Vehicle path tracking terminal sliding mode control method based on extended state observer

Abstract

The application provides a vehicle path tracking terminal sliding mode control method based on an extended state observer, parameter errors and external disturbances observed by the extended state observer are obtained in real time by using a non-singular terminal sliding mode controller, the parameter errors and external disturbances are input into the non-singular terminal sliding mode controller, and the non-singular terminal sliding mode controller outputs a control signal to control a front wheel steering angle of the vehicle according to the parameter errors and external disturbances.The non-singular terminal sliding mode controller has multiple advantages such as fast response, convergence in a limited time, high steady-state tracking precision and the like; the extended state observer can observe specific values of uncertain parameters and external disturbances during vehicle path tracking, and is integrated into a control algorithm to make path tracking better.The application can make errors between an actual path and an expected path quickly converge to zero, ensure that the vehicle accurately moves along the expected path, and has strong robustness.

Description

Technical Field

[0001] This invention relates to the field of autonomous driving, and specifically to a robust and fast-converging sliding mode control method for a vehicle path tracking terminal based on an extended state observer for autonomous vehicles. Background Technology

[0002] With the development of autonomous driving technology, improving the ability of autonomous vehicles to resist parameter uncertainties and complex disturbances under complex operating conditions is of great significance. However, most of the path tracking controllers used in current autonomous vehicle control methods are based on vehicle kinematics. However, vehicles have characteristics such as parameter uncertainty and strong disturbances during driving. It is necessary to consider the dynamic characteristics of the vehicle and add anti-interference technology to ensure the accuracy of path tracking. On the other hand, the few control methods that consider vehicle dynamics have the problem of slow convergence speed.

[0003] Therefore, it is necessary to provide a sliding mode controller and control method for vehicle path tracking terminals based on extended state observers, which has short convergence time and is resistant to system parameter uncertainties and unknown disturbances. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a vehicle path tracking terminal sliding mode control method based on an extended state observer. The method utilizes a non-singular terminal sliding mode controller to acquire parameter errors and external disturbances observed by the extended state observer in real time. These parameter errors and external disturbances are then input into the non-singular terminal sliding mode controller, enabling the controller to output control signals to control the front wheel steering angle of the vehicle based on the parameter errors and external disturbances.

[0005] The non-singular terminal sliding mode controller is constructed as follows:

[0006] Based on the vehicle's dynamic characteristics, a vehicle dynamics system model is constructed, including a linear tire dynamics model, a vehicle kinematics model, and a two-degree-of-freedom lateral dynamics model. Then, a second-order nonlinear vehicle model based on the aiming error is established. A nonsingular terminal sliding mode surface is constructed based on the second-order nonlinear vehicle model, and a nonsingular terminal sliding mode saturation function reaching law is constructed to reduce chattering problems in the control system. Based on the vehicle dynamics system model, the nonsingular terminal sliding mode surface, and the nonsingular terminal sliding mode saturation function reaching law, a nonsingular terminal sliding mode controller is constructed.

[0007] The second-order nonlinear model of the vehicle is as follows:

[0008]

[0009] In the formula: u is the front wheel steering angle, r(t) is the uncertain parameter and unknown disturbance (the uncertain parameter of the system may appear in factors such as side stiffness error, sensor measurement error, and changes in the vehicle environment), v x and v g C represents the longitudinal and lateral velocities of the vehicle's center of gravity, respectively. f C r These are the lateral stiffness of the front and rear wheels of the car, d f d r Let L represent the distance from the vehicle's center of gravity along the longitudinal axis to both ends of the vehicle, M represent the distance from the vehicle's center of gravity to the aiming point, and m represent the total mass of the vehicle. z The moment of inertia of the vehicle;

[0010] Construct the nonsingular terminal sliding surface S based on the second-order nonlinear model of the vehicle:

[0011]

[0012] In the formula: C h is the sliding surface coefficient, and C > 0; p and q are positive odd numbers, and p > q;

[0013] The non-singular terminal sliding mode saturation function reaching law is as follows:

[0014]

[0015] In the formula: ε and k are the reaching law coefficients, and ε > 0, k > 0;

[0016] The non-singular terminal sliding mode controller is:

[0017]

[0018] In the formula, r(t) b Let r(t) be an estimate.

[0019]

[0020] The extended state observer is constructed as follows:

[0021] Based on the established second-order nonlinear vehicle model, a third-order linear extended state observer is established. The third order represents the parameter uncertainties and unknown external disturbances. The third-order linear extended state observer is as follows:

[0022]

[0023] In the formula: e i For error parameters, This is the estimated value of x1 in the second-order nonlinear model of the vehicle. η is the estimated value of x2 in the second-order nonlinear model of the vehicle. i Q(t) is the adjustable parameter of the established linear extended state observer, and Q(t) is the first derivative of the uncertain parameter and the unknown disturbance.

[0024] The error matrix of the extended state observer is as follows:

[0025]

[0026] The beneficial effects of this invention are:

[0027] This invention provides a vehicle path tracking terminal sliding mode control method based on an extended state observer. This method acquires parameter errors and external disturbances observed by the extended state observer in real time, inputs these errors and disturbances into a non-singular terminal sliding mode controller (NMT). The NMT then outputs a control signal to control the front wheel steering angle of the vehicle based on these parameters and disturbances. Furthermore, it reduces chattering during path tracking by improving the sliding surface. The NMT has advantages such as fast response, convergence within a finite time, and high steady-state tracking accuracy. The extended state observer can observe the specific values ​​of uncertain parameters and external disturbances during vehicle path tracking, integrating them into the control algorithm for better path tracking performance. This invention enables the error between the actual path and the desired path to converge to zero quickly, ensuring the vehicle moves accurately along the desired path and exhibiting strong robustness. Attached Figure Description

[0028] Figure 1 This is a schematic diagram of the overall flow of the control method of the present invention;

[0029] Figure 2 This is a schematic diagram comparing the saturation function reaching law and the linear function reaching law of the present invention;

[0030] Figure 3 This is a schematic diagram comparing the desired path and the actual tracking path curves of a vehicle in the software simulation of an embodiment of the present invention.

[0031] Figure 4 This is a schematic diagram showing the comparison curve between the actual system value and the observed value of the extended state observer in the software simulation of this invention embodiment;

[0032] Figure 5 This is a schematic diagram comparing the actual value of the disturbance with the observed value of the disturbance from the extended state observer in the software simulation of this invention.

[0033] Figure 6 This is a schematic diagram of the code for the curvature change of the desired path set during software simulation in an embodiment of the present invention. Detailed Implementation

[0034] See Figure 1 As shown, this invention provides a vehicle path tracking terminal sliding mode control method based on an extended state observer. The established anticipation error model (vehicle second-order nonlinear model) can output anticipation error to the established non-singular terminal sliding mode controller after obtaining the vehicle's desired trajectory and various vehicle dynamic parameters provided by the on-board sensors. The non-singular terminal sliding mode controller can acquire the parameter errors and unknown disturbances observed by the extended state observer in real time. The parameter errors and unknown disturbances are input into the non-singular terminal sliding mode controller, so that the non-singular terminal sliding mode controller outputs control signals to control the front wheel steering angle of the vehicle according to the anticipation error, parameter error and unknown disturbances, thereby realizing the lateral control of the vehicle.

[0035] The non-singular terminal sliding mode controller is constructed as follows:

[0036] Based on the vehicle's dynamic characteristics, a vehicle dynamics system model is constructed, including a linear tire dynamics model, a vehicle kinematics model, and a two-degree-of-freedom lateral dynamics model. Then, a second-order nonlinear vehicle model based on the aiming error is established. Based on this model, a nonsingular terminal sliding surface is constructed, and a reaching law for the nonsingular terminal sliding saturation function is developed to reduce chattering in the control system. Figure 2 As shown; based on the vehicle dynamics system model, the non-singular terminal sliding mode surface, and the convergence law of the non-singular terminal sliding mode saturation function, a non-singular terminal sliding mode controller is constructed.

[0037] The second-order nonlinear model of the vehicle is as follows:

[0038]

[0039] In the formula: u is the front wheel steering angle, r(t) is the uncertain parameter and unknown disturbance (the uncertain parameter of the system may appear in factors such as side stiffness error, sensor measurement error, and changes in the vehicle environment), v x and v y C represents the longitudinal and lateral velocities of the vehicle's center of gravity, respectively. f C r These are the lateral stiffness of the front and rear wheels of the car, d f f r Let L represent the distance from the vehicle's center of gravity along the longitudinal axis to both ends of the vehicle, M represent the distance from the vehicle's center of gravity to the aiming point, and m represent the total mass of the vehicle. z The moment of inertia of the vehicle;

[0040] Construct the nonsingular terminal sliding surface S based on the second-order nonlinear model of the vehicle:

[0041]

[0042] In the formula: Ch is the sliding surface coefficient, and C > 0; p and q are positive odd numbers, and p > q;

[0043] The non-singular terminal sliding mode saturation function reaching law is as follows:

[0044]

[0045] In the formula: ε and k are the reaching law coefficients, and ε > 0, k > 0;

[0046] To meet the requirement of convergence of the sliding surface within a finite time, and considering the uncertain parameters of the system and external disturbances, the Lyapunov function is selected: Taking the derivative with respect to V yields the equivalent control term, ultimately resulting in the non-singular terminal sliding mode controller:

[0047]

[0048] In the formula, r(t) b Let r(t) be an estimate.

[0049]

[0050] The extended state observer is constructed as follows:

[0051] Based on the established second-order nonlinear vehicle model, a third-order linear extended state observer is established. The third order represents the parameter uncertainties and unknown external disturbances. The third-order linear extended state observer is as follows:

[0052]

[0053] In the formula: e i For error parameters, This is the estimated value of x1 in the second-order nonlinear model of the vehicle. η is the estimated value of x2 in the second-order nonlinear model of the vehicle. i Q(t) is the adjustable parameter of the established linear extended state observer, and Q(t) is the first derivative of the uncertain parameter and the unknown disturbance.

[0054] The error matrix of the extended state observer is as follows:

[0055]

[0056] To verify the convergence of the vehicle path tracking terminal sliding mode control method based on the extended state observer described in this invention, the following proof process is performed in this embodiment:

[0057] For non-singular terminal sliding mode controllers, the following functions are first selected as Lyapunov functions:

[0058]

[0059] Differentiating the expression and substituting the derivative of the non-singular terminal sliding surface and the designed non-singular terminal sliding controller, we obtain:

[0060]

[0061] For the extended state observer:

[0062] The formula can be changed to:

[0063]

[0064] In the formula: C = [0, 0, 1] T If q = Q(t), then the characteristic polynomial of B is:

[0065] f(λ)=-(λ 3 +η1λ 2 +η2λ+η3) (10)

[0066] When the expression satisfies the following characteristic polynomials:

[0067]

[0068] That is, η1 = -3w0, η2 = -3w0 2 η3=-w0 3 If the error value of the established extended state observer satisfies the Hurwitz stability criterion, then the following third-order linear extended state observer is established:

[0069]

[0070] The error value of the extended state observer can be expressed by the following equation:

[0071]

[0072] By setting The error value of the extended state observer described above can then be described by the following formula:

[0073]

[0074] In the formula: σ=[σ1, σ2, σ3] T , d = Q(t), because matrix B satisfies the Herwitz stability condition, for all symmetric positive definite matrices N, a corresponding positive definite matrix G can be found that satisfies the following formula:

[0075] B TG+BG=-N (15)

[0076] Make the following assumptions: expansion state The derivative of is unknown but bounded, i.e. in It is an unknown normal value.

[0077] Construct the following Lyapunov function:

[0078] V0=σ T Gσ (16)

[0079] The derivative of V0 is:

[0080]

[0081] Based on the above assumptions, Therefore, the following formula holds true:

[0082]

[0083] in Therefore, by designing a suitable matrix N such that w0N-I>0, the designed extended state observer can obtain the ability to estimate the state of the vehicle and the total disturbance it experiences.

[0084] In summary, the vehicle path tracking terminal sliding mode control method based on the extended state observer of the present invention can make the vehicle path tracking control system stable.

[0085] To further verify the effectiveness and feasibility of the control method of this invention, Matlab simulations were performed, and the simulation data are as follows:

[0086] d f =1.015; d r =1.895; m=1270; I z =1536.7; C f =40000; C r =40000;

[0087] C h =10; L=0.02; epsl=50; p=9; q=7; k1=0.7; ω0=70; The code for the desired path curvature change is as follows: Figure 6 As shown, the theoretical analysis was verified through simulation using the Matlab program. The simulation results are as follows. Figure 3 , Figure 4 , Figure 5 As shown.

[0088] like Figure 3 As shown, the car path tracking has high accuracy and robustness, even when adding features such as... Figure 5 Under the external interference conditions shown by the solid line, the error is controlled within 0.0004m, and there is almost no chattering problem.

[0089] like Figure 4 , Figure 5 As shown, the extended state observer has a good interference observation effect and produces a small observation error. After adding high-frequency interference, it can quickly track the actual system value.

[0090] In summary, Matlab simulation experiments have verified the effectiveness and feasibility of the sliding mode control method for vehicle path tracking terminals based on extended state observers in this invention.

Claims

1. A non-singular terminal sliding mode controller characterized by: Constructed using the following method: Based on the vehicle's dynamic characteristics, a vehicle dynamics system model is constructed, including a linear tire dynamics model, a vehicle kinematics model, and a two-degree-of-freedom lateral dynamics model. A second-order nonlinear vehicle model based on the aiming error is established. A nonsingular terminal sliding mode surface is constructed based on the second-order nonlinear vehicle model, and a nonsingular terminal sliding mode saturation function reaching law is constructed to reduce chattering in the control system. Based on the vehicle dynamics system model, the nonsingular terminal sliding mode surface, and the nonsingular terminal sliding mode saturation function reaching law, a nonsingular terminal sliding mode controller is constructed. The second-order nonlinear model of the vehicle is as follows: In the formula: u is the front wheel steering angle, r(t) is the uncertain parameter and unknown disturbance, v x and v y C represents the longitudinal and lateral velocities of the vehicle's center of gravity, respectively. f C r These are the lateral stiffness of the front and rear wheels of the car, d f d r Let L represent the distance from the vehicle's center of gravity along the longitudinal axis to both ends of the vehicle, M represent the distance from the vehicle's center of gravity to the aiming point, and m represent the total mass of the vehicle. z The moment of inertia of the vehicle; Construct the nonsingular terminal sliding surface S based on the second-order nonlinear model of the vehicle: In the formula: C h is the sliding surface coefficient, and C > 0; p and q are positive odd numbers, and p > q; The non-singular terminal sliding mode saturation function reaching law is as follows: In the formula: ε and k are the reaching law coefficients, and ε > 0, k > 0; The non-singular terminal sliding mode controller is: where r(t) b is an estimate of r(t), 2. An extended state observer-based vehicle path tracking terminal sliding mode control method, characterized in that: The non-singular terminal sliding mode controller acquires the parameter error and external disturbance observed by the extended state observer in real time. The parameter error and external disturbance are input into the non-singular terminal sliding mode controller, so that the non-singular terminal sliding mode controller outputs a control signal to control the front wheel steering angle of the vehicle according to the parameter error and external disturbance. The non-singular terminal sliding mode controller is constructed using the following method: Based on the vehicle's dynamic characteristics, a vehicle dynamics system model is constructed, including a linear tire dynamics model, a vehicle kinematics model, and a two-degree-of-freedom lateral dynamics model. Then, a second-order nonlinear vehicle model based on the aiming error is established. A nonsingular terminal sliding mode surface is constructed based on the second-order nonlinear vehicle model, and a nonsingular terminal sliding mode saturation function reaching law is constructed to reduce chattering problems in the control system. Based on the vehicle dynamics system model, the nonsingular terminal sliding mode surface, and the nonsingular terminal sliding mode saturation function reaching law, a nonsingular terminal sliding mode controller is constructed.

3. The vehicle path tracking terminal sliding mode control method based on an extended state observer according to claim 2, characterized in that: The second-order nonlinear model of the vehicle is as follows: In the formula: u is the front wheel steering angle, r(t) is the uncertain parameter and unknown disturbance, v x and v y C represents the longitudinal and lateral velocities of the vehicle's center of gravity, respectively. f C r These are the lateral stiffness of the front and rear wheels of the car, d f d r Let L represent the distance from the vehicle's center of gravity along the longitudinal axis to both ends of the vehicle, M represent the distance from the vehicle's center of gravity to the aiming point, and m represent the total mass of the vehicle. z The moment of inertia of the vehicle; Construct the nonsingular terminal sliding surface S based on the second-order nonlinear model of the vehicle: wherein: C h is a slip surface coefficient, and C > 0; p, q are positive odd numbers, and p > q; The non-singular terminal sliding mode saturation function reaching law is as follows: In the formula: ε and k are the reaching law coefficients, and ε > 0, k > 0; The non-singular terminal sliding mode controller is: where r(t) b is an estimate of r(t), 4. The vehicle path tracking terminal sliding mode control method based on an extended state observer according to claim 2, characterized in that: The extended state observer is constructed using the following method: Based on the established second-order nonlinear vehicle model, a third-order linear extended state observer is established. The third order represents the parameter uncertainties and unknown external disturbances. The third-order linear extended state observer is as follows: In the formula: e i For error parameters, This is the estimated value of x1 in the second-order nonlinear model of the vehicle. η is the estimated value of x2 in the second-order nonlinear model of the vehicle. i Q(t) is the adjustable parameter of the established linear extended state observer, and Q(t) is the first derivative of the uncertain parameter and the unknown disturbance. The error matrix of the extended state observer is as follows:

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