A finite-time adaptive trajectory tracking control method for autonomous vehicles

Abstract

The application discloses a kind of finite time adaptive trajectory tracking control methods of autonomous car, comprising, constructing autonomous car kinematics and dynamics model, obtaining the pose coordinates of current and reference position and respectively calculating attitude angle, horizontal coordinate, longitudinal coordinate, linear velocity and angular velocity error vector, according to the first control law, attitude angle error vector is adjusted, according to the second control law, horizontal coordinate error vector, longitudinal coordinate error vector is adjusted, first torque, second torque and adaptive law are designed, the value of adaptive law is obtained according to neural network, the parameter in first torque and second torque is adjusted according to the value of adaptive law, linear velocity and angular velocity error vector are adjusted according to the first torque and second torque after adjustment, and autonomous car travels according to adjusted attitude angle, horizontal coordinate, longitudinal coordinate, linear velocity and angular velocity. So that the error between current position and reference position is reduced to a certain small interval in finite time, and the tracking precision is improved.

Description

Technical Field

[0001] This invention relates to the field of vehicle tracking control, and more particularly to a finite-time adaptive trajectory tracking control method for autonomous vehicles. Background Technology

[0002] With the general improvement of people's living standards, more and more families own cars. While cars bring convenience to people's lives, the accident rate due to driver negligence is also increasing year by year. Therefore, improving the assisted driving technology of autonomous vehicles is particularly important. In recent years, trajectory tracking control has received widespread attention and research from domestic scholars. In the existing technology, in order to achieve tracking of the reference speed, a PID dynamic controller for mobile robots is designed, which combines PID control and adaptive control to achieve good tracking of the reference speed. However, conventional PID controllers are troubled by the complexity of parameter tuning methods and do not consider the case of unknown autonomous vehicle parameters. To address the problem of parameter uncertainty in the dynamic model of wheeled mobile robots, a model reference adaptive control scheme composed of a kinematic controller and a dynamic controller is proposed. However, the implementation of the adaptive method is relatively complex, and it is difficult to meet the real-time requirements of general wheeled mobile robot control, and it does not consider the case of uncertain external disturbances of the autonomous vehicle. For the mathematical model of a two-degree-of-freedom mobile robot, a time-varying state feedback trajectory tracking control method based on backstepping control is proposed. A trajectory tracking algorithm is designed based on backstepping recursion technology, but it only considers the asymptotic convergence of the error between the autonomous vehicle's expected trajectory and the actual trajectory. The sliding mode controller for trajectory tracking based on the dynamic model proposed by WMR exhibits good robustness against external disturbances and parameter uncertainties. However, the discontinuous terms in the switching control law of the sliding mode control method directly affect the output term, leading to unavoidable chattering due to high-speed switching between different control logics.

[0003] In summary, the existing technology is superior because it does not consider unknown parameters, which leads to a decrease in tracking accuracy and reduces the reliability of tracking control. The discontinuity of the control law also leads to a decrease in the stability of tracking control. Summary of the Invention

[0004] This invention provides a finite-time adaptive trajectory tracking control method for autonomous vehicles to overcome the aforementioned technical problems.

[0005] A finite-time adaptive trajectory tracking control method for autonomous vehicles includes,

[0006] Step 1: Construct the kinematic and dynamic models of the rear-wheel differential drive four-wheel autonomous vehicle. Based on the kinematic model, obtain the pose coordinates of the autonomous vehicle at its current position and the pose coordinates of a reference position. The pose coordinates include attitude angles, abscissa, and ordinate. Calculate the attitude angle error vector based on the pose angles of the current and reference positions. Calculate the abscissa error vector based on the abscissas of the current and reference positions. Calculate the ordinate error vector based on the ordinates of the current and reference positions.

[0007] Step 2: Design the first virtual control law, adjust the attitude angle error vector according to the first virtual control law, and then adjust the attitude angle of the autonomous vehicle according to the adjusted attitude angle error vector.

[0008] Step 3: Design the second virtual control law. Adjust the position coordinates of the horizontal and vertical coordinate error vectors according to the second virtual control law. Then, adjust the horizontal and vertical coordinates of the autonomous vehicle based on the adjusted horizontal and vertical coordinate error vectors.

[0009] Step 4: Based on the autonomous vehicle's dynamics model, obtain the linear velocity and angular velocity of the autonomous vehicle at its current position and at the reference position. Calculate the linear velocity error vector based on the linear velocity of the autonomous vehicle at its current position and the linear velocity at the reference position. Calculate the angular velocity error vector based on the angular velocity of the autonomous vehicle at its current position and the angular velocity at the reference position.

[0010] Step 5: Design the first torque in the linear velocity error vector and the second torque in the angular velocity error vector. Design an adaptive law and obtain the value of the adaptive law based on the neural network. Adjust the parameters in the first and second torques according to the value of the adaptive law. Adjust the linear velocity error vector and angular velocity error vector according to the adjusted first and second torques. Adjust the linear velocity and angular velocity of the autonomous vehicle according to the adjusted linear velocity error vector and angular velocity error vector. The autonomous vehicle travels according to the adjusted attitude angle, abscissa, ordinate, linear velocity, and angular velocity.

[0011] Preferably, adjusting the attitude angle error vector according to the first virtual control law includes:

[0012] The attitude angle error vector e3 is obtained according to formula (1).

[0013] e3=θ r -θ (1)

[0014] Differentiating both sides of equation (1) with respect to t, we get:

[0015]

[0016] Design the first virtual control law wc ,

[0017]

[0018] Substituting equation (3) into equation (2) yields the adjusted attitude angle error vector:

[0019]

[0020] Where θ is the pose angle of the autonomous vehicle at its current position, θ r Let w be the pose angle of the autonomous vehicle's reference position, and w be the angular velocity of the autonomous vehicle's current position. r Let ω be the angular velocity of the autonomous vehicle at its reference position, k1 > 0, k2 > 0, and <β1 < 1, which are design parameters.

[0021] Preferably, the adjustment of the horizontal axis error vector and the vertical axis error vector according to the second virtual control law includes,

[0022] The position tracking error vector is obtained according to formula (5).

[0023]

[0024] Differentiating both sides of formula (5) with respect to t, we get:

[0025]

[0026] Design the second virtual control law v c ,

[0027]

[0028] Substituting equation (7) into equation (6) yields the adjusted horizontal coordinate error vector and vertical coordinate error vector.

[0029]

[0030] In the formula, (x, y) are the x and y coordinates of the autonomous vehicle at its current position, respectively. r y r Let ) represent the x and y coordinates of the autonomous vehicle at the reference position, and v = (v... L +v R ) / 2 represents the linear velocity of the autonomous vehicle at its current position, v L v R Here, k4>0, k5>0, <β2<1, <β3<1 are design parameters, and v and w are the linear velocities of the left and right wheels of the autonomous vehicle, respectively. r w r e1 represents the linear velocity and angular velocity at the reference position of the autonomous vehicle, respectively, and e2 represents the attitude angle error vector.

[0031] Preferably, the first torque in the linear velocity error vector and the second torque in the angular velocity error vector include designing a first torque u1 and a second torque u2 according to formula (9).

[0032]

[0033] Where c1, c2, c3, and c4 are design constants that are greater than zero. This is a vector consisting of the weights from each hidden layer to the input layer in the neural network. for The estimated value, H(x)=[h1(X),h2(X),...,h N (X)] T An N-dimensional column vector consisting of basis functions for each hidden layer, where Gaussian functions are used as the basis functions. The input to the neural network is [the input of the neural network]; the output of the neural network is [the output of the neural network]. and and This is an adaptive law.

[0034] Preferably, the and Calculated according to formula (10),

[0035]

[0036] Where γ1, γ2, D1, and D2 are design constants that are greater than zero.

[0037] This invention provides a finite-time adaptive trajectory tracking control method for autonomous vehicles. By constructing kinematic and dynamic control laws for the autonomous vehicle, the error between the current state and the desired trajectory is reduced to a certain small range within a finite time, thereby achieving better trajectory tracking control and improving tracking accuracy. Attached Figure Description

[0038] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0039] Figure 1 This is a flowchart of the method of the present invention;

[0040] Figure 2 This is a simplified structural diagram of the autonomous vehicle of this invention;

[0041] Figure 3 This is a schematic diagram of trajectory tracking according to the present invention;

[0042] Figure 4 This is the control input u1 of the present invention;

[0043] Figure 5 This is the control input u2 of the present invention;

[0044] Figure 6 These are two-dimensional view comparison diagrams of the present invention;

[0045] Figure 7 These are comparison images of the three-dimensional views of this invention;

[0046] Figure 8 This is the error between θr and θ in this invention;

[0047] Figure 9 This is a diagram of the co-simulation system of the present invention;

[0048] Figure 10 This is the first control algorithm module of the present invention;

[0049] Figure 11 This is the second control algorithm module of the present invention;

[0050] Figure 12 This is the vehicle model of the present invention;

[0051] Figure 13 This is the road model of the present invention;

[0052] Figure 14 This is the main interface of the CarSim software of this invention;

[0053] Figure 15 This is the Simulink model of the present invention;

[0054] Figure 16 This is the input of the autonomous vehicle of the present invention;

[0055] Figure 17 This invention is an autonomous vehicle output;

[0056] Figure 18(a) is a first animation effect diagram of trajectory tracking according to the present invention;

[0057] Figure 18(b) is a second animation effect diagram of trajectory tracking according to the present invention. Detailed Implementation

[0058] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0059] Figure 1 This is a flowchart of the method of the present invention, as shown below. Figure 1 As shown, the method in this embodiment may include:

[0060] Step 1: Construct the kinematic and dynamic models of the rear-wheel differential drive four-wheel autonomous vehicle. Based on the kinematic model, obtain the pose coordinates of the autonomous vehicle at its current position and the pose coordinates of a reference position. The pose coordinates include attitude angles, abscissa, and ordinate. Calculate the attitude angle error vector based on the pose angles of the current and reference positions. Calculate the abscissa error vector based on the abscissas of the current and reference positions. Calculate the ordinate error vector based on the ordinates of the current and reference positions.

[0061] Step 2: Design the first virtual control law, adjust the attitude angle error vector according to the first virtual control law, and then adjust the attitude angle of the autonomous vehicle according to the adjusted attitude angle error vector.

[0062] Step 3: Design the second virtual control law. Adjust the position coordinates of the horizontal and vertical coordinate error vectors according to the second virtual control law. Then, adjust the horizontal and vertical coordinates of the autonomous vehicle based on the adjusted horizontal and vertical coordinate error vectors.

[0063] Step 4: Based on the autonomous vehicle's dynamics model, obtain the linear velocity and angular velocity of the autonomous vehicle at its current position and at the reference position. Calculate the linear velocity error vector based on the linear velocity of the autonomous vehicle at its current position and the linear velocity at the reference position. Calculate the angular velocity error vector based on the angular velocity of the autonomous vehicle at its current position and the angular velocity at the reference position.

[0064] Step 5: Design the first torque in the linear velocity error vector and the second torque in the angular velocity error vector. Design an adaptive law and obtain the value of the adaptive law based on the neural network. Adjust the parameters in the first and second torques according to the value of the adaptive law. Adjust the linear velocity error vector and angular velocity error vector according to the adjusted first and second torques. Adjust the linear velocity and angular velocity of the autonomous vehicle according to the adjusted linear velocity error vector and angular velocity error vector. The autonomous vehicle travels according to the adjusted attitude angle, abscissa, ordinate, linear velocity, and angular velocity.

[0065] Based on the above scheme, for a rear-wheel differential drive four-wheel autonomous vehicle model, considering the unknown parameters of the model itself and external uncertainties, an intelligent model of the autonomous vehicle is established by utilizing the approximation capability of neural networks for nonlinear functions. Kinematic and dynamic control laws are constructed using inversion methods and finite-time control techniques, reducing the error between the current state and the desired trajectory to a small range within a finite time, thereby improving the trajectory tracking control performance of the autonomous vehicle.

[0066] The realization of autonomous vehicle trajectory tracking and obstacle avoidance control requires effective control of the vehicle's kinematics or dynamics system. Establishing a reasonable vehicle system state model can provide data support for trajectory tracking and obstacle avoidance control of autonomous vehicles in complex extreme road conditions and low-adhesion high-speed driving environments. Therefore, this embodiment uses a rear-wheel differential drive four-wheel autonomous vehicle model as the controlled object.

[0067] Step 1: Construct the kinematic and dynamic models of the rear-wheel differential drive four-wheel autonomous vehicle. Based on the kinematic model, obtain the pose coordinates of the autonomous vehicle at its current position and the pose coordinates of a reference position. The pose coordinates include attitude angles, abscissa, and ordinate. Calculate the attitude angle error vector based on the pose angles of the current and reference positions. Calculate the abscissa error vector based on the abscissas of the current and reference positions. Calculate the ordinate error vector based on the ordinates of the current and reference positions.

[0068] Specifically, in the rear-wheel differential drive four-wheel autonomous vehicle model, the rear two wheels are differential drive wheels, and the front two wheels are steering wheels. Figure 2 This is a simplified diagram of the autonomous vehicle's structure. XOY forms a generalized coordinate system; xoy is a local coordinate system, and the center point M of the two rear wheels is the centroid of the autonomous vehicle.

[0069] The coordinates of the autonomous vehicle's center of gravity in the generalized coordinate system are (x, y), where θ is the angle between the x-axis of the local coordinate system and the x-axis of the generalized coordinate system. This angle can represent the autonomous vehicle's heading angle, denoted by q = [x, y, θ]. T This represents the pose vector of the autonomous vehicle in the generalized coordinate system.

[0070] Let v = (v L +v R () / 2 is the linear velocity of the autonomous vehicle, and w is the angular velocity of the autonomous vehicle. L v R Let f be the linear velocities of the left and right wheels, respectively. The wheel radius is f, and the center distance between the two wheels is 2b.

[0071] Autonomous vehicle kinematic model: Kinematics refers to the study of the laws governing the motion of objects through geometric approaches, including the changes in parameters such as spatial position and velocity over time.

[0072] Under low-speed driving conditions on good road surfaces, the dynamics related to vehicle stability control can be ignored, and a two-degree-of-freedom kinematic model can be used to describe the vehicle's kinematic characteristics.

[0073] Under the condition of pure rolling and no lateral slippage, the autonomous vehicle is subject to nonholonomic constraints, and the constraint equations are as follows:

[0074]

[0075] Using point M as a reference point, the autonomous vehicle converts its linear velocity and angular velocity [v, w] into its velocity in the generalized coordinate system. The kinematic model of the autonomous vehicle can then be described as (2),

[0076]

[0077] Where S(q) is a Jacobian matrix. Considering the computational cost of the model in the control algorithm, a two-degree-of-freedom model of the autonomous vehicle is adopted. The motion of the autonomous vehicle is only planar motion, and the planar motion of the autonomous vehicle has two directions: longitudinal motion and yaw motion. Autonomous vehicle dynamics model (3),

[0078]

[0079] In the formula, m is the mass of the autonomous vehicle, r is the radius of the wheel, b is the distance from point M to any wheel, I is its moment of inertia at point M, and u1 = T. R +T L u2 = T R -T L T R T L d1 and d2 represent the torques provided by the left and right wheels of the autonomous vehicle in the forward direction. w is the angular velocity of the autonomous vehicle. d1 and d2 represent external disturbances to the autonomous vehicle system.

[0080] The following lemma will be used in the subsequent control design:

[0081] Lemma 1.1: Defining a function

[0082] f(x)=[f1(x), f1(x),..., f n (x)] T (4)

[0083] Defined as with respect to {r1, r2, ..., r n A continuous second-order vector field with degree K < 0, r i >0, if any ε>0, then

[0084]

[0085] Consider the following system;

[0086]

[0087] f(x) is a function of (r1, r2, ..., r) n A continuous homogeneous vector field with homogeneity k < 0. satisfy Assume x = 0 is the system The asymptotically stable equilibrium. Then, if,

[0088]

[0089] in Then x = 0 represents a locally stable equilibrium in finite time.

[0090] Lemma 1.2: For some real numbers λ1 > 0, λ2 > 0, 0 < γ < 1, an extended Lyapunov condition for finite-time stability is:

[0091]

[0092] The required settling time is estimated using equation (8).

[0093]

[0094] Corollary 1.1: Consider the system If there exists a continuous function V(X) with scalars a > 0, b > 0, 0 < γ < 1, 0 < c < ∞, then...

[0095]

[0096] Then it is called a system. The trajectory is locally finite-time stable, the system The residual set of the solution is given by the following formula;

[0097]

[0098] Where θ0 satisfies 0 < θ0 < 1.

[0099] The steady-state time is bounded as follows:

[0100]

[0101] The design of the trajectory tracking controller for autonomous vehicles includes the following:

[0102] M represents the current position of the autonomous vehicle, and its generalized pose coordinates are q = [x, y, θ]. TM1 is the current reference position of the autonomous vehicle, and its position and attitude information is q. r =[x r y r θ r ] T .

[0103] Let e1, e2, and e3 represent the error between the current position and the current reference position of the autonomous vehicle in the forward direction in the local coordinate system, the deviation perpendicular to the forward direction, and the deviation of the autonomous vehicle's heading angle, respectively. For example... Figure 3 The diagram shows the trajectory tracking of the autonomous vehicle.

[0104] The pose deviation of the incomplete autonomous vehicle can be represented by a three-dimensional vector as follows:

[0105]

[0106] Differentiating both sides of the above equation with respect to time t, we get:

[0107]

[0108] Where v and w are the current linear velocity and angular velocity of the autonomous vehicle, respectively. r w r These are the linear velocity and angular velocity currently referenced by the autonomous vehicle, respectively.

[0109] Control objective: For the deviations e1, e2, e3 between the reference position and attitude and the actual position (including x, y) and attitude, approach zero in a finite time, design a finite-time adaptive neural network trajectory tracking control algorithm for the autonomous vehicle, so that the autonomous vehicle system with unknown model parameters and uncertain external disturbances can track the desired trajectory and desired attitude angle.

[0110] Step 2: Design the first virtual control law, adjust the attitude angle error vector according to the first virtual control law, and then adjust the attitude angle of the autonomous vehicle according to the adjusted attitude angle error vector.

[0111] The adjustment of the attitude angle error vector according to the first virtual control law includes...

[0112] The attitude angle error vector e3 is obtained according to formula (14).

[0113] e3=θ r -θ (14)

[0114] Differentiating both sides of equation (14) with respect to t, we get:

[0115]

[0116] Design the first virtual control law w c Virtual control law wc Make e3 approach zero in a finite amount of time.

[0117]

[0118] Substituting equation (16) into equation (15) yields the adjusted attitude angle error vector:

[0119]

[0120] Where θ is the pose angle of the autonomous vehicle at its current position, θ r Let w be the pose angle of the autonomous vehicle's reference position, and w be the angular velocity of the autonomous vehicle's current position. r Let ω be the angular velocity of the autonomous vehicle at its reference position, k1 > 0, k2 > 0, and <β1 < 1, which are design parameters.

[0121] Step 3: Design the second virtual control law, adjust the horizontal and vertical coordinate error vectors according to the second virtual control law, and adjust the horizontal and vertical coordinates of the autonomous vehicle according to the adjusted horizontal and vertical coordinate error vectors. The adjustment of the horizontal and vertical coordinate error vectors according to the second virtual control law includes...

[0122] The position tracking error vector is obtained according to formula (18).

[0123]

[0124] Differentiating both sides of formula (18) with respect to t, we get...

[0125]

[0126] Design the second virtual control law v c Virtual control law v c So that e1 and e2 are in a finite time t xy It approaches zero.

[0127]

[0128] Substituting equation (20) into equation (19) yields the adjusted horizontal coordinate error vector and vertical coordinate error vector.

[0129]

[0130] In the formula, (x, y) are the x and y coordinates of the autonomous vehicle at its current position, respectively. r y r Let ) represent the x and y coordinates of the autonomous vehicle at the reference position, and v = (v... L +v R ) / 2 represents the linear velocity of the autonomous vehicle at its current position, v Lv R Here, k4>0, k5>0, <β2<1, <β3<1 are design parameters, and v and w are the linear velocities of the left and right wheels of the autonomous vehicle, respectively. r w r e1 represents the linear velocity and angular velocity at the reference position of the autonomous vehicle, respectively, and e2 represents the attitude angle error vector.

[0131] To achieve better speed tracking, the uncertainty of unknown parameters and external disturbances is overcome by utilizing the approximation capability of neural networks, and a finite-time inversion adaptive neural network dynamic control law is designed.

[0132] Step 4: Based on the autonomous vehicle's dynamics model, obtain the linear velocity and angular velocity of the autonomous vehicle at its current position and at the reference position. Calculate the linear velocity error vector based on the linear velocity of the autonomous vehicle at its current position and the linear velocity at the reference position. Calculate the angular velocity error vector based on the angular velocity of the autonomous vehicle at its current position and the angular velocity at the reference position.

[0133] Step 5: Design the first torque in the linear velocity error vector and the second torque in the angular velocity error vector. Design an adaptive law and obtain the value of the adaptive law based on the neural network. Adjust the parameters in the first and second torques according to the value of the adaptive law. Adjust the linear velocity error vector and angular velocity error vector according to the adjusted first and second torques. Adjust the linear velocity and angular velocity of the autonomous vehicle according to the adjusted linear velocity error vector and angular velocity error vector. The autonomous vehicle travels according to the adjusted attitude angle, abscissa, ordinate, linear velocity, and angular velocity.

[0134] Specifically, this includes obtaining the linear velocity and angular velocity of the autonomous vehicle, e v e w These are the error vectors for linear velocity and angular velocity, respectively.

[0135]

[0136] Differentiating both sides of the above equation with respect to time t, we get:

[0137]

[0138] Substituting equation (3) into equation (23), we get:

[0139]

[0140] u1 = T R +T L u2 = T R -T L T R T LThese are the torques provided by the left and right wheels of the autonomous vehicle in the forward direction, respectively, with u1 being the first torque and u2 being the second torque.

[0141] The first torque in the linear velocity error vector and the second torque in the angular velocity error vector include the design of the first torque u1 and the second torque u2 according to formula (25).

[0142]

[0143] Where c1, c2, c3, and c4 are design constants that are greater than zero. This is a vector consisting of the weights from each hidden layer to the input layer in the neural network. for The estimated value, H(x)=[h1(X),h2(X),...,h N (X)] T An N-dimensional column vector consisting of basis functions for each hidden layer, where Gaussian functions are used as the basis functions. The input to the neural network is [the input of the neural network]; the output of the neural network is [the output of the neural network]. and and This is an adaptive law.

[0144] The and Calculated according to formula (26),

[0145]

[0146] Where γ1, γ2, D1, and D2 are design constants that are greater than zero.

[0147] Uncertain parameters and external disturbances of autonomous vehicles can be approximated using neural networks as follows:

[0148]

[0149] Where ε1 and ε2 are the approximation errors of the neural network.

[0150] This embodiment uses Lyapunov stability theory to prove the stability of the system. The proof of the boundedness of the closed-loop system is divided into three parts.

[0151] Theorem 1.1: Consider the mathematical model of an autonomous vehicle and a closed-loop system consisting of a virtual control law, control input, adaptive law, unknown parameters, and uncertain external disturbances. All signals within the closed-loop system eventually become uniformly bounded, and the position tracking error and attitude tracking error converge to the neighborhood of the zero point.

[0152] prove:

[0153] Part 1: Constructing the Lyapunov function V1:

[0154]

[0155] Considering equation (29), taking the derivative with respect to V1, we get:

[0156]

[0157] Where a = 2k1,

[0158] As can be seen from Lemma 2, e3 approaches zero in finite time.

[0159] Part Two: Constructing the Lyapunov function V2:

[0160]

[0161] Considering equation (30), taking the derivative with respect to V2, we get:

[0162]

[0163] We can then conclude that states e1 and e2 can approach zero. If the system simultaneously satisfies global asymptotic stability and local finite-time stability, then global finite-time stability can be achieved.

[0164] We will now prove that states e1 and e2 converge in locally finite time. The position error can be divided into two parts.

[0165]

[0166] in,

[0167]

[0168]

[0169] First consider

[0170] Construct Lyapunov functions.

[0171]

[0172] Differentiate both sides of the above equation with respect to time t:

[0173]

[0174] Based on Lyapunov stability theory, (e1, e2) = (0, 0) is an asymptotically stable equilibrium point for the system's position error. If we choose... It is easy to see that g(e1, e2) with variables (e1, e2) is homogeneous with respect to (σ1, σ2). As for When σ1=1, have

[0175]

[0176] According to Lemma 1, the system error is locally finite-time stable. Therefore, it can be concluded that the system position error and attitude angle error are globally finite-time stable under the action of the first and second virtual control laws.

[0177] Part 3: Constructing Lyapunov functions V3:

[0178]

[0179] Considering equation (37), taking the derivative with respect to V3, we get:

[0180]

[0181] again

[0182]

[0183] Similarly

[0184]

[0185] Substituting equations (39) and (40) into equation (38) yields...

[0186]

[0187] if have,

[0188]

[0189] if have,

[0190]

[0191] From equations (42) and (43), we know that...

[0192]

[0193] Similarly,

[0194]

[0195] So there is.

[0196]

[0197] in,

[0198]

[0199]

[0200]

[0201]

[0202] By Lemma 2, e v e w , The system achieves stability and boundedness within a finite time. The above proof demonstrates that, under the proposed finite-time adaptive neural network trajectory tracking control scheme for autonomous vehicles, all signals within the position and attitude closed-loop subsystem eventually become uniformly bounded. Furthermore, by selecting appropriate parameters, the tracking errors in position and attitude can converge to the neighborhood of zero.

[0203] This embodiment conducts a simulation study. The parameter model of the autonomous vehicle is: m = 4.5, I = 2.7, r = 0.05, b = 0.20; when the reference trajectory is a circular arc, the trajectory equation is: x r (t)=-sin(t), y r (t)=cos(t), θ r (t) = t; Initial value of reference trajectory: x r (0)=0, y r (0)=1, θ r (0) = pi; Initial reference velocity: v r =-1; w r =1; Controller parameters: k1=5, k2=4, k4=6, k5=6, β1=0.37, β2=0.75, β3=0.5, c1=12, c2=2, c3=14.95, c4=1.85, γ1 = 799, γ2 = 799, D1 = 18, D2 = 18, d1 = 10sin(t), d2 = 10sin(t). The input image is controlled as follows: Figure 4 As shown in Figure 5; a comparison diagram of the reference pose and the actual pose is shown in Figure 6. Figure 6 As shown in 7 and 8.

[0204] Based on virtual vehicle simulation experiments, CarSim and Simulink each have their own advantages and disadvantages, which complement each other perfectly. Therefore, co-simulation using CarSim and Simulink has been widely used in recent years. CarSim allows the creation of vehicle models, road models, driver models, etc., and Simulink can then combine these models for control, performing low-level logic control and solving for the results. Furthermore, because CarSim allows the simulation results to be observed graphically and with 3D animations, the co-simulation results can be displayed very vividly within CarSim, helping to intuitively see the solution.

[0205] Steps for co-simulation using CarSim and Simulin:

[0206] (1) Build such a system in Simulink Figure 9 The image shows a joint simulation diagram of CarSim and Simulin, where... Figure 10 The construction of the control logic algorithm shown is crucial, and its stability and effectiveness have been verified in simulation studies; for example... Figure 10 The control algorithm module one shown includes the desired and actual position and attitude angle inputs, the error between the desired and actual position and attitude angles, the position and attitude angle control law, and the neural network, etc. Figure 11 The control algorithm module 2 shown is an S-function module with a specified function, which is equivalent to a solver. It mainly solves the adaptive law to obtain W1-W10; then it outputs the control quantity and converts it into the input torque tau1 and tau2 of the autonomous vehicle; finally, the autonomous vehicle outputs the actual and reference position and attitude angles and returns to module 1.

[0207] (2) In CarSim, set up as follows Figure 12 The vehicle model shown is as follows: Figure 13 The road model, vehicle model, and road condition model shown are as follows: Figure 14 The settings are shown in the leftmost of the three parts of the CarSim software main interface.

[0208] (3) Set the simulation parameters and interfaces of the control model in the middle part of the CarSim software main interface, and combine them as follows: Figure 15 The Simulink model shown includes a step size, frequency, and the input / output of the virtual autonomous vehicle. Figure 16 The inputs shown are the longitudinal linear velocity of the vehicle body and the angular velocities of the left and right rear wheels, respectively; for example... Figure 17 The outputs shown are the actual coordinates, reference coordinates, local linear velocity, and yaw angle, respectively. Click the green arrow to run after completion.

[0209] (4) After the operation is completed, the first and second animation results shown in Figure 18(a) and (b) can be viewed on the far right part of the CarSim software main interface.

[0210] By constructing a closed-loop system in Simulink, comprising a virtual controller, control inputs, vehicle position parameters, and uncertain external disturbances, into a systematic control logic algorithm, and then setting up the vehicle and road models in CarSim, configuring the vehicle's inputs and outputs, and selecting Simulink as the solution method, the Simulink model built in the first step is entered, and some solution parameters are set, the "Send to Simulink" button is clicked to package the current vehicle and road models and send them back to the CarSim S-Function module in Simulink. In this way, the vehicle and road models built in CarSim are quickly incorporated into the Simulink model. The solution is then run in Simulink. The joint simulation results of CarSim and Simulink fully demonstrate the accuracy and feasibility of the proposed autonomous vehicle finite-time adaptive neural network control scheme.

[0211] Overall beneficial effects:

[0212] This invention provides a finite-time adaptive trajectory tracking control method for autonomous vehicles. By constructing kinematic and dynamic control laws for the autonomous vehicle, the error between the current state and the desired trajectory is reduced to a certain small range within a finite time, thereby achieving better trajectory tracking control and improving tracking accuracy.

[0213] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A finite-time adaptive trajectory tracking control method for an autonomous vehicle, characterized in that, include, Step 1: Construct the kinematic and dynamic models of the rear-wheel differential drive four-wheel autonomous vehicle. Based on the kinematic model, obtain the pose coordinates of the autonomous vehicle at its current position and the pose coordinates of a reference position. The pose coordinates include attitude angles, abscissa, and ordinate. Calculate the attitude angle error vector based on the pose angles of the current and reference positions. Calculate the abscissa error vector based on the abscissas of the current and reference positions. Calculate the ordinate error vector based on the ordinates of the current and reference positions. Step 2: Design the first virtual control law, adjust the attitude angle error vector according to the first virtual control law, and then adjust the attitude angle of the autonomous vehicle according to the adjusted attitude angle error vector. Step 3: Design the second virtual control law. Adjust the position coordinates of the horizontal and vertical coordinate error vectors according to the second virtual control law. Then, adjust the horizontal and vertical coordinates of the autonomous vehicle based on the adjusted horizontal and vertical coordinate error vectors. Step 4: Based on the autonomous vehicle's dynamics model, obtain the linear velocity and angular velocity of the autonomous vehicle at its current position and at the reference position. Calculate the linear velocity error vector based on the linear velocity of the autonomous vehicle at its current position and the linear velocity at the reference position. Calculate the angular velocity error vector based on the angular velocity of the autonomous vehicle at its current position and the angular velocity at the reference position. Step 5: Design the first torque in the linear velocity error vector and the second torque in the angular velocity error vector; design an adaptive law for the neural network to adjust the neural network weights; adjust the parameters in the first and second torques according to the values ​​of the neural network weights; adjust the linear velocity error vector and angular velocity error vector according to the adjusted first and second torques; adjust the linear velocity and angular velocity of the autonomous vehicle according to the adjusted linear velocity error vector and angular velocity error vector; the autonomous vehicle travels according to the adjusted attitude angle, horizontal coordinate, vertical coordinate, linear velocity, and angular velocity; the adjustment of the attitude angle error vector according to the first virtual control law includes... The attitude angle error vector is obtained according to formula (1). , （1） Equation (1) has the following two ends: Taking the derivative, （2） Design the first virtual control law , （3） Substituting equation (3) into equation (2) yields the adjusted attitude angle error vector: （4） in, The pose angle of the autonomous vehicle at its current position. The pose angle of the autonomous vehicle's reference position. Let ω be the angular velocity of the autonomous vehicle at its current position. The angular velocity at the reference position of the autonomous vehicle. These are design parameters; the adjustment of the horizontal and vertical coordinate error vectors according to the second virtual control law includes... The position tracking error vector is obtained according to formula (5). （5） Formula (5) has both ends opposite to each other. Taking the derivative, （6） Design the second virtual control law , （7） Substituting equation (7) into equation (6) yields the adjusted horizontal coordinate error vector and vertical coordinate error vector. （8） In the formula, Here are the x and y coordinates of the autonomous vehicle at its current position. The x and y coordinates of the autonomous vehicle at the reference position are: Let be the linear velocity of the autonomous vehicle at its current position. , These represent the linear velocities of the left and right wheels of the autonomous vehicle, respectively. These are design parameters. and These are the linear velocity and angular velocity of the autonomous vehicle at its current position, respectively. , These are the linear velocity and angular velocity at the reference position of the autonomous vehicle, respectively. The attitude angle error vector; the first torque in the designed linear velocity error vector and the second torque in the angular velocity error vector include the first torque designed according to formula (9). Second torque , (9) in , , , It is a design constant that is greater than zero. , This is a vector consisting of the weights from each hidden layer to the input layer in the neural network. for The estimated value, , An N-dimensional column vector consisting of basis functions for each hidden layer, where Gaussian functions are used as the basis functions. The input to the neural network is [the input of the neural network]; the output of the neural network is [the output of the neural network]. and , and For adaptive laws, , These are the error vectors for linear velocity and angular velocity, respectively. 。 2. The finite-time adaptive trajectory tracking control method for an autonomous vehicle according to claim 1, characterized in that, The and Calculated according to formula (10), (10) in , , , It is a design constant that is greater than zero.

Images