the system's dynamics and establish a system dynamics model. However, in practice, the system has problems of parameter uncertainty and disturbance perturbation. Therefore, a controller designed solely based on a system state model with constant parameters is difficult to ensure driving stability when the actual state of the vehicle is greatly different, and higher requirements are placed on dynamic performance and robust performance.

[0005] Immerion and Invariance (I&I) is a method for designing nonlinear and adaptive controllers. It was proposed by A. Atolfi and R. Ortega in 2003. The idea is to select a stable low-order target system and an immersion map, and design a control law to immerse the controlled object into the target system, so that any trajectory of the controlled system is the image of the target system under the immersion map, ensuring the global asymptotic stability of the controlled system. In addition, for the adaptive estimation problem of perturbation parameters of nonlinear systems, the adaptive estimator design method based on I&I theory introduces the adjustment function into the parameter estimation error manifold surface, and ensures that the parameter estimation value converges asymptotically to the true value by making the manifold surface invariant and attractive; the adaptive controller based on this theory includes two independent modules, the control law and the parameter estimator. The characteristics of the independent modules can be designed separately, which reduces the difficulty of adjusting the parameters of the controller. At present, the control method based on I&I theory has been applied to systems such as quadcopters, unmanned helicopters, and aerospace engines.

[0006] Although there are many studies on vehicle trajectory tracking control, none of them can perform high-precision lateral tracking of the uncertain lateral acceleration of the leading vehicle target. In particular, in robust control and adaptive control, unknown parameters need to be estimated, and the estimated values ​​still have steady-state errors, which need to be compensated to improve the tracking control accuracy. Summary of the invention

[0007] In view of the deficiencies of the above-mentioned prior art, the purpose of the present invention is to provide a vehicle tracking control method based on immersion and invariant manifolds, so as to solve the problem that the parameter estimation value of the adaptive controller in the prior art cannot absolutely converge to the true value, the maximum error of the controller is still determined by the uncertainty of the model parameters, and the tracking accuracy needs to be further improved; the method of the present invention adopts the immersion and invariant manifold estimation method to estimate the target acceleration, and designs the control law to reduce the system error when the vehicle is modeled, compensates the front wheel angle through the RBF neural network, reduces the steady-state error of the designed controller, and further improves the accuracy of trajectory tracking.

[0008] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0009] The present invention provides a vehicle tracking control method based on immersion and invariant manifold, and the steps are as follows:

[0010] 1) Immersion and invariant manifold parameter estimator design: obtain the state variables of the front vehicle and establish the relative motion equation; obtain the lateral acceleration of the front vehicle by estimating the parameters of the lateral acceleration of the front vehicle;

[0011] 2) Immersion and invariant manifold lateral tracking controller design: Take the lateral acceleration of the leading vehicle obtained in step 1) as the control target of the ego vehicle, establish the vehicle dynamics model, select the asymptotically stable target system, determine the immersion mapping, design the control law to ensure that the manifold is an invariant attracting manifold, and the controller output is the change in the front wheel steering angle;

[0012] 3) Training the RBF neural network: Using the training sample set to train the RBF neural network, the weights, center vector and base width vector of the RBF neural network are corrected;

[0013] 4) RBF neural network compensation for additional front wheel steering angle change: using the RBF neural network trained in step 3) to calculate the additional front wheel steering angle change;

[0014] 5) Sum the front wheel steering angle change obtained in step 2) and the additional front wheel steering angle change obtained in step 4) to obtain a front wheel steering angle control instruction to control the vehicle.

[0015] Furthermore, the state variables of the preceding vehicle in step 1) are obtained by: collecting parameter information including the azimuth angle θ and the relative distance dr of the preceding vehicle through the radar of the own vehicle; obtaining the driving angle difference between the own vehicle and the preceding vehicle in the ground coordinate system through V2V communication parameter information.

[0016] Furthermore, the relative motion equation is established in step 1), specifically including:

[0017] The transformation relationship between the two coordinate systems is:

[0018]

[0019] In the formula, is the angle between the front vehicle’s direction and the straight line between the two vehicles, X O , Y O They represent the horizontal and vertical coordinates in the vehicle coordinate system, X O′ , Y O′ Respectively represent the horizontal and vertical coordinates in the front vehicle coordinate system;

[0020] The relative speed V between the front vehicle and the vehicle o It is expressed as:

[0021]

[0022] The relative motion equation between the front vehicle and the ego vehicle is:

[0023]

[0024] In the formula, a xO 、a yO are the longitudinal acceleration and lateral acceleration of the vehicle, respectively, xO′ 、a yO′ are the longitudinal acceleration and lateral acceleration of the front vehicle respectively;

[0025] Establish an auxiliary coordinate system, the X O * The axis is along the dr direction, and the relative motion equation between the front vehicle and the self-vehicle is expressed in the auxiliary coordinate system as follows:

[0026]

[0027] In the formula, a xO * 、a yO * They represent the longitudinal acceleration and lateral acceleration of the vehicle in the auxiliary coordinate system respectively; a xO′ * 、a yO′ *They respectively represent the longitudinal acceleration and lateral acceleration of the front vehicle in the auxiliary coordinate system.

[0028] Furthermore, the parameter estimation of the lateral acceleration of the preceding vehicle in step 1) specifically includes:

[0029] 11) Select the state variables and control quantities of the parameter estimator to estimate the lateral acceleration of the vehicle ahead. As a state quantity The lateral acceleration of the vehicle is the control variable u=a yO * ;

[0030] For the lateral acceleration of the vehicle ahead The expression is:

[0031]

[0032] 12) Define the estimated acceleration of the preceding vehicle as follows:

[0033]

[0034] In the formula, κ is the adaptive parameter, η is the nonlinear function to be designed to ensure the manifold remains unchanged;

[0035] 13) Define the estimation error for:

[0036]

[0037] The estimated error equation is:

[0038]

[0039] 14) Define the partial manifold coordinates of the invariant manifold as: Ensure that the acceleration estimation error meets the asymptotic stability condition;

[0040] 15) Design the adaptive parameter update law as:

[0041]

[0042] At this time, the error equation is:

[0043]

[0044] The designed nonlinear function is:

[0045] η=Γ(dr+ε)(x(t)-x(0)) (11)

[0046] in, is the update law gain; ε is a small positive constant to ensure that the gain is not 0;

[0047] When the target acceleration changes slowly, the error equation of the lateral acceleration estimation of the front vehicle is:

[0048]

[0049] From formula (12), we can see that the partial coordinate asymptotic stability condition of the invariant manifold defined in step 14) is met;

[0050] Substituting κ and η into formula (6), we can estimate the lateral acceleration of the front vehicle:

[0051] Furthermore, in step 2), the estimated lateral acceleration of the preceding vehicle is As the control target, the desired lateral acceleration of the vehicle

[0052] Furthermore, the establishment of the kinetic model in step 2) is specifically as follows:

[0053] 21) A linear two-degree-of-freedom vehicle model is established to describe the vehicle dynamics. The dynamic equations of the slip angle and yaw rate of the linear two-degree-of-freedom vehicle model are as follows:

[0054]

[0055] Where β is the sideslip angle of the center of mass, ψ is the yaw angle, m is the vehicle mass, and L is f is the distance from the vehicle's center of mass to the front axle, L r V is the distance from the vehicle's center of mass to the rear axle. x is the longitudinal velocity of the vehicle, μ is the road adhesion coefficient, I z is the moment of inertia of the vehicle around the z-axis, C f , C r is the total cornering stiffness of the front and rear wheels of the vehicle, δ is the front wheel turning angle;

[0056] The control target is to minimize the lateral displacement, so the lateral error is:

[0057]

[0058] In the formula, a y is the lateral acceleration of the vehicle, a yref is the expected lateral acceleration of the vehicle, and the expected lateral acceleration of the vehicle is written as: yref =V x 2 ρ, ρ is the road curvature;

[0059] According to the relationship between lateral acceleration, sideslip angle and yaw angle, we can get:

[0060] So we have:

[0061]

[0062] The above dynamic equation (13) is written as a state space equation, which is:

[0063]

[0064] In the formula,

[0065] The controller input is the rotation angle , the output is the lateral displacement error e, and the control goal is to eliminate the lateral error, that is, The state space is described as:

[0066]

[0067] In the formula,

[0068] The control input at the equilibrium point is:

[0069]

[0070] The above steady-state solution formula (16) (17) is used as reference input to redefine the new control quantity in,

[0071] The vehicle dynamics model is established as:

[0072]

[0073] 22) Control law design: lateral control is achieved by controlling the front wheel angle. Considering the robustness requirements of lateral position tracking control, immersion and invariant manifolds are used for position tracking control. An asymptotically stable target system is selected, the immersion mapping is determined, and the control law is designed to ensure that the manifold is an invariant attracting manifold.

[0074] Furthermore, the step 22) specifically includes:

[0075] 221) The process of establishing the target dynamic system is as follows:

[0076] The target state vector of the system is taken as (ξ1,ξ2), where ξ1 and ξ2 represent and Therefore, the steady-state control input is:

[0077]

[0078] Substitute it into the system state equation (19), and describe the target state in the state space form as follows:

[0079]

[0080] Establish the target dynamic system as shown in equation (21) above, and prove that the target dynamic system is globally asymptotically stable at the origin;

[0081] 222) The process of determining the immersion conditions is as follows:

[0082] The control target and target system are known, and the mapping π(ξ) is selected as The immersion condition is still satisfied and c is selected as the controller The manifold can be guaranteed to remain unchanged;

[0083] 223) The process of defining an implicit manifold is as follows:

[0084] The implicit description of the manifold surface is: M = {x∈R 2 |φ(x)=0}, during the vehicle trajectory tracking process, the system has a global asymptotic stability characteristic at the origin, so the partial manifold coordinates are defined as:

[0085]

[0086] 224) The process of designing manifold attraction and trajectory boundedness is as follows:

[0087] To ensure that the partial manifold coordinate z converges to zero, the following formula is designed to hold:

[0088]

[0089] Among them, k1, k2 are constants greater than 0;

[0090] Therefore, the controller input is:

[0091]

[0092] Furthermore, the RBF neural network in step 3) has 3 layers, including: an input layer, a hidden layer and an output layer, wherein the input layer has 2 neurons, the hidden layer has 5 neurons, and the output layer has 1 neuron;

[0093] The activation function of the neurons in the hidden layer is a Gaussian function:

[0094]

[0095] In the formula, represents the input vector of the neural network; c j =[c j1 c j2 ]T represents the center vector value of the jth node; b j =[b j1 b j2 ] T The vector representing the basis width values ​​of the Gaussian basis function of the jth node.

[0096] Furthermore, in step 3), the RBF neural network is corrected using the training sample set, and the weights (w1, w2, . . . , w5) and the center vector c of the neural network are adjusted using the gradient descent method. j =[c j1 c j2 ] T and base width vector b j =[b j1 b j2 ] T The value of is corrected, and its mathematical expression is:

[0097] The error criterion function is:

[0098]

[0099] In the formula, d represents the expected output and y represents the actual output of the network;

[0100] The training of the neural network is done by adjusting the weights, center vector, and base width vector until E reaches the minimum. The correction process of the gradient descent method is:

[0101]

[0102] In the formula, χ is the learning rate, is the partial derivative operator, ΔW, Δc j ,Δb j They represent the adjustment amounts of weight, center vector, and basis width vector respectively.

[0103] Furthermore, the training sample set in step 3) includes vehicle state information and expected output of the vehicle path tracking process, and specific parameters include the vehicle front wheel turning angle, the distance between the vehicle and the preceding vehicle, and the vehicle expected lateral acceleration.

[0104] Furthermore, in step 4), the additional front wheel steering angle change is calculated using the trained RBF neural network, and the output of the RBF neural network output layer is:

[0105]

[0106] Where W = [w1,w2,···,w5] T is the weight matrix of the RBF neural network, H = [h1,h2,···,h5] Tis the hidden layer output of the RBF neural network.

[0107] Furthermore, the step 5) specifically includes: summing the front wheel steering angle variation obtained in step 2) and the additional front wheel steering angle variation obtained in step 4), and calculating the front wheel steering angle control law after RBF neural network compensation as follows:

[0108]

[0109] Beneficial effects of the present invention:

[0110] 1. Aiming at the trajectory tracking problem of the front and rear vehicles, the present invention innovatively proposes a control method for realizing lateral trajectory tracking, designs an immersion and invariant manifold parameter estimator, and estimates the lateral acceleration of the front vehicle target through the immersion and invariant manifold parameter estimator according to the relative motion equations of the front and rear vehicles, thereby improving the dynamic characteristics of the estimator.

[0111] 2. The present invention designs an immersed and invariant manifold lateral tracking controller to improve the robustness and adaptability of the control system, effectively handle the uncertainty of the control target parameters in the trajectory tracking process, and improve the smoothness of the steering process. It has obvious advantages especially for parameter perturbation problems, and can ensure the tracking performance and stability of the trajectory tracking process.

[0112] 3. The present invention designs an RBF neural network to compensate for the absolute error of the parameter estimation of the immersion and invariant manifold lateral tracking controller and the uncertainty of the dynamic model, thereby improving the tracking control accuracy and reducing the error. At the same time, the significant advantages of RBF, such as fast convergence speed and strong error approximation ability, are considered without affecting the unique dynamic performance of the immersion and invariant manifold lateral tracking controller itself. BRIEF DESCRIPTION OF THE DRAWINGS

[0113] Figure 1 is a flow chart of the method of the present invention;

[0114] Figure 2 It is a schematic diagram of the relative motion relationship of trajectory tracking in the present invention;

[0115] Figure 3 is a design flow chart of the immersion and invariant manifold parameter estimator in the present invention;

[0116] Figure 4 It is a linear two-degree-of-freedom dynamic model diagram of the vehicle in the present invention;

[0117] Figure 5 It is a flow chart of the lateral tracking control law design in the present invention. DETAILED DESCRIPTION

[0118] In order to facilitate the understanding of those skilled in the art, the present invention is further described below in conjunction with embodiments and drawings. The contents mentioned in the implementation modes are not intended to limit the present invention.

[0119] Reference Figure 1 As shown, a vehicle tracking control method based on immersion and invariant manifold of the present invention comprises the following steps:

[0120] 1) Immersion and invariant manifold parameter estimator design: obtain the state variables of the front vehicle and establish the relative motion equation; obtain the lateral acceleration of the front vehicle by parameter estimation of the lateral acceleration of the front vehicle; wherein, the state variables of the front vehicle in step 1) specifically include: collecting parameter information including the azimuth angle θ and relative distance dr of the front vehicle through the radar of the own vehicle; obtaining the driving angle difference between the own vehicle and the front vehicle in the ground coordinate system through V2V communication Parameter information; such as Figure 2 The figure shows a schematic diagram of the relative motion relationship of trajectory tracking of the present invention. The process of establishing the relative motion equation between the leading vehicle and the vehicle based on the relative motion relationship specifically includes:

[0121] The transformation relationship between the two coordinate systems is:

[0122]

[0123] In the formula, is the angle between the front vehicle’s direction and the straight line between the two vehicles, X O , Y O They represent the horizontal and vertical coordinates in the vehicle coordinate system, X O′ , Y O′ Respectively represent the horizontal and vertical coordinates in the front vehicle coordinate system;

[0124] The relative speed V between the front vehicle and the vehicle o It is expressed as:

[0125]

[0126] The relative motion equation between the front vehicle and the ego vehicle is:

[0127]

[0128] In the formula, a xO 、a yO are the longitudinal acceleration and lateral acceleration of the vehicle, respectively, xO′ 、a yO′ are the longitudinal acceleration and lateral acceleration of the front vehicle respectively;

[0129] Establish an auxiliary coordinate system, such as Figure 2 The coordinate system corresponding to the dashed line is shown in the figure. The XO * The axis is along the dr direction, and the relative motion equation between the front vehicle and the self-vehicle is expressed in the auxiliary coordinate system as follows:

[0130]

[0131] In the formula, a xO * 、a yO * They represent the longitudinal acceleration and lateral acceleration of the vehicle in the auxiliary coordinate system respectively; a xO′ * 、a yO′ * They respectively represent the longitudinal acceleration and lateral acceleration of the front vehicle in the auxiliary coordinate system.

[0132] like Figure 3 The figure shows a design flow chart of an immersion and invariant manifold parameter estimator, wherein the parameter estimator performs parameter estimation on the lateral acceleration of the preceding vehicle and specifically comprises the following steps:

[0133] 11) Select the state variables and control quantities of the parameter estimator to estimate the lateral acceleration of the vehicle ahead. As a state quantity The lateral acceleration of the vehicle is the control variable u=a yO * ;

[0134] For the lateral acceleration of the vehicle ahead The expression is:

[0135]

[0136] 12) Define the estimated acceleration of the preceding vehicle as follows:

[0137]

[0138] In the formula, κ is the adaptive parameter, η is the nonlinear function to be designed to ensure the manifold remains unchanged;

[0139] 13) Define the estimation error for:

[0140]

[0141] The estimated error equation is:

[0142]

[0143] 14) Define the partial manifold coordinates of the invariant manifold as: Ensure that the acceleration estimation error meets the asymptotic stability condition;

[0144] 15) Design the adaptive parameter update law as:

[0145]

[0146] At this time, the error equation is:

[0147]

[0148] The designed nonlinear function is:

[0149] η=Γ(dr+ε)(x(t)-x(0)) (11)

[0150] in, is the update law gain; ε is a small positive constant to ensure that the gain is not 0;

[0151] When the target acceleration changes slowly, the error equation of the lateral acceleration estimation of the front vehicle is:

[0152]

[0153] From formula (12), we can see that the partial coordinate asymptotic stability condition of the invariant manifold defined in step 14) is met;

[0154] Substituting κ and η into formula (6), we can estimate the lateral acceleration of the front vehicle:

[0155] 2) Immersion and invariant manifold lateral tracking controller design: Take the lateral acceleration of the leading vehicle obtained in step 1) as the control target of the ego vehicle, establish the vehicle dynamics model, select the asymptotically stable target system, determine the immersion mapping, design the control law to ensure that the manifold is an invariant attracting manifold, and the controller output is the change in the front wheel steering angle;

[0156] Wherein, the estimated lateral acceleration of the preceding vehicle in step 2) is As the control target, the vehicle's desired lateral acceleration

[0157] The specific details of establishing the kinetic model are as follows:

[0158] 21) Establish a linear two-degree-of-freedom vehicle model that describes the vehicle dynamics characteristics, such as Figure 4 The figure shows the linear two-degree-of-freedom dynamic model of the whole vehicle. After dynamic analysis, the dynamic equations of the slip angle and yaw angular velocity of the linear two-degree-of-freedom whole vehicle model are as follows:

[0159]

[0160] Where β is the sideslip angle of the center of mass, ψ is the yaw angle, m is the vehicle mass, and L is fis the distance from the vehicle's center of mass to the front axle, L r V is the distance from the vehicle's center of mass to the rear axle. x is the longitudinal velocity of the vehicle, μ is the road adhesion coefficient, I z is the moment of inertia of the vehicle around the z-axis, C f , C r is the total cornering stiffness of the front and rear wheels of the vehicle, δ is the front wheel turning angle;

[0161] The control target is to minimize the lateral displacement, so the lateral error is:

[0162]

[0163] In the formula, a y is the lateral acceleration of the vehicle, a yref is the expected lateral acceleration of the vehicle, and the expected lateral acceleration of the vehicle is written as: yref =V x 2 ρ, ρ is the road curvature;

[0164] According to the relationship between lateral acceleration, sideslip angle and yaw angle, we can get:

[0165] So we have:

[0166]

[0167] The above dynamic equation (13) is written as a state space equation, which is:

[0168]

[0169] In the formula,

[0170] The controller input is the rotation angle The output is the lateral displacement error e, and the control goal is to eliminate the lateral error, that is, The state space is described as:

[0171]

[0172] In the formula,

[0173] The control input at the equilibrium point is:

[0174]

[0175] The above steady-state solution formula (16) (17) is used as reference input to redefine the new control quantity in,

[0176] The vehicle dynamics model is established as:

[0177]

[0178] 22) Control law design: lateral control is achieved by controlling the front wheel angle. Considering the robustness requirements of lateral position tracking control, immersion and invariant manifolds are used for position tracking control. An asymptotically stable target system is selected, the immersion mapping is determined, and the control law is designed to ensure that the manifold is an invariant attracting manifold.

[0179] like Figure 5 As shown, it is a flow chart of the lateral tracking control law design of step 22), and the control law design steps specifically include:

[0180] 221) The process of establishing the target dynamic system is as follows:

[0181] The target state vector of the system is taken as (ξ1,ξ2), where ξ1 and ξ2 represent and Therefore, the steady-state control input is:

[0182]

[0183] Substitute it into the system state equation (19), and describe the target state in the state space form as follows:

[0184]

[0185] Establish the target dynamic system as shown in equation (21) above, and prove that the target dynamic system is globally asymptotically stable at the origin;

[0186] 222) The process of determining the immersion conditions is as follows:

[0187] The control target and target system are known, and the mapping π(ξ) is selected as The immersion condition is still satisfied and c is selected as the controller The manifold can be guaranteed to remain unchanged;

[0188] 223) The process of defining an implicit manifold is as follows:

[0189] The implicit description of the manifold surface is: M = {x∈R 2 |φ(x)=0}, during the vehicle trajectory tracking process, the system has a global asymptotic stability characteristic at the origin, so the partial manifold coordinates are defined as:

[0190]

[0191] 224) The process of designing manifold attraction and trajectory boundedness is as follows:

[0192] To ensure that the partial manifold coordinate z converges to zero, the following formula is designed to hold:

[0193]

[0194] Among them, k1, k2 are constants greater than 0;

[0195] Therefore, the controller input is:

[0196]

[0197] 3) Training the RBF neural network: Using the training sample set to train the RBF neural network, the weights, center vector and base width vector of the RBF neural network are corrected;

[0198] The RBF neural network in step 3) has 3 layers, including: an input layer, a hidden layer and an output layer, wherein the input layer has 2 neurons, the hidden layer has 5 neurons, and the output layer has 1 neuron;

[0199] The activation function of the neurons in the hidden layer is a Gaussian function:

[0200]

[0201] In the formula, represents the input vector of the neural network; c j =[c j1 c j2 ] T represents the center vector value of the jth node; b j =[b j1 b j2 ] T The vector representing the basis width values ​​of the Gaussian basis function of the jth node.

[0202] In step 3), the RBF neural network is corrected by using the training sample set, and the weights (w1, w2, . . . , w5) and the center vector c of the neural network are adjusted by the gradient descent method. j =[c j1 c j2 ] T and base width vector b j =[b j1 b j2 ] T The value of is corrected, and its mathematical expression is:

[0203] The error criterion function is:

[0204]

[0205] In the formula, d represents the expected output and y represents the actual output of the network;

[0206] The training of the neural network is done by adjusting the weights, center vector, and base width vector until E reaches the minimum. The correction process of the gradient descent method is:

[0207]

[0208] In the formula, χ is the learning rate, is the partial derivative operator, ΔW, Δc j ,Δb j They represent the adjustment amounts of weight, center vector, and basis width vector respectively.

[0209] The training sample set in step 3) includes vehicle state information and expected output of the vehicle path tracking process, and specific parameters include the vehicle front wheel turning angle, the distance between the vehicle and the preceding vehicle, and the vehicle expected lateral acceleration.

[0210] 4) RBF neural network compensation for additional front wheel steering angle: using the RBF neural network trained in step 3) to calculate the additional front wheel steering angle change;

[0211] Wherein, in step 4), the additional front wheel steering angle is calculated using the trained RBF neural network, and the output of the RBF neural network output layer is:

[0212]

[0213] Where: W = [w1, w2, ···, w5] T is the weight matrix of the RBF neural network, H = [h1,h2,···,h5] T is the hidden layer output of the RBF neural network.

[0214] 5) summing the front wheel steering angle change obtained in step 2) and the additional front wheel steering angle change obtained in step 4) to obtain a front wheel steering angle control instruction to control the vehicle;

[0215] The front wheel steering angle change obtained in step 2) and the additional front wheel steering angle change obtained in step 4) are summed to calculate the front wheel steering angle control law after RBF neural network compensation:

[0216]

[0217] The present invention has many specific application paths. The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements can be made without departing from the principle of the present invention. These improvements should also be regarded as the protection scope of the present invention.

Claims

1. A vehicle tracking control method based on immersion and invariant manifold, characterized in that: Here are the steps: 1) Immersion and invariant manifold parameter estimator design: obtain the state variables of the front vehicle and establish the relative motion equation; obtain the lateral acceleration of the front vehicle by estimating the parameters of the lateral acceleration of the front vehicle; 2) Immersion and invariant manifold lateral tracking controller design: Take the lateral acceleration of the leading vehicle obtained in step 1) as the control target of the ego vehicle, establish the vehicle dynamics model, select the asymptotically stable target system, determine the immersion mapping, design the control law to ensure that the manifold is an invariant attracting manifold, and the controller output is the change in the front wheel steering angle; 3) Training the RBF neural network: Using the training sample set to train the RBF neural network, the weights, center vector and base width vector of the RBF neural network are corrected; 4) RBF neural network compensation for additional front wheel steering angle: using the RBF neural network trained in step 3) to calculate the additional front wheel steering angle change; 5) summing the front wheel steering angle change obtained in step 2) and the additional front wheel steering angle change obtained in step 4) to obtain a front wheel steering angle control instruction to control the vehicle; The state variables of the preceding vehicle in step 1) are obtained by: collecting parameter information including the azimuth angle θ and the relative distance dr of the preceding vehicle through the radar of the own vehicle; obtaining the driving angle difference between the own vehicle and the preceding vehicle in the ground coordinate system through V2V communication; Parameter information of The relative motion equation is established in step 1), specifically including: The transformation relationship between the two coordinate systems is: In the formula, is the angle between the front vehicle’s direction and the straight line between the two vehicles, They represent the horizontal and vertical coordinates in the vehicle coordinate system, X O′ , Y O′ Respectively represent the horizontal and vertical coordinates in the front vehicle coordinate system; The relative speed V between the front vehicle and the vehicle o It is expressed as: The relative motion equation between the front vehicle and the ego vehicle is: In the formula, a xO 、a yO are the longitudinal acceleration and lateral acceleration of the vehicle, respectively, xO′ 、a yO′ are the longitudinal acceleration and lateral acceleration of the front vehicle respectively; Establish an auxiliary coordinate system, the X O * The axis is along the dr direction, and the relative motion equation between the front vehicle and the self-vehicle is expressed in the auxiliary coordinate system as follows: In the formula, a xO * 、a yO * They represent the longitudinal acceleration and lateral acceleration of the vehicle in the auxiliary coordinate system respectively; a xO′ * 、a yO′ * They represent the longitudinal acceleration and lateral acceleration of the front vehicle in the auxiliary coordinate system respectively; The parameter estimation of the lateral acceleration of the preceding vehicle in step 1) specifically includes: 11) Select the state variables and control quantities of the parameter estimator to estimate the lateral acceleration of the vehicle ahead. As a state quantity The lateral acceleration of the vehicle is the control quantity u=a yO * ; For the lateral acceleration of the vehicle ahead The expression is: 12) Define the estimated acceleration of the preceding vehicle as follows: In the formula, κ is the adaptive parameter, η is the nonlinear function to be designed to ensure the manifold remains unchanged; 13) Define the estimation error for: The estimated error equation is: 14) Define the partial manifold coordinates of the invariant manifold as: Ensure that the acceleration estimation error meets the asymptotic stability condition; 15) Design the adaptive parameter update law as: At this time, the error equation is: The designed nonlinear function is: η=Γ(dr+ε)(x(t)-x(0)) (11) In the formula, is the update law gain; ε is a small positive constant to ensure that the gain is not 0; When the target acceleration changes slowly, the error equation of the lateral acceleration estimation of the front vehicle is: From formula (12), we can see that the partial coordinate asymptotic stability condition of the invariant manifold defined in step 14) is met; Substituting κ and η into formula (6), we can estimate the lateral acceleration of the front vehicle: In step 2), the estimated lateral acceleration of the preceding vehicle As the control target, the desired lateral acceleration of the vehicle The specific details of establishing the kinetic model in step 2) are as follows: 21) A linear two-degree-of-freedom vehicle model is established to describe the vehicle dynamics characteristics. The dynamic equations of the slip angle and yaw rate of the linear two-degree-of-freedom vehicle model are as follows: Where β is the sideslip angle of the center of mass, ψ is the yaw angle, m is the vehicle mass, and L is f is the distance from the vehicle's center of mass to the front axle, L r V is the distance from the vehicle's center of mass to the rear axle. x is the longitudinal velocity of the vehicle, μ is the road adhesion coefficient, I z is the moment of inertia of the vehicle around the z-axis, C f , C r is the total cornering stiffness of the front and rear wheels of the vehicle, δ is the front wheel turning angle; The control target is to minimize the lateral displacement, so the lateral error is: In the formula, a y is the lateral acceleration of the vehicle, a yref is the expected lateral acceleration of the vehicle, and the expected lateral acceleration of the vehicle is written as: yref =V x 2 ρ, ρ is the road curvature; According to the relationship between lateral acceleration, sideslip angle and yaw angle, we can get: So we have: The above dynamic equation (13) is written as a state space equation, which is: In the formula, The controller input is the rotation angle The output is the lateral displacement error e, and the control goal is to eliminate the lateral error, that is, The state space is described as: In the formula, The control input at the equilibrium point is: The above steady-state solution formula (16) (17) is used as reference input to redefine the new control quantity ;in, The vehicle dynamics model is established as: 22) Control law design: lateral control is achieved by controlling the front wheel angle. Considering the robustness requirements of lateral position tracking control, immersion and invariant manifolds are used for position tracking control. An asymptotically stable target system is selected, the immersion mapping is determined, and the control law is designed to ensure that the manifold is an invariant attracting manifold. The step 22) specifically includes: 221) The process of establishing the target dynamic system is as follows: The target state vector of the system is assumed to be (ξ1,ξ2), where ξ1 and ξ2 represent and The steady-state control input is: Substitute it into the system state equation (19), and describe the target state in the state space form as follows: Establish the target dynamic system as shown in equation (21) above, and prove that the target dynamic system is globally asymptotically stable at the origin; 222) The process of determining the immersion conditions is as follows: The control target and target system are known, and the mapping π(ξ) is selected as The immersion condition is still satisfied and c is selected as the controller The manifold can be guaranteed to remain unchanged; 223) The process of defining an implicit manifold is as follows: The implicit description of the manifold surface is: M = {x∈R 2 |φ(x)=0}, during the vehicle trajectory tracking process, the system has a global asymptotic stability characteristic at the origin, so the partial manifold coordinates are defined as: 224) The process of designing manifold attraction and trajectory boundedness is as follows: To ensure that the partial manifold coordinate z converges to zero, the following formula is designed to hold: In the formula, k1, k2 are constants greater than 0; Therefore, the controller input is: The RBF neural network in step 3) has 3 layers, including: an input layer, a hidden layer and an output layer, wherein the input layer has 2 neurons, the hidden layer has 5 neurons, and the output layer has 1 neuron; The activation function of the neurons in the hidden layer is a Gaussian function: In the formula, represents the input vector of the neural network; c j =[c j1 c j2 ] T represents the center vector value of the jth node; b j =[b j1 b j2 ] T The vector representing the basis width values ​​of the Gaussian basis function of the jth node.

2. The vehicle tracking control method based on immersion and invariant manifold according to claim 1 is characterized in that: In the step 4), the additional front wheel steering angle change is calculated using the trained RBF neural network, and the output of the RBF neural network output layer is: Where W = [w1,w2,···,w5] T is the weight matrix of the RBF neural network, H = [h1,h2,···,h5] T is the hidden layer output of the RBF neural network.

3. The vehicle tracking control method based on immersion and invariant manifold according to claim 2 is characterized in that: The step 5) specifically includes: summing the front wheel steering angle variation obtained in step 2) and the additional front wheel steering angle variation obtained in step 4), and calculating the front wheel steering angle control law after RBF neural network compensation as follows:

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