A Tubular Model Predictive Control Method for Unmanned Vehicles Based on Disturbance Prediction

Abstract

A tubular model predictive control method for an unmanned vehicle based on disturbance prediction belongs to the field of automatic driving and is characterized in that the method comprises a reference path module, a disturbance prediction module, a tubular model predictive controller and a vehicle model; the reference path module obtains the expected path of the controller according to road information, including lateral displacement and yaw angle, and inputs it to the disturbance prediction module and the tubular model predictive controller; on this basis, the disturbance prediction module predicts the tire cornering stiffness at a future moment by inversely solving the vehicle motion model, and regards the deviation between the predicted value and the actual value as a bounded disturbance, and constructs a disturbance prediction model to predict the disturbance range; the tubular model predictive controller calculates the robust invariant set offline according to the predicted disturbance range, and tightens the nominal system constraints, solves the optimal front wheel steering angle through online multi-objective optimization, and obtains the actual control action input into the vehicle model in combination with state feedback, so as to control the vehicle to achieve path tracking.

Description

Technical field:

[0001] The present invention belongs to the field of autonomous driving, and in particular to a tubular model predictive control method for an unmanned vehicle based on disturbance prediction. Background technology:

[0002] With the increase in the number of vehicles, traffic safety and commuting efficiency issues are becoming increasingly prominent. Autonomous vehicles are seen as the key to solving these problems, and their control technology is crucial to this. Path tracking is an important part of the motion control module of unmanned vehicles, and its purpose is to ensure that the vehicle can drive safely, accurately and stably according to the predetermined trajectory. During the tracking control process, the dynamic behavior of the vehicle is directly affected by the forces between the tires and the road surface. Due to the complexity and variability of the driving environment, these forces will show nonlinear changes due to changes in tire pressure, load and road conditions. Among them, the interference of tire parameters mainly comes from two aspects: one is that the ideal system fails to fully consider the nonlinear characteristics of the tire; the other is that when the road adhesion condition changes, the actual tire cornering stiffness does not match the cornering stiffness in the ideal system. Therefore, in tracking control, the uncertainty factor of the tire cornering stiffness will have an adverse effect on the tracking accuracy and the stability of the vehicle. Since traditional model predictive control (MPC) has a strong dependence on the model, when subjected to external disturbances, the controller may violate the system constraints and fail to achieve the expected control efficiency. In response to this problem, the academic community has launched research on how to deal with the impact of future evolution uncertainty. In this context, robust MPC (RMPC) and stochastic MPC (SMPC) have become two mainstream methods, using bounded sets and probability theory to describe future uncertainties, respectively. However, uncertainties such as model mismatch are difficult to accurately describe by probability. Therefore, in the field of autonomous driving control, RMPC shows a broader application prospect than SMPC. At present, min-max model predictive control (Min-max MPC) and tubular model predictive control (Tube-MPC) are the two main ideas for implementing RMPC. The former considers the "worst" case caused by uncertainty. If the system can operate stably under this condition, it can operate stably for any uncertainty in the future. However, this method has too high computational cost, and being too conservative may cause the model solution to diverge. The latter separates the nominal system from the actual system through a separation control strategy, transforms the control of the actual system into the control of the nominal system, and controls the system state in a subset of state constraints (i.e., Tube). The uncertainty problem of the system is solved by tightening the state constraints and applying disturbance feedback control, and the robustness and stability of constraint satisfaction are guaranteed at a low computational cost.

[0003] The tubular model predictive control method can adapt to changes in the external environment and the instability of the internal model, and improve the robustness and reliability of the system. However, the size and shape of the tubular set directly depend on the uncertainty range of the system model and the estimation of the noise level. The existing tubular model predictive control method cannot obtain the precise range of external disturbances. At the same time, in order to improve robustness, tubular model predictive control may introduce conservatism. As a result, the controller may be too conservative in some cases, limiting the control performance of the controller. Summary of the invention:

[0004] To solve the above problems, the present invention proposes a tubular model predictive control method for unmanned vehicles based on disturbance prediction. First, according to the desired tracking path and the vehicle motion model, the nonlinear change of the tire cornering stiffness at the future moment is predicted. Then, the deviation between the predicted value and the actual value is regarded as an additive disturbance, and a disturbance prediction model is constructed. Finally, according to the predicted disturbance range, a more compact disturbance polyhedron is obtained by the rolling prediction method, and the constraints of the nominal system are tightened to reduce the conservatism of the traditional Tube-MPC, so as to achieve the path tracking control effect.

[0005] The technical solution adopted by the present invention to solve the technical problem is as follows:

[0006] A tubular model predictive control method for an unmanned vehicle based on disturbance prediction belongs to the field of automatic driving and is characterized in that the method comprises a reference path module, a disturbance prediction module, a tubular model predictive controller and a vehicle model; the reference path module obtains the expected path of the controller according to road information, including lateral displacement and yaw angle, and inputs it to the disturbance prediction module and the tubular model predictive controller; on this basis, the disturbance prediction module predicts the tire cornering stiffness at a future moment by inversely solving the vehicle motion model, and regards the deviation between the predicted value and the actual value as a bounded disturbance, thereby constructing a disturbance prediction model to predict the disturbance range; the tubular model predictive controller calculates the robust invariant set offline according to the predicted disturbance range, tightens the constraints of the nominal system, solves the optimal front wheel steering angle through online multi-objective optimization, obtains the actual control action input into the vehicle model in combination with the state feedback quantity, and controls the vehicle to achieve path tracking.

[0007] The method comprises the following steps:

[0008] Step 1: Reference path module design: The desired path of the controller is obtained according to the road information, including lateral displacement and yaw angle. The process includes the following sub-steps:

[0009] Step 1.1: Controller planning uses the Sigmoid function method to solve the lateral displacement and yaw angle of the controller reference to obtain the desired path of the controller.

[0010] Step 2: Design of disturbance prediction module; the process includes the following sub-steps:

[0011] Step 2.1, disturbance prediction:

[0012] Construct the vehicle dynamics model, which is expressed as:

[0013]

[0014] Where m is the vehicle mass, v x is the longitudinal velocity of the vehicle, v y is the lateral velocity of the vehicle, ω r is the vehicle yaw rate, C f , C r are the cornering stiffness of the front and rear tires, δ is the front wheel turning angle, l f and l r are the distances from the vehicle's center of mass to the front and rear axles, I z is the yaw moment of inertia about the vertical axis of the vehicle's center of mass, is the vehicle lateral speed, is the vehicle yaw angle, is the lateral velocity of the car in the geodetic coordinate system;

[0015] According to formula (1), we can get:

[0016]

[0017] Where, the yaw angular velocity ω r With lateral velocity v y After rearranging formula (1), we can obtain:

[0018]

[0019] The reference value Y obtained by the reference path module ref , and its first and second derivatives with respect to time Substituting into formula (3), we get:

[0020]

[0021] Therefore, the predicted cornering stiffness of the front and rear wheels is:

[0022]

[0023] Among them, C f,pre , C r,pre are the predicted front and rear wheel cornering stiffnesses, and λ FAn adjustment factor to compensate for the influence of the adhesion coefficient.

[0024] The road adhesion coefficient adjustment factor is introduced into formula (4) and formula (5) to compensate for the influence of the adhesion coefficient on the predicted value of the cornering stiffness.

[0025] Due to the influence of the tire force adhesion limit, the cornering stiffness value obtained by formula (5) should satisfy the constraint:

[0026]

[0027] Among them, F z,j is the vertical load of the tire, μ is the road adhesion coefficient, j=f, r represents the front and rear wheels respectively.

[0028] Step 2.2: Construction of disturbance prediction model:

[0029] First, the predicted values ​​of the front and rear wheel cornering stiffness C are obtained by formula (5): f,pre , C r,pre . The deviation between the predicted value and the actual value at the current moment is regarded as a disturbance:

[0030]

[0031] Therefore, by taking N reference path data points forward, the disturbance in the future prediction time domain can be obtained as:

[0032]

[0033] Here, function f(·) represents the functional relationship among formula (4), formula (5) and formula (7), and n=0, 1, …, N.

[0034] The predicted disturbance change can be expressed as:

[0035] Δs(k+n|k)=s(k+n|k)-s(k+n-1|k) (9)

[0036] Finally, the predicted disturbance in the prediction time domain is:

[0037]

[0038] From formula (6), we can see that the change of tire cornering stiffness is bounded, so the disturbance variable is bounded:

[0039] s(k)∈[s min ,s max ] (11)

[0040] Δs(k)∈[Δs min ,Δs max ] (12)

[0041] Where s(k) represents the deviation between the predicted value and the actual value of the tire cornering stiffness at time k, that is, the disturbance at time k; Δs(k) represents the rate of change of the disturbance at time k; s min ,s max Indicates the limit value of the disturbance; Δs min ,Δs max Indicates the limiting value of the disturbance change rate.

[0042] Because the error between the predicted value and the actual value is bounded, the error range in the prediction time domain can be expressed as:

[0043]

[0044] in:

[0045] s min (k+n|k)=min(max(0,s(k)+nΔs max ),s max ) (14)

[0046] s max (k+n|k)=max(min(0,s(k)+nΔs min ),s min ) (15)

[0047] According to formula (1) and formula (10), the vehicle dynamics model is reversely solved to obtain the state prediction deviation (disturbance) range of the nominal system and the actual system as w(k)∈W.

[0048] Step 3: Design a tubular model predictive control controller; the process includes the following sub-steps:

[0049] Step 3.1: Prediction model construction:

[0050] Rearranging formula (1), we get the state space equation:

[0051]

[0052] Among them, the state quantity Control quantity u=δ.

[0053]

[0054]

[0055] Discretize formula (16) by zero-order hold:

[0056] x(k+1)=A d x(k)+B d u(k)(17)

[0057] Among them, A d =e AT ; T is the discrete time.

[0058] The nonlinearity of the tire model is regarded as the uncertainty of the tire parameters, and the state prediction deviation w(k)∈W is obtained by the disturbance prediction module. Then the actual controlled system is expressed as:

[0059] x(k+1)=A d x(k)+B d u(k)+w(k)(18)

[0060] Formula (18) is a real system, whose state quantity x(k)∈R 4 , control quantity u(k)∈R, bounded disturbance quantity w(k)∈R 4 The actual system is subject to the constraints x(k)∈X, u(k)∈U, w(k)∈W. Separating the impact of bounded disturbances on the system, the nominal system is defined as:

[0061] z(k+1)=A d z(k)+B d v(k)(19)

[0062] in, is the nominal system state; v(k) = δ v is the nominal system control quantity.

[0063] According to formula (18) and formula (19), the state quantity deviation between the actual system and the nominal system can be obtained as:

[0064] e(k)=x(k)-z(k)(20)

[0065] Note that the system error e(k) is determined by the disturbance term, and the control law of the Tube-MPC controller is defined as:

[0066] u(k)=v(k)+K c e(k)(21)

[0067] Where v(k) = δ v is the front wheel steering angle obtained by optimizing the nominal system, K c e(k)=δ K is the state feedback control input, K c ∈R 1×4 is the state feedback gain matrix. This control law obtains the system deviation compensation angle through state feedback calculation, so that the nominal system state is as close to the reference state as possible.

[0068] Combining formula (20) and formula (21), the evolution of the error system can be obtained as follows:

[0069] e(k+1)=A K e(k)+w(k)(22)

[0070] Among them, A K =A d +B d K c .

[0071] Define E as the robust invariant set (RPI) of the error system, also known as Tube. For any bounded disturbance, when the error state is within the RPI, its state evolution must also be within the RPI:

[0072]

[0073] The collection form is expressed as:

[0074]

[0075] in, Represents the Minkowski sum operation between sets.

[0076] Then, for a given time k, the nominal system state z(k) and control input v(k) will be constrained within the bounds tightened by the robust invariant set E, which can be expressed as:

[0077]

[0078] Here, Θ represents the Pontryagin difference operation between sets.

[0079] Step 3.2, objective function construction:

[0080] The control objective is to keep the vehicle running smoothly while tracking the reference path with the minimum error and to ensure that each state quantity and control quantity cannot cross the constraint boundary.

[0081] The objective function of the Tube-MPC controller is defined as:

[0082]

[0083]

[0084] Where N is the prediction time domain; Q, R, and P are the weight matrices of state quantity, control quantity, and terminal cost respectively; x(0) is the actual system initial state; z(0) is the nominal system initial state; is the reference state of the nominal system.

[0085] The first term v of the optimal control sequence is obtained by optimizing formula (26): * (k) and the nominal state z(k), combined with the state feedback K c (x(k)-z(k)), so the final control quantity of the actual system is:

[0086] u * (k) = v * (k)+K c (x(k)-z(k))(27)

[0087] Finally, the optimized control action is input into the vehicle model to realize path tracking control.

[0088] The beneficial effects of the present invention are as follows: by predicting the nonlinear trend of tire cornering stiffness, the deviation between the predicted value and the true value is regarded as disturbance. The range of nominal system constraints is relaxed by rolling prediction disturbance range, thereby improving system robustness. The influence of uncertainty in cornering stiffness change is reduced by rolling prediction disturbance range, which effectively reduces conservatism and improves control performance compared to the existing Tube-MPC. Description of the drawings:

[0089] Figure 1 It is a flow chart of the method of the present invention.

[0090] Figure 2 It is a disturbance prediction principle diagram of the present invention.

[0091] Figure 3 It is the structural diagram of the Tube-MPC controller of the present invention. Specific implementation method:

[0092] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0093] like Figure 1As shown, the method includes a reference path module (1), a disturbance prediction module (2), a Tube-MPC controller (3) and a vehicle model (4); the reference path module (1) accurately calculates reference values ​​such as lateral displacement, yaw angle, lateral velocity and yaw angular velocity of the vehicle at each path point according to the expected road trajectory; the disturbance prediction module (2) predicts the nonlinear change of tire cornering stiffness through the vehicle motion model according to the reference information, regards the deviation between the predicted value and the actual value as a bounded disturbance, and constructs a disturbance prediction model to accurately predict the disturbance range; the Tube-MPC controller (3) calculates the robust invariant set of the disturbance offline according to the predicted disturbance range, and then tightens the constraints of the nominal system through the robust invariant set of the disturbance, solves the optimal front wheel steering angle through online multi-objective optimization, and obtains the actual control brake in combination with the state feedback; the vehicle model (4) outputs the actual state quantity of the vehicle, including the lateral velocity, yaw angular velocity, lateral displacement and yaw angle of the vehicle.

[0094] The design of the reference path module (1) is as follows:

[0095] The Sigmoid function method is used for path planning, and its expression is:

[0096]

[0097]

[0098] Where X is the longitudinal position, D is the lateral collision avoidance distance, c is half of the longitudinal collision avoidance distance, a is the inclination of the collision avoidance path, L is the preview distance, and Y is the vertical position. ref is the expected lateral displacement, is the desired yaw angle.

[0099] The disturbance prediction module (2) includes the following parts: 2.1 constructing a two-degree-of-freedom dynamic model of the vehicle, 2.2 linearizing the tire model, 2.3 disturbance prediction, and 2.4 constructing a disturbance prediction model.

[0100] In Section 2.1, a two-degree-of-freedom dynamic model of the vehicle is constructed:

[0101]

[0102] Where m is the vehicle mass, v x is the longitudinal velocity of the vehicle, v y is the lateral velocity of the vehicle, ω r is the vehicle yaw rate, F y,f 、F y,r are the lateral forces of the front and rear tires, δ is the front wheel turning angle, l f and l r are the distances from the vehicle's center of mass to the front and rear axles, I zis the yaw moment of inertia about the vertical axis of the vehicle's center of mass, is the vehicle yaw angle, is the lateral velocity of the car in the geodetic coordinate system;

[0103] In Section 2.2, the tire model is linearized:

[0104] The UniTire tire model is used to characterize the changing characteristics of tire force during the actual driving process of the vehicle. The cornering stiffness is defined as the ratio of the lateral force to the side slip angle, and its expression is:

[0105]

[0106] Among them, C j is the tire cornering stiffness, F y,j is the tire cornering force, α j is the tire slip angle, j = f, r refers to the front wheel and rear wheel respectively;

[0107] The cornering stiffness of each tire can be obtained from formula (4). Therefore, the lateral force of the front and rear tires can be linearly expressed as:

[0108] F y,j =C j α j (5)

[0109] The front and rear tire slip angles are defined as:

[0110]

[0111] In Section 2.3, the cornering stiffness is predicted based on the known desired lateral displacement and yaw angle as follows:

[0112] Substituting tire model formula (5) into formula (3), the vehicle motion model is obtained as follows:

[0113]

[0114] According to formula (7), we can get:

[0115]

[0116] Where, the yaw angular velocity ω r With lateral velocity v y After rearranging formula (7), we can obtain:

[0117]

[0118] The reference value Y obtained by formula (1) and formula (2) ref , and its first and second derivatives with respect to time Substituting into formula (9), we get:

[0119]

[0120] Therefore, the predicted cornering stiffness of the front and rear wheels is:

[0121]

[0122] Among them, C f,pre , C r,pre are the predicted front and rear wheel cornering stiffnesses, and λ F An adjustment factor to compensate for the influence of the adhesion coefficient.

[0123] The road adhesion coefficient adjustment factor is introduced into formula (10) and formula (11) to compensate for the influence of the adhesion coefficient on the predicted value of the cornering stiffness.

[0124] Due to the influence of the tire force adhesion limit, the cornering stiffness value obtained by formula (11) should satisfy the constraint:

[0125]

[0126] Among them, F z is the vertical load of the tire, μ is the road adhesion coefficient, j=f, r represents the front and rear wheels respectively.

[0127] like Figure 2 As shown, in Section 2.4, the deviation between the predicted tire cornering stiffness value at the future moment and the actual tire cornering stiffness value at the current moment is obtained, and a prediction model of the error system is constructed to predict the disturbance change at the future moment and obtain the disturbance range.

[0128] First, the predicted values ​​of the front and rear wheel cornering stiffness C are obtained by formula (11): f,pre , C r,pre The tire cornering stiffness C at the current moment is obtained from formula (4): f , C r . The deviation between the predicted value and the actual value at the current moment is regarded as a disturbance:

[0129]

[0130] Therefore, by taking N reference path data points forward, the disturbance in the future prediction time domain can be obtained as:

[0131]

[0132] Wherein, function f(·) represents the functional relationship among formula (10), formula (11) and formula (13), and n=0, 1, …, N.

[0133] The predicted disturbance change can be expressed as:

[0134] Δs(k+n|k)=s(k+n|k)-s(k+n-1|k) (15)

[0135] Finally, the predicted disturbance in the prediction time domain is:

[0136]

[0137] From formula (12), we can see that the change of tire cornering stiffness is bounded, so the disturbance variable is bounded:

[0138] s(k)∈[s min ,s max ] (17)

[0139] Δs(k)∈[Δs min ,Δs max ] (18)

[0140] Where s(k) represents the deviation between the predicted value and the actual value of the tire cornering stiffness at time k, that is, the disturbance at time k; Δs(k) represents the rate of change of the disturbance at time k; s min ,s max Indicates the limit value of the disturbance; Δs min ,Δs max Indicates the limiting value of the disturbance change rate.

[0141] Because the error between the predicted value and the actual value is bounded, the error range in the prediction time domain can be expressed as:

[0142]

[0143] in:

[0144] s min (k+n|k)=min(max(0,s(k)+nΔs max ),s max ) (20)

[0145] s max (k+n|k)=max(min(0,s(k)+nΔs min ),s min ) (twenty one)

[0146] According to formula (7) and formula (16), the vehicle motion model is reversely solved to obtain the state prediction deviation (disturbance) range of the nominal system and the actual system as w(k)∈W.

[0147] like Figure 3 As shown, the tubular model predictive controller module (3) includes the following parts: 3.1 prediction model construction, 3.2 minimum robust invariant set approximation solution and 3.3 objective function construction.

[0148] In the prediction model construction section 3.1, formula (3), formula (5) and formula (7) are sorted out to obtain the state space equation:

[0149]

[0150] Among them, the state quantity Control quantity u=δ.

[0151]

[0152]

[0153] Formula (22) is discretized by zero-order hold:

[0154] x(k+1)=A d x(k)+B d u(k) (23)

[0155] Among them, A d =e AT ; T is the discrete time.

[0156] The nonlinearity of the tire model is regarded as the uncertainty of the tire parameters, and the state prediction deviation w(k)∈W is obtained by the disturbance prediction module. Then the actual controlled system is expressed as:

[0157] x(k+1)=A d x(k)+B d u(k)+w(k) (24)

[0158] Formula (24) is a real system, whose state quantity x(k)∈R 4 , control quantity u(k)∈R, bounded disturbance quantity w(k)∈R 4 The actual system is subject to the constraints x(k)∈X, u(k)∈U, w(k)∈W. Separating the impact of bounded disturbances on the system, the nominal system is defined as:

[0159] z(k+1)=A d z(k)+B d v(k)(25)

[0160] in, is the nominal system state; v(k) = δ v is the nominal system control quantity.

[0161] According to formula (24) and formula (25), the state quantity deviation between the actual system and the nominal system can be obtained as:

[0162] e(k)=x(k)-z(k)(26)

[0163] Note that the system error e(k) is determined by the disturbance term, and the control law of the Tube-MPC controller is defined as:

[0164] u(k)=v(k)+K c e(k)(27)

[0165] Where v(k) = δ v is the front wheel steering angle obtained by optimizing the nominal system, K c e(k)=δ K is the state feedback control input, K c ∈R 1×4 is the state feedback gain matrix. This control law obtains the system deviation compensation angle through state feedback calculation, so that the nominal system state is as close to the reference state as possible.

[0166] Combining formula (26) and formula (27), the evolution of the error system is as follows:

[0167] e(k+1)=A K e(k)+w(k)(28)

[0168] Among them, A K =A d +B d K c ;

[0169] Define E as the robust invariant set (RPI) of the error system, also known as Tube. For any bounded disturbance, when the error state is within the RPI, its state evolution must also be within the RPI:

[0170]

[0171] The collection form is expressed as:

[0172]

[0173] in, Represents the Minkowski sum operation between sets.

[0174] Then, for a given time k, the nominal system state z(k) and control input v(k) will be constrained within the bounds tightened by the robust invariant set E, which can be expressed as:

[0175]

[0176] Here, Θ represents the Pontryagin difference operation between sets.

[0177] 3.2 In the approximate solution of the minimum robust invariant set, the disturbance range w(k)∈W is obtained based on the disturbance prediction. The minimum robust invariant set is included in all robust invariant sets RPI, and the minimum robust invariant set is obtained by external approximation through a finite number of iterations.

[0178] According to formula (28), the robust invariant set can be expressed as:

[0179]

[0180] Where N = 1, 2, ...;

[0181] Since the perturbation set is bounded w(k)∈W, the expression is:

[0182]

[0183] The minimum robust invariant set is obtained by external approximation using a finite number of iterations. The goal is to find an array (N c ,α), so that it satisfies:

[0184]

[0185] Among them, N c ∈R,α∈(0,1);

[0186] From formula (33) and formula (34), the approximate expression of the minimum robust invariant set is:

[0187]

[0188]

[0189] 3.3 In the objective function construction part, the control goal is to keep the vehicle driving smoothly while tracking the reference path with the minimum error, and to ensure that each state quantity and control quantity cannot cross the constraint boundary.

[0190] The objective function of the Tube-MPC controller is defined as:

[0191]

[0192]

[0193] Where N is the prediction time domain; Q, R, and P are the weight matrices of state quantity, control quantity, and terminal cost respectively; x(0) is the actual system initial state; z(0) is the nominal system initial state; is the reference state of the nominal system.

[0194] The first term v of the optimal control sequence is obtained by optimizing formula (37): * (k) and the nominal state z(k), combined with the state feedback K c (x(k)-z(k)), so the final control quantity of the actual system is:

[0195] u * (k) = v * (k)+K c (x(k)-z(k))(38)

[0196] Finally, the optimized control action is input into the vehicle model to realize path tracking control.

Claims

1. A tubular model predictive control method for an unmanned vehicle based on disturbance prediction, characterized in that: The method includes a reference path module, a disturbance prediction module, a tubular model prediction controller and a vehicle model; the reference path module obtains the expected path of the controller according to the road information, including the lateral displacement Y ref and yaw angle And input it to the disturbance prediction module and the tubular model prediction controller; on this basis, the disturbance prediction module predicts the tire cornering stiffness C at the future moment by inversely solving the vehicle motion model. f,pre , C r,pre , and regard the deviation between the predicted value and the actual value as the disturbance s(k), so as to construct a disturbance prediction model to predict the disturbance range w(k)∈W; the tubular model predictive controller calculates the robust invariant set E of the disturbance offline according to the predicted disturbance range, tightens the constraints of the nominal system through the robust invariant set, and solves the optimal front wheel steering angle δ through online multi-objective optimization v * , combined with the state feedback quantity δ K , get the final actual control action δ, input the vehicle model, and control the vehicle to achieve path tracking.

2. The method for predictive control of a tubular model of an unmanned vehicle based on disturbance prediction according to claim 1, wherein the disturbance prediction module is characterized in that: Including building a two-degree-of-freedom dynamic model of the vehicle, linearizing the tire model, predicting disturbances, and building a disturbance prediction model; (1) Construct a two-degree-of-freedom dynamic model of the vehicle, which is expressed as follows: Where m is the vehicle mass, v x is the longitudinal velocity of the vehicle, v y is the lateral velocity of the vehicle, ω r is the vehicle yaw rate, F y,f 、F y,r are the lateral forces of the front and rear tires, δ is the front wheel turning angle, l f and l r are the distances from the vehicle's center of mass to the front and rear axles, I z is the yaw moment of inertia about the vertical axis of the vehicle's center of mass, is the vehicle yaw angle, is the lateral velocity of the car in the geodetic coordinate system; (2) Tire model linearization: The UniTire tire model is used to characterize the changing characteristics of tire force during actual vehicle driving. The cornering stiffness is defined as the ratio of the lateral force to the side slip angle at each side slip angle. Its expression is: Among them, C j is the tire cornering stiffness, F y,j is the tire cornering force, α j is the tire slip angle, j = f, r refers to the front wheel and rear wheel respectively; The cornering stiffness of each tire can be obtained from formula (2), and the lateral force of the front and rear tires can be linearly expressed as: F y,j =C j a j (3) (3) Disturbance prediction: The cornering stiffness is predicted based on the lateral displacement and yaw angle of the reference path. The specific method is as follows: Substituting the linear tire model formula (3) into formula (1), the vehicle motion model is obtained as follows: According to the above formula, we can get: Where, the yaw angular velocity ω r With lateral velocity v y After rearranging formula (4), we can obtain: Set the reference value Y of the reference path ref , and its first and second derivatives with respect to time Substituting into formula (6), we get: Therefore, the predicted cornering stiffness of the front and rear wheels is: Among them, C f,pre , C r,pre are the predicted front and rear wheel cornering stiffnesses, and λ F An adjustment factor to compensate for the effect of adhesion coefficient; In formula (7) and formula (8), a road adhesion coefficient adjustment factor is introduced to compensate for the influence of the adhesion coefficient on the predicted value of the cornering stiffness. Due to the influence of the tire force adhesion limit, the cornering stiffness value obtained by formula (8) should satisfy the constraint: Among them, F z,j is the vertical load of the tire, μ is the road adhesion coefficient, j=f, r represents the front and rear wheels respectively; (4) Construct disturbance prediction model: First, the predicted values ​​of the front and rear wheel cornering stiffness C are obtained by formula (8): f,pre , C r,pre ; The tire cornering stiffness C at the current moment is obtained from formula (2): f , C r ; Consider the deviation between the predicted value and the actual value at the current moment as a disturbance: Therefore, by taking N reference path data points forward, the disturbance in the future prediction time domain can be obtained as: Wherein, function f(·) represents the functional relationship among formula (7), formula (8) and formula (10), n=0,1,…,N; The predicted disturbance change can be expressed as: Δs(k+nk)=s(k+nk)-s(k+n-1k) (12) Finally, the predicted disturbance in the prediction time domain is: From formula (9), we can see that the change of tire cornering stiffness is bounded, so the disturbance variable is bounded: s(k)∈[s min ,s max ](14) Δs(k)∈[Δs min ,Δs max ](15) Where s(k) represents the deviation between the predicted value and the actual value of the tire cornering stiffness at time k, that is, the disturbance at time k; Δs(k) represents the rate of change of the disturbance at time k; s min ,s max Indicates the limit value of the disturbance; Δs min ,Δs max Indicates the limit value of the disturbance change rate; Because the error between the predicted value and the actual value is bounded, the error range in the prediction time domain can be expressed as: in: s min (k+nk)=min(max(0,s(k)+nΔs max ),s max ) (17) s max (k+nk)=max(min(0,s(k)+nΔs min ),s min ) (18) According to formula (4) and formula (13), the state deviation range between the nominal system and the actual system is obtained by inversely solving the vehicle motion model as w(k)∈W.

3. The method for predictive control of a tubular model of an unmanned vehicle based on disturbance prediction according to claim 1, wherein the tubular model predictive controller is characterized in that: Including building a prediction model and constructing an objective function; (1) Building a prediction model: Arranging formula (1), formula (3) and formula (4), we get the state space equation: Among them, the state quantity Control quantity u = δ; Discretize formula (19) by zero-order hold: x(k+1)=A d x(k)+B d u(k) (20) Among them, A d =e AT ; T is discrete time; The nonlinearity of the tire model is regarded as the uncertainty of the tire parameters, and the state prediction deviation w(k)∈W is obtained by the disturbance prediction module; then the actual controlled system is expressed as: x(k+1)=A d x(k)+B d u(k)+w(k) (21) Formula (21) is a real system, whose state quantity x(k)∈R 4 , control quantity u(k)∈R, bounded disturbance quantity w(k)∈R 4 , the actual system is subject to the constraints x(k)∈X, u(k)∈U, w(k)∈W; Define the nominal system: z(k+1)=A d from(k)+B d in (22) in, is the nominal system state; v(k) = δ v is the nominal system control input; According to formula (21) and formula (22), the state quantity deviation between the actual system and the nominal system can be obtained as: e(k)=x(k)-z(k) (23) Note that the system error e(k) is determined by the disturbance term, and the control law of the tubular model predictive controller is defined as: u(k)=v(k)+K c e(k) (24) Where v(k) = δ v is the front wheel steering angle obtained by optimizing the nominal system, K c e(k)=δ K is the state feedback control input, K c ∈R 1×4 is the state feedback gain matrix. This control law obtains the system deviation compensation angle through state feedback calculation, so that the nominal system state is as close to the reference state as possible. Combining formula (23) and formula (24), the evolution of the error system is as follows: e(k+1)=A K e(k)+w(k) (25) Among them, A K =A d +B d K c ; Define E as the robust invariant set of the error system, also known as Tube. For any bounded disturbance, when the error state is within the robust invariant set, its state evolution must also be within the robust invariant set: The collection form is expressed as: in, Represents the Minkowski and operation between sets; Then, for a given time k, the nominal system state z(k) and control input v(k) will be constrained within the bounds tightened by the robust invariant set E, which can be expressed as: Where Θ represents the Pontryagin difference operation between sets; (2) Construct the objective function: The objective function of the tubular model predictive controller is defined as: Where N is the prediction time domain; Q, R, and P are the weight matrices of state quantity, control quantity, and terminal cost respectively; x(0) is the actual system initial state; z(0) is the nominal system initial state; is the reference state of the nominal system; The first term v of the optimal control sequence is obtained by optimizing formula (29): * (k) and the nominal state z(k), combined with the state feedback K c (x(k)-z(k)), so the final control quantity of the actual system is: u * (k)=v * (k)+K c (x(k)-z(k)) (30) Finally, the optimized control action is input into the vehicle model to realize path tracking control.

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