A path tracking method and system for a front-wheel-steering rear-wheel-distributed-drive vehicle

Abstract

The present application relates to the technical field of auxiliary driving, in particular to a path tracking method for a front-wheel-steering rear-wheel-distributed driving vehicle. The method comprises the following steps: S1, establishing a nonlinear vehicle dynamics model of the front-wheel-steering rear-wheel-distributed driving vehicle; S2, establishing a path tracking task constraint; S3, designing an adaptive robust controller based on the task constraint; S4, analyzing the stability of the adaptive robust controller and the constraint following error performance based on Lyapunov; and S5, using the controller in step S3 to control the vehicle to track the path. The path tracking control algorithm proposed in the present application establishes a model that is more consistent with the actual dynamics characteristics of the vehicle, and considers and processes the case of large initial tracking deviation, which can improve the control stability of the vehicle under the influence of uncertain factors and large initial tracking deviation, and limit the tracking error within a specified range.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of auxiliary driving, in particular to a path tracking method for a front-wheel-steering rear-wheel-distributed-drive vehicle. BACKGROUND

[0002] Path tracking is one of the important functions of an autonomous vehicle, and its purpose is to make the vehicle follow a given desired path by controlling the steering mechanism. The given desired path point information is generally issued by the decision planning module, and the issued desired path point usually includes information such as desired speed, lateral and longitudinal coordinates, and yaw angle. In the lateral path tracking of an autonomous vehicle, a reasonable controller needs to be designed to make the vehicle complete the specified steering action to track the desired lateral and longitudinal coordinates and yaw angle.

[0003] A vehicle with front-wheel-steering rear-wheel-distributed-drive has two control modes for realizing vehicle steering, i.e., front-wheel-steering control and rear-axle-active yaw moment control. For a path tracking control method with expected steering angle and active yaw moment as control outputs, there are currently methods such as sliding mode control, model predictive control (MPC), and composite nonlinear feedback control.

[0004] In the prior art, W. Zhenpo et al. proposed a hierarchical control architecture. The upper controller is based on a two-degree-of-freedom dynamic model, and a sliding surface is designed directly based on the tracking error. The designed sliding mode control law outputs the steering angle and the yaw moment control quantity to track the expected yaw angular velocity. In the lower controller, a torque optimization distribution strategy is designed to distribute the required torque to the driving wheels to enhance the stability of the vehicle. However, the designed hierarchical sliding mode control method focuses on the stability and steady-state performance of the tracking error in vehicle control, and ignores the changes of the tracking error in the transient convergence process, so it cannot guarantee the transient and steady-state safety of the vehicle in path tracking. Moreover, it directly takes the tracking error as the controlled object, and when the initial tracking error is large, the control force based on error feedback is large, which is easy to cause actuator saturation, and lacks effective control under this special condition.

[0005] Qifan Tan et al. proposed a hierarchical control architecture that combines model predictive control and torque distribution strategy. In the upper controller design, based on the path tracking error model, the general disturbance caused by distribution error and the sudden disturbance caused by external force are considered in the model, and the robust MPC control law outputting the steering angle and the expected yaw moment is obtained by converting the robustness constraint into a linear matrix inequality. The lower controller distributes the expected yaw moment obtained by the upper controller to the drive wheels, and combines the steering control to track the path. The hierarchical control architecture based on the model predictive control method also focuses on the steady-state performance of the tracking error, aiming to finally converge the tracking error to a small interval, while ignoring the transient performance of the tracking error in the convergence process. In addition, its solution based on rolling optimization requires high controller computing power.

[0006] R. Wang et al. designed a composite nonlinear feedback controller composed of a linear feedback part and a nonlinear feedback part. The linear part includes a reference yaw rate derivative term related to the change of road curvature. Considering that the vehicle lateral velocity is usually difficult to measure with low-cost sensors, a reduced-order observer is designed to estimate the lateral velocity only using the measured value of the yaw rate. When the vehicle tracking error is close to converge to 0, the nonlinear part is used to increase the damping ratio, thereby eliminating the overshoot. This control method makes the vehicle yaw rate and lateral velocity track the respective expected values with relatively low overshoot and steady-state error. This method lacks consideration of the time-varying uncertainty that may exist in the actual vehicle dynamics. When the initial tracking error is large, the error-based feedback term in the controller is large, which can cause actuator saturation, and cannot guarantee effective control of the vehicle under large initial tracking error conditions.

[0007] In addition, the current commonly used lateral path tracking control method is difficult to handle the actuator saturation problem that may be caused under large initial tracking error, and actuator saturation can worsen the control performance. In the case of vehicle model uncertainty, this control instability caused by actuator saturation will be exacerbated, and the transient performance of the tracking error cannot be guaranteed, and the tracking error may be too large to exceed the safety boundary, so the safety of the automatic driving vehicle in performing the path tracking task under this initial condition cannot be strictly guaranteed. SUMMARY

[0008] The purpose of the present invention is to address the problems existing in the background technology and to propose a path tracking method for a front-wheel steering, rear-wheel distributed drive vehicle. The present invention designs a path tracking robust control method for front-wheel steering, rear-wheel distributed drive vehicles that ensures preset performance of tracking error. The control method mainly consists of vehicle dynamics modeling, tracking kinematics modeling, path tracking constraint establishment and robust controller design. The path tracking control algorithm proposed in the present invention establishes a model that is more in line with the actual dynamic characteristics of the vehicle, and takes into account and handles the situation of large initial tracking deviations. It can improve the control stability of the vehicle under the influence of uncertain factors and large initial tracking deviations, and limit the tracking error sample to a specified area.

[0009] A first aspect of the present invention provides a path tracking method for a front-wheel steering and rear-wheel distributed drive vehicle, comprising the following specific steps:

[0010] S1. Establish a nonlinear vehicle dynamics model with front-wheel steering and rear-wheel distributed drive;

[0011] S11. Constructing a vehicle lateral dynamics model;

[0012] S12, constructing a path tracking operational model;

[0013] S2. Establish path tracking task constraints;

[0014] S21, introduce auxiliary variables to correct the bilateral constraints of lateral errors;

[0015] S22, perform state bijective transformation to convert the bounded state into an unbounded state;

[0016] S23, establishing path tracking equality constraints;

[0017] S3. Design an adaptive robust controller based on task constraints;

[0018] S31. Design the servo control law for the nominal system;

[0019] S32. Design the error feedback partial control law;

[0020] S33. Design an adaptive compensation control law to compensate for the initial deviation and uncertainty of the system;

[0021] S4. Analysis of the stability and constrained following error performance of adaptive robust controllers based on Lyapunov;

[0022] S5. Use the controller in step S3 to control the vehicle to perform path tracking.

[0023] Preferably, the nonlinear vehicle dynamics model of front-wheel steering and rear-wheel distributed drive established in step S1 includes:

[0024] The vehicle longitudinal axis direction is x axis, and the vehicle lateral axis direction is y axis, forming an xoy vehicle body coordinate system, and CoG is the vehicle center of gravity; the vehicle front axle distance from the center of gravity is l f , and the rear axle distance from the center of gravity is l r ;

[0025] The vehicle front axle has a steering function, and it is assumed that the turning angles of the two front wheels are consistent, and a front wheel turning angle δ f control interface; the two rear wheels are driving wheels, and provide driving force / braking force F x3 , F x4 interface;

[0026] The model further includes a positioning module, a perception module, a decision planning module and a control module; at the same time, a turning angle sensor and a wheel speed sensor are provided for obtaining a vehicle front wheel turning angle δ f and a steering angular velocity The planning module provides expected path information and curvature information c R of the expected path to the control module, and the control module obtains an active yaw moment and an expected turning angle control amount according to a designed path tracking algorithm, and the active yaw moment and the turning angle are input to the driving wheels and the steering mechanism in the chassis module after driving force distribution.

[0027] Preferably, in step S11, a vehicle lateral dynamics model with a second-order inertia time delay link is established as follows:

[0028]

[0029] Wherein, m is the vehicle mass, I z is the vehicle moment of inertia, Ω1 and Ω2 are time-varying bounded uncertainty parameters caused by model errors and external disturbances; δ f，des is the vehicle expected front wheel turning angle; ξ and w n are system parameters of the second-order steering system with time delay, and their specific values need to be obtained through steering test calibration;

[0030] The specific expressions of other dynamic parameters a1-a6 are as follows:

[0031]

[0032] Wherein, C f is the front wheel cornering stiffness, C r is the rear wheel cornering stiffness; in practice, the dynamic parameters m, I z , C f , C r , l f , l r in the above formula are difficult to identify, so it is assumed that the parameters a1-a6 are all from the nominal part and an unknown and time-varying uncertainty part Δa i composition.

[0033] Preferably, in step S12, the vehicle obtains its pose information such as longitudinal and lateral coordinates and yaw angle in the geodetic coordinate system through an inertial measurement unit, and obtains the expected path point longitudinal and lateral coordinates, yaw angle and road curvature information through an upper planning module; the yaw angle error of the vehicle relative to the expected path can be expressed as:

[0034]

[0035] wherein, is the yaw angle error, is the yaw angle; is the ideal yaw angle of the expected path point, and the ideal yaw angle change rate can be expressed as:

[0036]

[0037] v x is the longitudinal velocity;

[0038] Then the first and second order forms of are as follows:

[0039]

[0040] The lateral error is defined as the shortest distance between the current position of the vehicle and the nearest expected path point, and according to the kinematic relationship, the first and second order forms of the lateral error are as follows:

[0041]

[0042] In order to facilitate subsequent controller design, the vehicle lateral dynamics formula is integrated, and the state space equation based on error dynamics is established as follows:

[0043]

[0044] wherein, the vector is the state variable, and U(t) = [ΔM, δ f，des ] T is the control input; the specific expressions of other parts M, W, C, B and g are as follows:

[0045]

[0046] Preferably, in step S21, the path tracking lateral offset of the vehicle needs to satisfy the following boundary conditions:

[0047]

[0048] wherein, and are the allowed minimum and maximum lateral offsets, respectively;

[0049] Introduce Definition 1 : If the following condition is satisfied, it is a conversion function:

[0050] (1) and is monotonically increasing on [0, T) and remains constant on [T, +∞), where T is a preset time;

[0051] (2) is and is bounded for all t≥0, n is the order of the controlled system;

[0052] The initial position of the vehicle can be far from the nearest point of the desired path, i.e. e y (0) is too large; introduce an auxiliary variable ψ(t) to correct the lateral error, and the corrected error is as follows:

[0053]

[0054] wherein, Conversion function According to Definition 1, the following is selected:

[0055]

[0056] Based on the above correction, the corrected lateral error has the following properties:

[0057]

[0058] The following constraint is imposed on the corrected lateral error:

[0059]

[0060] The above formula is re-expressed as:

[0061]

[0062] wherein, preset performance boundary parameter and satisfy the following inequality:

[0063]

[0064] The original lateral error is limited in a more stringent strip-shaped region.

[0065] Preferably, in step S22, the bounded state ​Transformed into unbounded state z1(t), z1(t)∈(-∞, +∞), the barrier transformation function based on tangent function aims to achieve the following transformation:

[0066]

[0067] Wherein,

[0068] Derivation of the above formula with respect to time t is as follows:

[0069]

[0070] Let z2 represent the vehicle yaw angle error, i.e. Let z3=δ f Therefore, the controlled state quantity Can be converted into a new state Z=[z1, z2, z3] T ;

[0071] The following formula is obtained:

[0072]

[0073] Wherein

[0074]

[0075] Since for all z1>0, Φ2(z1)>0 is established, Ξ2 is full rank; after state transformation, the dynamics equation of state Z about the unconstrained variable z1 can be expressed as:

[0076]

[0077] Wherein

[0078]

[0079] Because Ξ2(Y) and B are full rank, Ξ2(Y)B is also full rank, i.e. Is also invertible.

[0080] Preferably, in step S23, the goal of the autonomous vehicle path tracking task is to make the path tracking error converge to 0, i.e. the vehicle travels on the desired path point; the convergence performance is expressed as the following first and second order equation constraints about the system state:

[0081]

[0082] Solving the differential equation of the above formula, the correction of lateral error and yaw angle error will be And ​and as time approaches 0; based on the properties of the state transformation, impose equal constraints on the transformed states:

[0083]

[0084] Write the above equality constraints in matrix form Let which represents the constraint following error;

[0085] where,

[0086] The second order form of the constraints is:

[0087] where,

[0088] Preferably, in step S3, the parameter matrix of the dynamics equation of the state Z about the unconstrained variable z1 after the state transformation is decomposed into the following nominal part and uncertain part:

[0089]

[0090] where the matrix with a horizontal line is the known nominal part, and the other matrices represent the unknown uncertain part; for simplicity of notation, let I is the identity matrix;

[0091] First, design the following nominal control law for the nominal system:

[0092]

[0093] For the initial constraint following error of the system, design the feedback control law part:

[0094]

[0095] For the uncertain part of the system, introduce the following reasonable assumptions:

[0096] Assumption 1: for (Z, t) ∈ R 3 × R + , A is full rank; therefore AA T is invertible;

[0097] Assumption 2: according to assumption 1, for a given P ∈ R 3×3 , P > 0, let

[0098]

[0099] There is a constant ρ E > -1 such that for all (Z, t) ∈ R 3 × R + ,

[0100]

[0101] in, represents the minimum eigenvalue of the matrix in brackets;

[0102] Assumption 3: For all There exists an unknown constant vector α∈(0,+∞) κ and a known function Therefore, there is

[0103]

[0104] The specific parameter perturbation is unknown, but α T Π constrains the overall bounds of these uncertainties; for specific values ​​of α, an adaptive law is designed to update the estimate

[0105]

[0106] in, is a vector The i-th component of ; k1, k2 are scalar constants;

[0107] Based on the above assumptions about uncertainty boundaries, the following control components are designed to compensate for the uncertainty:

[0108]

[0109] in

[0110]

[0111] The total control input is thus defined as

[0112] U=p1+p2+p3

[0113] The controller consists of three parts: p1 is the nominal system control, p2 processes the initial constraint following deviation of the system, and p3 uses Dealing with system uncertainty; κ in p2 represents the control parameter, P∈R in p3 3 is a constant matrix given in advance; the value of the uncertainty parameter α is estimated by the adaptive law.

[0114] Preferably, in step S4, the Lyapunov function is selected as follows:

[0115]

[0116] Taking the derivative of the above formula with respect to time, we get the first-order derivative of the Lyapunov function as follows:

[0117]

[0118] By inequality scaling, we can get:

[0119]

[0120] where,

[0121] Let Then according to Lyapunov min-max principle, the uniform boundedness of the constraint following error β and the uncertainty parameter estimation error is obtained as follows:

[0122]

[0123] where r>0 is a given constant, and the final uniform boundedness: The uniform boundedness guarantees that β and are bounded, and the final uniform boundedness guarantees that β and will eventually converge to a neighborhood around 0 with time, and according to the uniform boundedness of β, it is obtained that z i is bounded, and according to the properties of state transformation, it is obtained that the modified error constraint is strictly guaranteed, so that the tight strip performance of the original lateral error is guaranteed. y The final uniform boundedness guarantees that the tracking error e and will eventually converge to a neighborhood around 0.

[0124] The second aspect of the application provides a path tracking system for a front-wheel-steering rear-wheel-distributed-drive vehicle, comprising a planning layer, a control layer, a drive / brake force distribution and a vehicle model.

[0125] The planning layer is used to input the desired speed and the desired path.

[0126] The control layer receives the desired speed information and the desired path information of the planning layer, and obtains the lateral and longitudinal positions, the speed, the yaw angle, the steering angle and the steering angular velocity of the vehicle through the vehicle-mounted inertia unit, and obtains the desired steering angle and the active yaw moment through the proposed path tracking control algorithm and the drive / brake force distribution.

[0127] The drive / brake force distribution module distributes the active yaw moment into the desired driving force required by each driving wheel, and inputs the desired steering angle calculated by the control layer into the chassis motion control module of the vehicle model to drive the vehicle motion.

[0128] Compared with the prior art, the application has the following beneficial technical effects:

[0129] 1. The application is based on a vehicle dynamics model, inertia time delay is added in the modeling of the vehicle dynamics model, and modeling errors and external disturbances and other uncertain factors are considered, which is more in line with the actual vehicle dynamics characteristics.

[0130] 2. In the modeling of lateral tracking error, an auxiliary variable based on a conversion function is introduced to correct the original lateral error, and the lateral error is corrected as the control object, so that the lateral error can be kept at a small value (initial value is 0), thus the large initial tracking error can be adapted, and the actuator saturation can be avoided.

[0131] 3. The application obtains the error state without constraints by applying additional constraints to the corrected error and state transformation technology. By ensuring the consistent bounded performance of the unconstrained system, the lateral tracking error can be strictly limited in the preset compact band region at the transient and steady state level, and the safety of the vehicle in the execution of the path tracking task can be ensured. BRIEF DESCRIPTION OF DRAWINGS

[0132] Figure 1 is a schematic diagram of a front-wheel-steering rear-wheel-distributed drive vehicle of an embodiment of the application;

[0133] Figure 2 is a schematic diagram of a path tracking error of an embodiment of the application;

[0134] Figure 3 is a flow chart of a control method of an embodiment of the application;

[0135] Figure 4 is a system diagram of an embodiment of the application. DETAILED DESCRIPTION

[0136] Embodiment 1

[0137] The front-wheel-steering rear-wheel-distributed drive vehicle dynamics model considered by the application is shown in Figure 1 , the vehicle longitudinal axis direction is x axis, the vehicle lateral axis direction is y axis, forming the xoy vehicle body coordinate system, CoG is the vehicle center of gravity. The front axle of the vehicle is l f from the center of gravity, the rear axle is l r from the center of gravity. The front axle of the vehicle has a steering function, it is assumed that the steering angles of the two front wheels are consistent, and the front wheel steering angle δ f control interface is set. The two rear wheels of the vehicle are driving wheels, providing driving / braking force F x3 , F x4Interface. Delta M is the active yaw moment, which is the moment generated by the driving force / braking force of the left and right drive wheels of the rear axle around the center of mass. After obtaining Delta M, it is distributed to the left and right drive wheels of the rear axle according to the corresponding distribution rule. In addition, the automatic driving vehicle is equipped with a positioning module, a perception module, a decision planning module and a control module. At the same time, it is equipped with a steering angle sensor and a wheel speed sensor, so that the vehicle front wheel steering angle f and the steering angular velocity The planning module provides the desired path information and the curvature information c R of the desired path for the control module. y The control module obtains the active yaw moment and the expected steering angle control amount according to the designed path tracking algorithm, and the active yaw moment and the steering angle are input to the drive wheels and the steering mechanism in the chassis module after the driving force distribution. The path tracking error model is shown in Figure 2 e y is the tracking lateral error, which is the lateral distance from the center of gravity of the vehicle to the nearest expected path point, is the yaw angle error, which is the difference between the vehicle yaw angle and the direction of the nearest expected path point. The vehicle can obtain the relative position between the vehicle and the expected path through calculation. In addition, the vehicle can obtain its own motion information: longitudinal speed v x , lateral speed v y , yaw angle yaw angular velocity

[0138] The vehicle lateral path tracking controller designed according to the preset performance steps is as follows:

[0139] Construct a vehicle lateral dynamics model

[0140] The lateral dynamics of the actual front-wheel-steering rear-wheel-distributed driving vehicle is affected by many factors. In order to balance the analysis simplicity and accuracy of the model, the following reasonable assumptions are made:

[0141] (1) Assume that the frame and suspension are rigid structures, and ignore their weak nonlinear effects. In addition, the vehicle roll and pitch dynamics can be ignored, and the main concern is the lateral and yaw dynamics of the vehicle.

[0142] (2) Assume that the front and rear axles have the same tire side stiffness, side slip angle, and front axle left and right steering wheel steering angle.

[0143] Since any mechanical system has time delay, especially the steering mechanism of a vehicle, the steering mechanism needs a certain time to complete the steering operation after the controller sends the steering signal, and the delay time is called the inertia time delay of the steering mechanism. The existence of time delay problem poses a great challenge to the safety of autonomous vehicles, and this factor cannot be ignored when designing the controller. Therefore, combined with Newtonian mechanics and the theorem of rigid body rotation, a vehicle lateral dynamics model with a second-order inertia time delay link is established as follows:

[0144]

[0145] where m is the mass of the vehicle, I z is the rotational inertia of the vehicle, Ω1 and Ω2 are time-varying bounded uncertainty parameters caused by model errors and external disturbances. δ f,des is the desired front wheel steering angle of the vehicle. ξ and w n are system parameters of the second-order steering system with time delay, and their specific values need to be obtained in advance by steering test calibration. The specific expressions of other dynamic parameters a1-a6 are as follows:

[0146]

[0147] where C f is the front wheel cornering stiffness, C r is the rear wheel cornering stiffness. In practice, the dynamic parameters in (4) and (5) (such as m, I z , C f , C r , l f , l r ) are difficult to identify because they can be time-varying. Therefore, it is assumed that the parameters a1-a6 are composed of a nominal part and an unknown and time-varying uncertainty part Δa i .

[0148] Constructing a path tracking kinematic model

[0149] The vehicle obtains its pose information such as longitudinal and lateral coordinates and yaw angle in the geodetic coordinate system through the inertial measurement unit (IMU), and obtains the expected path point information such as longitudinal and lateral coordinates, yaw angle, and road curvature through the upper planning module. The yaw angle error of the vehicle relative to the expected path can be expressed as:

[0150]

[0151] where, is the ideal yaw angle of the expected path point, and the ideal yaw angle rate of change can be expressed as:

[0152]

[0153] The first and second order forms of are as follows:

[0154]

[0155] Assume that the rate of change of road curvature is small, so the term in equation (9) can be neglected. The lateral error is defined as the shortest distance from the current vehicle position to the nearest desired path point. According to the kinematic relationship, the first and second order forms of the lateral error are as follows:

[0156]

[0157] To facilitate the subsequent controller design, the vehicle lateral dynamics (1)-(6) and equations (9)-(12) are integrated to establish the state space equation based on error dynamics as follows:

[0158]

[0159] where the vector is the state variable, and U(t) = [AM, δ f，des ] T is the control input. The specific expressions of the other parts M, W, C, B, g are as follows:

[0160]

[0161] It is noted that the above system with steering mechanism time delay is a typical under-actuated system, which has three state variables (lateral error, heading error, and actual steering angle) but only two control inputs. This under-actuated characteristic combined with vehicle dynamics uncertainty makes vehicle lateral path tracking control a challenge. The robust control method based on constraint following theory to be designed next can handle the above problems.

[0162] 2.2.3 Building constraints for path tracking task

[0163] (1) Introducing auxiliary variables

[0164] The actual road has boundaries, so it is necessary to ensure that the lateral deviation of the vehicle path tracking is within the safe range of the road. We express this safety constraint as the following inequality:

[0165]

[0166] where and are the minimum and maximum allowed lateral deviation, respectively.

[0167] First, introduce Definition 1: If the following conditions are met, it is a conversion function:

[0168] (1) and is monotonically increasing on [0, T) and remains where T is a pre-set time.

[0169] (2) is and is bounded for all t ≥ 0, n is the order of the controlled system.

[0170] The initial position of the vehicle can be far away from the nearest point of the desired path (i.e. e y (0) is too large), which will cause the controller to generate a saturated control force. The long-time actuator saturation phenomenon will deteriorate the control performance, and even cause actuator failure, which will lead to safety accidents. Therefore, an auxiliary variable ψ(t) is introduced to modify the lateral error, and the modified error is as follows:

[0171]

[0172] where, The conversion function According to Definition 1, the following is selected:

[0173]

[0174] Based on the above modification, combined with (15) and (16), we can get the modified lateral error with the following properties:

[0175]

[0176] Combined with equation (15), in order to keep the original lateral error still satisfy the double inequality after modification, the following constraints are imposed on the modified lateral error:

[0177]

[0178] Substitute equation (16) into (19), combined with equation (15), in order to strictly limit the original lateral error within the pre-set strip region, equation (19) needs to be re-expressed as:

[0179]

[0180] where, the pre-set performance boundary parameter and satisfy the following inequalities:

[0181]

[0182] This is to limit the original lateral error in a more stringent strip region, which also means that the safety of the vehicle is strictly guaranteed in the transient adjustment of the lateral error. We will achieve this goal later in combination with the state transformation technique.

[0183] (2) State transformation

[0184] This part proposes a transformation method based on the barrier transformation function of the obstacle, which converts the bounded state into an unbounded state z1(t), z1(t)∈(-∞, +∞). The barrier transformation function based on the tangent function aims to achieve the following transformation:

[0185]

[0186] Where,

[0187] Differentiate equation (23) with respect to time t to get:

[0188]

[0189] In addition, we use z2 to represent the vehicle yaw angle error, that is, Let z3=δ f Therefore, the controlled state variable can be converted into a new state Z=[z1, z2, z3] T . Then the following equation can be obtained:

[0190]

[0191] Where

[0192]

[0193] Since Φ2(z1)>0 holds for all z1>0, Ξ2 is full rank. After state transformation, the dynamics equation of state Z about the unconstrained variable z1 can be expressed as:

[0194]

[0195] Where

[0196]

[0197] Because Ξ2(Y) and B are full rank, is also full rank, that is, is also invertible. In addition, the premise of the above transformation is that the initial value of satisfies the constraint condition of equation (19). Obviously, after introducing the auxiliary variable correction, this condition is naturally satisfied, because holds always. G(·) and G -1 (·) are monotonically increasing functions. Combining the condition G(0) = 0, we can conclude that Z→0 is a necessary and sufficient condition for X→. Through this transformation, the bilateral inequality constraints of X are equivalent to the uniform boundedness of the new state Z. Next we aim to design a controller to guarantee the uniform boundedness and ultimate uniform boundedness of the transformed state Z in the presence of time-varying uncertainties.

[0198] (3) Establish equality constraints

[0199] The goal of the path following task for autonomous vehicles is to let the path following error converge to 0, i.e., the vehicle drives on the desired path point. This convergence performance can be translated into the following first and second order equality constraints on the system states:

[0200]

[0201] Solving the differential equations of (30) and (31), the corrections of lateral error and yaw angle error will be and and approach to 0 as time goes to infinity. Based on the properties of the state transformation, the same constraints are imposed on the transformed state:

[0202]

[0203] Write the above equality constraints in matrix form and let which represents the constraint following error.

[0204] where,

[0205] The second order form of the constraints is:

[0206] where,

[0207] Adaptive Robust Controller Design

[0208] This section will introduce the steps to design a robust controller based on the constraint following theory. First, design a servo control law for the nominal system without considering the initial constraint following error and uncertainties. Second, design the feedback part of the control law and the uncertainty compensation part of the control law to compensate for the initial deviation and uncertainties of the system.

[0209] Decompose the parameter matrix in (28) into the following nominal part and uncertainty part:

[0210]

[0211] The matrix with horizontal lines is the known nominal part, and the other matrices represent the unknown uncertain parts. To simplify the notation, let I is the identity matrix.

[0212] First, the following nominal control law is designed for the nominal system:

[0213]

[0214] For the initial constrained following error of the system, design the feedback control law part:

[0215]

[0216] For the system uncertainty part, the following reasonable assumptions are introduced:

[0217] Assumption 1: For (Z, t)∈R 3 ×R + , A is full rank. So AA T It is reversible.

[0218] Assumption 2: According to Assumption 1, for a given P∈R 3×3 , P>0, let

[0219]

[0220] There exists a constant (possibly unknown) ρ E > -1 so that for all (Z, t)∈R 3 ×R + ,have

[0221]

[0222] in, Represents the smallest eigenvalue of the matrix in brackets.

[0223] Assumption 3: For all There is an unknown constant vector and a known function Therefore, there is

[0224]

[0225] The specific parameter perturbation is unknown, but α T Π limits the overall bounds of these uncertainties. For specific values ​​of α, an adaptive law is designed to update the estimate

[0226]

[0227] in, ( is the i-th component of the vector k1, k2 are scalar constants.

[0228] Based on the above assumptions for the uncertainty bound, the following control parts are designed to compensate the uncertainty:

[0229]

[0230] where

[0231]

[0232] Thus the total control input is defined as

[0233] U = p1 + p2 + p3 (44)

[0234] The controller consists of three parts, p1 is the nominal system control, p2 handles the initial constraint following deviation, and p3 handles the system uncertainty by p2 is represented by κ, and p3 is represented by P ∈ R 3 which is a constant matrix given in advance. The value of the uncertainty parameter α is estimated by an adaptive law.

[0235] Stability and safety analysis

[0236] Lyapunov stability theory is used to analyze the stability of the controller and the constraint following error performance, thus the lateral tracking error performance. The Lyapunov function is chosen as follows:

[0237]

[0238] Taking the derivative of the above equation with respect to time, the first order derivative of the Lyapunov function is obtained as follows:

[0239]

[0240] Combining equations (28) and (35)-(41), and by inequality scaling, we can get:

[0241]

[0242] where,

[0243] Let Then according to the Lyapunov min-max principle, the uniform boundedness and the ultimate uniform boundedness of the constraint following error β and the uncertainty parameter estimation error are obtained. The uniform boundedness guarantees that β and are bounded, and the ultimate uniform boundedness guarantees that β and converges to a neighborhood around 0 eventually in time. i is uniformly bounded according to the property of β, we can get that z y is bounded, and according to the property of state transformation, we can get the conclusion that constraint (19) is strictly guaranteed, thus guaranteeing the compact strip performance of the original lateral error e y . and will converge to a neighborhood around 0 eventually.

[0244] Drive / brake force distribution

[0245] The control amount U(t) = [ΔM, δ f，des ] T in which ΔM is a combination of driving forces of the left and right rear drive wheels and cannot be directly input to the chassis for motion control, and needs to be distributed to the left and right rear drive wheels according to the following drive / brake force distribution rule:

[0246]

[0247] where F x is the total driving force calculated for vehicle longitudinal speed control, and the present application does not consider longitudinal control. w is the wheelbase of the vehicle.

[0248] The present application is different from existing lateral path tracking control algorithms in terms of vehicle dynamics modeling and path tracking task modeling. In the dynamics model, inertia time delay and dynamic uncertainty factors are integrated, which is more in line with the actual vehicle motion characteristics. The auxiliary variable based on the conversion function is introduced to modify the original lateral error, so that its initial value is 0, which can adapt to large initial tracking error conditions and can avoid actuator saturation. Through state transformation, the uniform boundedness and the ultimate uniform boundedness of the unconstrained system are realized, the preset compact strip zone performance of the tracking error is strictly guaranteed, and the safety of the autonomous vehicle when performing the path tracking task is improved.

[0249] The embodiments of the present application are described in detail above in combination with the drawings, but the present application is not limited thereto, and various changes can be made within the scope of knowledge possessed by those skilled in the art without departing from the purpose of the present application.

Claims

1. A path tracking method for a front-wheel-steering rear-wheel-distributed-drive vehicle, characterized by, The method comprises the following specific steps: S1, establishing a nonlinear vehicle dynamics model of front-wheel steering and rear-wheel distributed drive; S11, constructing a vehicle lateral dynamics model; S12, constructing a path tracking operation model; S2, establishing path tracking task constraints; S21, introducing auxiliary variables to correct lateral error bilateral constraints; S22, performing state bijective transformation to convert bounded states into unbounded states; S23, establishing path tracking equation constraints; S3, designing an adaptive robust controller based on task constraints; S31, designing a servo control law for a nominal system; S32, designing an error feedback part control law; S33, designing an adaptive compensation part control law to compensate for system initial deviation and uncertainty; S4, analyzing stability of the adaptive robust controller and constraint following error performance based on Lyapunov; S5, controlling the vehicle to track a path by using the controller in step S3.

2. The front wheel turning rear wheel distributed drive vehicle path tracking method according to claim 1, characterized by, The nonlinear vehicle dynamics model of front-wheel steering and rear-wheel distributed drive established in step S1 comprises: The vehicle longitudinal axis direction is x axis, the vehicle lateral axis direction is y axis, and an xoy vehicle body coordinate system is formed, and CoG is the vehicle gravity center; the vehicle front wheelbase gravity center is l f , and the rear wheelbase gravity center is l r ; The front axle of the vehicle has a steering function, assuming that the turning angles of the two front wheels are consistent, and the turning angle of the front wheels is δ f The control interface; the two rear wheels are driving wheels, providing driving force / braking force F x3 , F x4 The interface; The model further comprises a positioning module, a perception module, a decision planning module and a control module; meanwhile, a corner sensor and a wheel speed sensor are provided for obtaining a front wheel corner δ f and a steering angle speed The planning module provides the control module with expected path information and curvature information c R of the expected path, the control module obtains an active yaw moment and an expected corner control amount according to a designed path tracking algorithm, and the active yaw moment and the expected corner control amount are input into the driving wheels and the steering mechanism in the chassis module after being distributed by a driving force.

3. The front wheel turning rear wheel distributed drive vehicle path tracking method according to claim 2, characterized by, In step S11, the vehicle lateral dynamics model with a second-order inertia time delay link is established as follows: where m is the vehicle mass, I z is the vehicle rotational inertia, Ω1 and Ω2 are time-varying bounded uncertainty parameters caused by model errors and external disturbances; v x , v y are the longitudinal and lateral velocities, respectively, is the yaw angle, ΔM is the active yaw moment; δ f，des is the vehicle desired front wheel steering angle; ξ and w n are system parameters related to the second-order steering system with time delay, the specific values of which need to be obtained through steering tests. Specific expressions of other dynamic parameters a1-a6 are as follows: where C f is the front cornering stiffness, C r is the rear cornering stiffness; in practice the dynamic parameters m, I z , C f , C r , I f , I r are difficult to identify, so the parameters a1-a6 are assumed to be composed of a nominal part and an unknown and time-varying uncertainty part Δa i .

4. The front wheel turning rear wheel distributed drive vehicle path tracking method according to claim 3, characterized by, In step S12, the vehicle obtains its longitudinal and lateral coordinates and yaw angle pose information in a geodetic coordinate system through an inertial measurement unit, and obtains expected path point longitudinal and lateral coordinates, a yaw angle and road curvature information through an upper planning module; a yaw angle error of the vehicle relative to the expected path can be expressed as: wherein is the yaw angle error, is the yaw angle; is the ideal yaw angle of the desired path point, the ideal yaw angle rate of change can be expressed as a function of the road curvature: v x For longitudinal velocity; then get The first and second order forms are as follows: In the above formula, c R is the curvature information; the lateral error is defined as the shortest distance from the current position of the vehicle to the nearest desired path point, and according to the kinematic relationship, the first and second order forms of the lateral error are as follows: The state space equation based on error dynamics is established as follows: where the vector is the state variable, U(t) = [AM, AS f，des ] T is the control input; the specific expressions of the other coefficient matrices M, W, C, B, g are as follows:

5. The front wheel turning rear wheel distributed drive vehicle path tracking method according to claim 4, characterized by, In step S21, the path tracking lateral deviation of the vehicle needs to satisfy the following boundary conditions: wherein, and are the allowed minimum and maximum lateral offset, respectively; Introduce definition A: If the following conditions are met, it is a conversion function: A、 and is monotonically increasing on [0, T) and remains constant on [T, +∞) where T is a preset time; B、 For and bounded for all t ≥ 0, n is the order of the controlled system; The initial position of the vehicle can be far from the closest point of the desired path, i.e. e y (0) too large; introduce auxiliary variable ψ(t) to correct lateral error, the corrected error is as follows: wherein conversion function According to the definition A takes the following: Based on the above correction, the corrected lateral error has the following properties: The following constraints are imposed on the corrected lateral error: The above formula is re-expressed as: wherein the preset performance boundary parameter and satisfies the following inequality: The original lateral error is limited in a more stringent strip-shaped region.

6. A path tracking system for a front wheel steered rear wheel distributed drive vehicle, the vehicle tracked using the method of any one of claims 1 to 5, characterised in that, The method comprises a planning layer, a control layer, drive / brake force distribution and a vehicle model; The planning layer is used to input an expected speed and an expected path; The control layer receives expected speed information and expected path information of the planning layer, and obtains vehicle longitudinal and lateral positions, speeds, yaw angles and steering angles and steering angular velocities through a vehicle-mounted inertial unit, and obtains an expected steering angle and a main yaw moment through the proposed path tracking method and drive / brake force distribution; The drive / brake force distribution module distributes the main yaw moment into expected driving forces required by each driving wheel, and inputs the expected driving forces into a chassis motion control module of the vehicle model to drive vehicle motion, in combination with the expected steering angle calculated by the control layer.

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