A path tracking control method and device for a four-wheel independent steering vehicle

Abstract

The application discloses a path tracking control method and device for a four-wheel independent steering vehicle, and the path tracking control method comprises the following steps: acquiring a current vehicle state; according to the input vehicle state, an upper controller combines a four-wheel independent steering vehicle kinematics model to calculate a steering radius; according to the calculated steering radius, a lower controller combines a steering dynamics model with uncertainty of the four-wheel independent steering vehicle, and converts a steering angle consistent coordination control target meeting the steering radius and Ackerman steering relationship into a coupling constraint between the steering angles, and the coupling constraint is used to calculate a torque control output. The application can solve the problems of path tracking performance deterioration and tire wear caused by steering dynamics uncertainty and inconsistency of the four-wheel independent steering vehicle in the path tracking process, and meanwhile, the constraint satisfaction in the control process is considered.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of automatic driving, in particular to a path tracking control method and device for a four-wheel independent steering vehicle. BACKGROUND

[0002] The most basic function of an automatic driving vehicle is to perform a path tracking task on a known path. Traditional path tracking control techniques mostly focus on front-wheel steering vehicles, but the feature that they rely solely on front-wheel steering angles to control steering undoubtedly limits the steering performance of the vehicle to some extent.

[0003] At present, four-wheel independent steering vehicles with high flexibility and good passability are gradually attracting widespread attention. The steering relationship between the four wheels of a four-wheel independent steering vehicle has no mechanical constraints, and path tracking is achieved through coordinated steering of the four wheels. The steering system of a four-wheel independent steering vehicle is essentially a redundant drive system, which can achieve front-wheel steering mode, four-wheel Ackerman steering mode, diagonal motion mode, and even in-place rotation mode by reducing degrees of freedom. However, the inconsistency of multiple actuators required by the redundant drive system and system uncertainties make the path tracking problem of a four-wheel independent steering vehicle a difficult point. SUMMARY

[0004] The present application aims to provide a path tracking control method and device for a four-wheel independent steering vehicle, which can solve the problems of path tracking performance deterioration and tire wear caused by steering dynamics uncertainty and inconsistency during the path tracking process of a four-wheel independent steering vehicle, and also considers the satisfaction of constraints during control.

[0005] To achieve the above-mentioned purpose, the present application provides a path tracking control method for a four-wheel independent steering vehicle, which comprises:

[0006] obtaining the current vehicle state;

[0007] According to the input vehicle state, the upper controller combines the four-wheel independent steering vehicle kinematics model to calculate the steering radius;

[0008] According to the calculated steering radius, the lower controller combines the steering dynamics model with uncertainty of the four-wheel independent steering vehicle to convert the steering angle consistent and coordinated control target that meets the steering radius and Ackerman steering relationship into a coupling constraint between the steering angles, which is used to calculate the torque control output.

[0009] Further, the four-wheel independent steering vehicle kinematics model is described as formula (3):

[0010]

[0011] where X, Y are the lateral and longitudinal coordinates of the vehicle's center of mass in the earth coordinate system, v, θ, R, δ1, L and B are the vehicle's longitudinal velocity, heading angle, steering radius, steering angle of the left front wheel, front-to-rear wheel distance and left-to-right wheel distance, respectively.

[0012] Further, the steering dynamics model of the four-wheel independent steering vehicle with uncertainties is described as equation (5):

[0013]

[0014] where B represents the control coefficient matrix, σ represents a p-dimensional uncertain parameter containing multiple sources of uncertainties, U = [T e1 ,T e2 ,T e3 ,T e4 ] represents the steering control vector, T e1 , T e2 , T e3 , T e4 represent the output torques of the vehicle's left front wheel, right front wheel, left rear wheel and right rear wheel, respectively, J = diag(J1, J2, J3, J4) represents the moment of inertia matrix, J1, J2, J3, J4 represent the moments of inertia of the vehicle's left front wheel, right front wheel, left rear wheel and right rear wheel, respectively, q = [δ1, δ2, δ3, δ4] represents the steering angle vector, δ1, δ2, δ3, δ4 represent the steering angles of the vehicle's left front wheel, right front wheel, left rear wheel and right rear wheel, respectively, and represent the first and second derivatives of q, respectively, C = diag(B m1 ,B m2 ,B m3 ,B m4 ) represents the vehicle's viscous friction resistance coefficient matrix, B m1 , B m2 , B m3 , B m4 represent the viscous friction resistance coefficients of the vehicle's left front wheel, right front wheel, left rear wheel and right rear wheel, respectively, g = [T L1 ,T L2 ,T L3 ,T L4 ] T represents the vehicle's load torque matrix, T L1 , T L2 , T L3 , T L4 represent the load torques of the vehicle's left front wheel, right front wheel, left rear wheel and right rear wheel, respectively.

[0015] Further, M, C, g, B are set to include the nominal part and the corresponding bounded uncertainty part ΔM, ΔC, Δg, ΔB, described as equation (6):

[0016]

[0017] Further, the coupling constraint includes formula (13) or formula (16):

[0018]

[0019] wherein,

[0020]

[0021]

[0022] In the formula, A represents a state constraint matrix, c represents a first-order constraint vector, R, δ1, L and B respectively represent a turning radius of the vehicle, a steering angle of the left front wheel, a front-rear wheelbase and a left-right wheelbase, h1, h2, h3 and h4 are all scalar constants greater than 0, e1, e2, e3 and e4 respectively represent Ackerman steering angle errors of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel of the vehicle.

[0023]

[0024] wherein,

[0025]

[0026]

[0027]

[0028] In the formula, A represents a state constraint matrix, c represents a first-order constraint vector, b represents a second-order constraint vector, b1 and b2 are both intermediate parameters for simplifying the formula, R, δ1, L and B respectively represent a turning radius of the vehicle, a steering angle of the left front wheel, a front-rear wheelbase and a left-right wheelbase, h1, h2, h3 and h4 are all scalar constants greater than 0, respectively represent first-order derivatives of Ackerman steering angle errors of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel of the vehicle.

[0029] Further, the coupling constraint also includes an Ackerman steering principle constraint error β defined by formula (19):

[0030]

[0031] Further, the torque control output U is described as formula (32):

[0032]

[0033] wherein,

[0034]

[0035]

[0036]

[0037] where p1 and p2 represent the nominal part of the control law of the kinetic system, p3 represents the robust control law, represents the estimation of the unknown vector a, κ>0 represents an adjustable parameter, P is a given matrix, P∈R 4×4 and P>0, γ represents a selection function, μ represents a function with respect to the constraint error, is a known function.

[0038] The application also provides a path tracking control device for a four-wheel independent steering vehicle, comprising:

[0039] an upper controller configured to calculate a steering radius according to an input vehicle state and in combination with a four-wheel independent steering vehicle kinematics model;

[0040] a lower controller configured to transform a steering angle consistent coordination control target satisfying the steering radius and Ackerman steering relationship into a coupling constraint between the steering angles according to the calculated steering radius and in combination with a steering dynamics model of the four-wheel independent steering vehicle with uncertainty, and to calculate a torque control output according to the coupling constraint.

[0041] Further, the four-wheel independent steering vehicle kinematics model is described as formula (3), and the steering dynamics model of the four-wheel independent steering vehicle with uncertainty is described as formula (5):

[0042]

[0043]

[0044] where B represents a control coefficient matrix, σ represents a p-dimensional uncertain parameter containing multiple sources of uncertainty, U=[T e1 ,T e2 ,T e3 ,T e4 ] represents a steering control vector, T e1 ,T e2 ,T e3 ,T e4represent the output torques of the left front wheel, right front wheel, left rear wheel, right rear wheel of the vehicle, respectively, J = diag(J1, J2, J3, J4) represents a moment of inertia matrix, J1, J2, J3, J4 represent the moments of inertia of the left front wheel, right front wheel, left rear wheel, right rear wheel of the vehicle, respectively, q = [δ1, δ2, δ3, δ4] represents a steering angle vector, δ1, δ2, δ3, δ4 represent the steering angles of the left front wheel, right front wheel, left rear wheel, right rear wheel of the vehicle, respectively, represent the first and second derivatives of q, respectively, C = diag(B m1 ,B m2 ,B m3 ,B m4 ) represents a viscous friction resistance coefficient matrix of the vehicle, B m1 , B m2 , B m3 , B m4 represent the viscous friction resistance coefficients of the left front wheel, right front wheel, left rear wheel, right rear wheel of the vehicle, respectively, g = [T L1 , T L2 , T L3 , T L4 ] T represents a load torque matrix of the vehicle, T L1 , T L2 , T L3 , T L4 represent the load torques of the left front wheel, right front wheel, left rear wheel, right rear wheel of the vehicle, respectively.

[0045] Further, the torque control output is described as formula (32):

[0046]

[0047] wherein,

[0048]

[0049]

[0050]

[0051] wherein, p1and p2both represent control laws of a nominal part of the dynamic system, p3represents a robust control law, represents an estimated value of an unknown vector a, κ > 0 represents an adjustable parameter, P is a given matrix, P ∈ R 4×4 , P > 0, γ represents a selection function, μ represents a function with respect to a constraint error.

[0052] The application can effectively avoid the influence of external interference, parameter perturbation, incomplete modeling and other uncertain factors on the vehicle steering dynamics, effectively solve the steering inconsistency of the steering dynamics caused by different external loads and the difference in mechanical and electrical characteristics between the wheels, significantly improve the path tracking performance of the four-wheel independent steering vehicle, and greatly reduce the tire wear during the operation of the vehicle, thereby providing an important guarantee for the operation efficiency and stability of the four-wheel independent steering vehicle. BRIEF DESCRIPTION OF DRAWINGS

[0053] Figure 1 is a design flowchart in the embodiment of the application;

[0054] Figure 2 is an Ackerman steering mode schematic diagram of a four-wheel independent steering vehicle in the embodiment of the application;

[0055] Figure 3 is a wheel rotation center moving track schematic diagram in the embodiment of the application;

[0056] Figure 4 is a hierarchical control framework schematic diagram in the embodiment of the application;

[0057] Figure 5 is a path tracking control method schematic diagram of a four-wheel independent steering vehicle in the embodiment of the application. DETAILED DESCRIPTION

[0058] In the drawings, the same or similar notations are used to indicate the same or similar elements or elements with the same or similar functions. The embodiments of the application will be described in detail below with reference to the accompanying drawings.

[0059] In the description of the application, the terms 'center', 'longitudinal', 'transverse', 'front','rear', 'left', 'right','vertical', 'horizontal', 'top', 'bottom', 'inner', 'outer' and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the application and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation on the scope of protection of the application.

[0060] The path tracking control method of the four-wheel independent steering vehicle provided by the embodiment of the application comprises:

[0061] The current vehicle state is obtained. The embodiment uses the Ackerman steering mode, which requires all wheels to steer around a center point, which can effectively reduce tire wear and improve path tracking performance. For example, Figure 2As shown in the figure, in the Ackerman steering mode, C represents the wheel rotation center that satisfies Ackerman steering, CG represents the vehicle geometric center, L and B represent the front and rear wheelbase and left and right wheelbase respectively, θ represents the heading angle, v represents the longitudinal speed, R is the turning radius, δ i Indicates the wheel steering angle, i=1 corresponds to the left front wheel, i=2 corresponds to the right front wheel, i=3 corresponds to the left rear wheel, and i=4 corresponds to the right rear wheel.

[0062] In one embodiment, in order to facilitate derivation, the relationship between the wheel steering angle and the steering radius is reasonably simplified. Specifically, Figure 3 As shown, the wheel rotation center is set on a vertical line passing through the vehicle's geometric center and perpendicular to the vehicle body direction, as shown in Figure 3 The wheel rotation center C' in the figure is obtained, and the steering angle of the wheel on the same side is expressed as the following formula (1):

[0063]

[0064] It's important to note that placing the Ackermann center on the perpendicular line of the CG is a simple and intuitive choice. It leverages the vehicle's symmetry to simplify the complexity of the controller design. In practice, this embodiment can also design the vehicle's wheel rotation center at other locations and construct the corresponding Ackermann steering constraint.

[0065] pass Figure 2 and Figure 3 , when the turning radius is R, the four-wheel steering angle that strictly satisfies Ackerman steering can be described as formula (2):

[0066]

[0067] So far, this embodiment describes the kinematic model of the four-wheel independent steering vehicle as formula (3):

[0068]

[0069] Where X is the horizontal coordinate of the vehicle's center of mass in the geodetic coordinate system, and Y is the vertical coordinate of the vehicle's center of mass in the geodetic coordinate system.

[0070] like Figure 1 As shown, in order to realize the four-wheel coordinated control and Ackerman steering principle in the path tracking process, the path tracking control method of the four-wheel independent steering vehicle provided by the embodiment of the present invention performs hierarchical control. Figure 4 As shown, the controller is divided into two layers, namely the upper controller and the lower controller. Moreover, the upper controller calculates the turning radius R based on the input vehicle state and the four-wheel independent steering vehicle kinematic model.

[0071] In one embodiment, the steering dynamics equation of the four-wheel independent steering vehicle is described as formula (4):

[0072]

[0073] where subscript i corresponds to the ith wheel, T ei ,J i ,B mi and T Li represent the output torque, the moment of inertia, the viscous friction resistance coefficient and the load torque, respectively, and the elements in each matrix are composed of the corresponding dynamic parameters.

[0074] In another embodiment, the steering dynamics model of the four-wheel independent steering vehicle with uncertainty is described as formula (5):

[0075]

[0076] For the purpose of concise representation, without causing ambiguity, the brackets and parameters in the brackets following each parameter in the formula will be omitted in the text, for example: the control coefficient matrix B(σ(t), t) is omitted after the brackets and σ(t) and t in the brackets, and is represented as B, that is, B(σ(t), t) and B refer to the same thing. Similarly, other parameters in the text use the same omission method.

[0077] Therefore, in formula (5), B represents the control coefficient matrix, for example, B = diag(1, 1, 1, 1), where 1 represents that the control torque of each wheel is multiplied by 1, σ represents a p-dimensional uncertainty parameter containing multiple sources of uncertainty, such as modeling errors, parameter perturbations, external disturbances, etc., U = [T e1 ,T e2 ,T e3 ,T e4 ] represents the steering control vector, T e1 , T e2 , T e3 , T e4 represent the output torque of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel of the vehicle, respectively, J = diag(J1, J2, J3, J4) represents the moment of inertia matrix, J1, J2, J3, J4 represent the moment of inertia of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel of the vehicle, respectively, q = [δ1, δ2, δ3, δ4] represents the steering angle vector, δ1, δ2, δ3, δ4 represent the steering angle of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel of the vehicle, respectively, represent the first and second derivatives of q, respectively, C = diag(B m1 ,B m2 ,B m3 ,B m4) denotes the viscous frictional resistance coefficient matrix of the vehicle, B m1 m2 m3 m4 denote the viscous frictional resistance coefficients of the left front wheel, the right front wheel, the left rear wheel, and the right rear wheel of the vehicle, respectively, g = [T L1 L2 L3 L4 T denotes the load torque matrix of the vehicle, T L1 L2 L3 L4 denote the load torques of the left front wheel, the right front wheel, the left rear wheel, and the right rear wheel of the vehicle, respectively.

[0078] In one embodiment, due to the fact that the dynamics parameters in equations (4)-(5) are inconsistent, it can lead to problems such as different wheel steering speeds. This will cause each wheel to not respond to the expected steering angle at the same time, making it difficult to achieve consistent and coordinated control of four wheels and meet the Ackerman steering principle. In addition, M, C, g, B are difficult to be accurately identified because they can be time-varying and affected by external disturbances. Therefore, the present embodiment assumes that each parameter contains a known nominal part and an unknown time-varying uncertainty part Δ(·)(t), as and all uncertainties are bounded. Therefore, the matrices M, C, g, B can be represented as equation (6): setting M, C, g, B as including the nominal part and the corresponding bounded uncertainty part ΔM, ΔC, Δg, ΔB, described as equation (6):

[0079]

[0080] In the above embodiment, M, C, g, B represent the parameters of the actual steering actuators, and the nominal values of these parameters should be known. However, due to various factors, they may not completely match the nominal values and may fluctuate around the nominal values. However, because these actuators need to meet certain industrial factory conditions, their deviations are definitely limited within a certain range, but this range may not be the same for different types of actuators. Similarly, in other cases, for the parameters of a system, the approximate value of the parameters can be determined by estimation, fitting, etc. This value may not be accurate, but at least it is determined within a certain range. When a rough value is selected within this range, the uncertainty part ΔM, ΔC, Δg, ΔB has upper and lower boundaries. In addition, all nominal parts and uncertainty parts are continuous functions.

[0081] ​​​​​​​​​​To simplify the derivation, the following is assumed in this embodiment: I is an identity matrix, thus this embodiment can obtain formula (7):

[0082] ΔD(σ,t)=D(t)E(σ,t) (7)

[0083] According to the calculated steering radius, the lower layer controller combines the steering dynamics model with uncertainty of the four-wheel independent steering vehicle, and converts the steering angle consistent coordination control target that meets the steering radius and Ackerman steering relationship into a coupling constraint between the steering angles, which is used to calculate the torque control output.

[0084] In one embodiment, although formula (2) is sufficient to characterize the steering angle relationship in the Ackerman steering case, it still cannot achieve high coordination between the four wheels during steering. Specifically, in formula (2), each steering angle is described as a function of the steering radius R, which will change with R. However, there is no explicit relationship to describe the interaction between the wheels, especially between δ1 and δ2. The four wheels are relatively independent, which significantly increases the possibility of lack of coordination during steering. In other words, this can lead to the situation that the four wheels do not satisfy the Ackerman steering principle during steering, and further cause the path tracking performance to decrease and the tire wear to increase.

[0085] Therefore, it is crucial to set up mutual constraints between all wheels and reconstruct the steering angle expressions of the wheels. This embodiment reconstructs the four-wheel expected steering angles as formula (8), which represents the constraint relationship between the four wheels:

[0086]

[0087] Here, δ id (i=1,2,3,4) represents the expected steering angle, and δ i (i=1,2,3,4) represents the actual steering angle.

[0088] In this way, δ 2d ,δ 3d ,δ 4d are expressed as functions of δ1, and δ 1d is expressed as a function of R. Based on the coupling constraint (8), the expected steering angles δ 2d ,δ 3d ,δ 4dThe transitions of δ1 can be followed consistently in the control process. This means that the embodiment expects the variables δ2, δ3, δ4 to be implemented as much as possible to achieve the four-wheel consistent coordinated control based on δ1, and the four wheels work together to meet the Ackerman steering principle. Compared with other studies that ignore the inconsistency of steering dynamics, the study of the embodiment is undoubtedly more detailed and comprehensive. In addition, the embodiment uses δ1 instead of δ 1d to calculate δ 2d , δ 3d , δ 4d . The advantage of this method is that even if δ1 cannot accurately respond to δ 1d , the other three wheels can follow the changes of δ1 to meet the Ackerman steering principle, which is consistent with the goal of the embodiment.

[0089] In one embodiment, the control goal is to hope that equation (8) holds as much as possible, therefore, the control error model e(t) can be expressed as equation (9):

[0090]

[0091] Taking the derivative of e(t) gives equation (9):

[0092]

[0093] The error model proposed is still valid in the real environment, which will be explained from three aspects. First, the establishment of the error model has a theoretical basis. Some current studies also consider the influence of wheel coupling effect, form mutual constraints between wheels, and supplement with real vehicle experiments. The error model of the embodiment adds the consideration of inconsistency. Second, all variables are measurable and have actual physical meaning. In equation (9), δ1-δ4 can be obtained through angle sensors, L and B are known vehicle structure parameters, and R is a variable derived from the expected path. In equation (10), can be obtained through angular acceleration sensors, can be obtained through simple discrete-time differentiation method. Finally, the model considers the reality. For four-wheel steering angles, the influence of uncertainties such as unknown differences in steering dynamics parameters and external disturbances makes it impossible to accurately follow the derived steering radius R. This undoubtedly poses a challenge to the implementation of four-wheel consistent coordinated control, and reduces the path tracking performance and tire life. In order to solve this practical problem, mutual constraints must be established between the four wheels. This is also the innovation of the design, that is, considering both uncertainty and inconsistency in the path tracking control method.

[0094] So far, the Ackerman steering angle error e(t) and its derivative are converted into the forms of (9) and (10). In this embodiment, the coupling equation (11) of e(t) and are made to converge to 0 simultaneously.

[0095]

[0096] where h1, h2, h3, h4 are scalar constants greater than 0. By solving equation (11), formula (12) can be obtained:

[0097]

[0098] It is obvious that when t→∞, e1, e2, e3, e4→0. The convergence speed can be adjusted by adjusting the size of parameters h1~h4. At the same time, given formula (11), e2, e3, e4 can also converge to 0.

[0099] In one embodiment, based on formula (9)-(11), this embodiment constructs equation constraint (13). If equation constraint (13) is strictly satisfied, for any initial steering angle e(t0), e(t) and will converge to 0.

[0100]

[0101] where,

[0102]

[0103]

[0104] where A represents the state constraint matrix, c represents the first-order constraint vector, R, δ1, L and B represent the steering radius of the vehicle, the steering angle of the left front wheel, the front and rear wheelbase and the left and right wheelbase respectively, h1, h2, h3, h4 are all scalar constants greater than 0, e1, e2, e3, e4 represent the Ackerman steering angle error of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel of the vehicle respectively.

[0105] Exponential convergence of the Ackerman steering error can be achieved by formula (13), and formula (8) can be satisfied as much as possible.

[0106] Similarly, in another embodiment, formula (13) is applied to the second-order derivative form of the constraint. By differentiating formula (13), formula (16) can be obtained:

[0107]

[0108] where,

[0109] ​

[0110]

[0111] Where A represents the state constraint matrix, c represents the first-order constraint vector, b represents the second-order constraint vector, b1 and b2 are intermediate parameters used to simplify the formula, R, δ1, L and B represent the vehicle's turning radius, the steering angle of the left front wheel, the front and rear wheelbase and the left and right wheelbase, respectively, h1, h2, h3 and h4 are all scalar constants greater than 0. Represent the first-order derivatives of the Ackermann steering angle errors of the left front wheel, right front wheel, left rear wheel, and right rear wheel of the vehicle, respectively.

[0112] In one embodiment, during the steering process, due to factors such as uncertainty and initial state offset, the system is not always able to satisfy Equation (13). Therefore, the coupling constraint also includes the Ackerman steering principle constraint error β defined by Equation (19):

[0113]

[0114] Thus, the four-wheel coordinated control problem provided by Equation (5) is transformed into a constrained following problem. This transformation effectively transforms different four-wheel coordinated control requirements (such as convergence rate) into explicit equality constraints (linear or nonlinear, complete or incomplete), which is beneficial to solving the control law. In addition, this method also preserves the nonlinear and time-varying characteristics of the original system.

[0115] In one embodiment, the upper-level controller uses a pure tracking algorithm. This algorithm is simple in structure and suitable for controlling vehicle position. In addition, it has good performance at low speeds. Of course, other algorithms known in the art can also be used to solve the turning radius R that meets the path tracking performance.

[0116] The specific framework of the pure tracking control algorithm is as follows Figure 4 As shown in Figure 1, P0 and P1 represent the current geometric center position of the vehicle and the preview point on the target path respectively. p is the preview distance based on speed, and in this embodiment is simply set to a linear function related to speed. K is the control gain, and its specific value is given during the specific debugging process and is an empirical parameter. is the heading angle between the desired direction and the current direction. In this embodiment, the turning radius R can be expressed as formula (20):

[0117]

[0118] Since it may be necessary to track a straight line during the path tracking process, P1 is located right in front of the vehicle at this time. To avoid this situation causing the calculation error of formula (20), the embodiment replaces the original value of with a very small value, for example .

[0119] In an embodiment, considering the uncertainty and inconsistency, the lower controller is used to transform the steering angle consistent coordination control target that meets the steering radius and Ackerman steering relationship into a coupling constraint between the steering angles according to the calculated steering radius, in combination with the steering dynamics model with uncertainty of the four-wheel independent steering vehicle, and the coupling constraint is used to calculate the torque control output.

[0120] The control quantity U of the lower controller as a whole can be mainly divided into three parts p1, p2, and p3. Among them, p1 represents the nominal control law designed by the Udwadia-Kalaba method, which aims to minimize the tendency of the system to deviate from the built constraints. p2 represents the feedback control law for suppressing the initial deviation of the system and making the system meet the constraints. Both p1 and p2 are control laws for the nominal part of the dynamic system defined in formula (5), and their expressions are described as formulas (21) and (22) respectively:

[0121]

[0122]

[0123] In the formula, κ>0 is an adjustable parameter, and P is a given matrix, P∈R 4×4 , and P>0, and the specific values of κ and P are given in the specific debugging process, which are both empirical parameters.

[0124] On this basis, the embodiment designs the control law p3 considering the influence of uncertainty. First, the embodiment explains some symbols for the subsequent derivation. For a given matrix H∈R n×n , the embodiment can obtain the following formula (23) definition, where λ1, λ2, …, λ n are the eigenvalues of the matrix H.

[0125]

[0126] In the formula, λ j represents the jth eigenvalue of the matrix H, λ m represents the smallest eigenvalue of the matrix H, and λ M represents the largest eigenvalue of the matrix H.

[0127] In an embodiment, in order to be able to meet the Lyapunov stability, the embodiment proposes the following two assumptions:

[0128] Assumption 1: For a given matrix P, this embodiment sets equation (24) as

[0129]

[0130] where W1represents a product of a set of matrices, and has no specific physical meaning.

[0131] Then there exists a constant ρ m > -1, satisfying for any time t e R + , the following equations are all true:

[0132]

[0133] where ∑ is a set representing an uncertainty, and the uncertainty that the system is subjected to should be within the range of this set.

[0134] Assumption 1 shows that even if there is a parameter perturbation phenomenon in M -1 B, there still exists a one-sided boundary ρ m such that the direction of the control quantity U does not change.

[0135] Assumption 2: Based on assumption 1, there exists an unknown vector and a known function such that for all and σ e ∑, this embodiment has:

[0136]

[0137]

[0138] where W2represents a product of a set of matrices, and has no specific physical meaning.

[0139] Assumption 2 shows that there exists a continuous function about the state of the system that encloses all the effects of uncertainty. Since the system uncertainty is mostly compact, assumption 2 is true.

[0140] In fact, it is difficult to accurately obtain the value of the unknown vector α, so this embodiment uses the estimated value as a substitute in the controller design process, and updates it based on the system state according to the following leaky adaptive law.

[0141]

[0142] Here k1, k2 > 0 are scalar constants. The initial value of the element in α is set to a positive number, so that for all t > 0, this embodiment has Based on assumptions 1 and 2, and the estimated uncertainty boundary The present embodiment can propose a robust control law p3 as follows, where ε > 0 and is a scalar constant.

[0143]

[0144]

[0145]

[0146] Finally, the torque control output from the lower level controller is described as equation (32):

[0147]

[0148] In fact, pi and p2 are sufficient to ensure that the nominal system satisfies constraints (13) and (16), however, the nominal system is obviously not applicable to most cases, therefore, the present embodiment considers system uncertainty and introduces control law p3. For the consideration of simplifying design, only nominal dynamics parameters and estimated uncertainty boundary values are used in the control design process.

[0149] The present embodiment also provides a path following control device for a four-wheel independent steering vehicle, which comprises an upper level controller and a lower level controller, wherein:

[0150] The upper level controller is used to calculate a steering radius according to an input vehicle state, in combination with a four-wheel independent steering vehicle kinematics model.

[0151] The lower level controller is used to transform a steering angle consistent coordination control target, which satisfies the steering radius and Ackerman steering relationship, into a coupling constraint between steering angles for calculating a torque control output, according to the calculated steering radius, in combination with a steering dynamics model of the four-wheel independent steering vehicle with uncertainty.

[0152] The above embodiment is subjected to stability analysis. In this part, the present embodiment proposes theory 1 to analyze the stability of the constraint-guided consistent coordination steering controller, which is based on the Lyapunov maximum-minimum value method. The present embodiment sets wherein represents an estimated error of a.

[0153] Theory 1: based on assumption 1 and assumption 2, equation (32) can make satisfy the following performances under the conditions of parameters κ > 0, ε > 0, k1 > 0, k2 > 0 and P > 0:

[0154] (i) consistent boundedness (consistent bounded): for any r > 0, if then there is a d(r) < ∞ such that for all t ≥ t0,

[0155] (ii) Uniform ultimate boundedness (UUB): For any r > 0 and there exists a d > 0 such that for all at the time and .

[0156] Proof: Choose a Lyapunov candidate function as follows:

[0157]

[0158] Take the first order derivative of V with respect to t as:

[0159]

[0160] Based on (5), (6), (19) and (32), the first term on the right side of the above equation can be expressed as:

[0161]

[0162] Bring p1 into Λ1 to obtain:

[0163]

[0164] Based on p2, Λ2 can be expressed as:

[0165]

[0166] Considering hypothesis 2, Λ4+Λ5 can be expressed as:

[0167]

[0168] Based on the control law p3 and hypothesis 1, the Rayleigh principle [7] is adopted to obtain:

[0169]

[0170] According to (35)-(39), the present embodiment has:

[0171]

[0172] Since there are two size relationships of ||μ|| and ε, classification discussion is required. The present embodiment first discusses the case of ||μ||>ε, through γ=1 / ||μ|| and The present embodiment can obtain:

[0173]

[0174] In another case, we have

[0175]

[0176] Note that (1 + p m )ε / 2 > 0, thus for all ||μ||∈R + the following inequality always holds:

[0177]

[0178] Then, the second term on the right side of equation (34) can be transformed as:

[0179]

[0180] Based on the square difference formula, equation (44) can be simplified as:

[0181]

[0182] Finally, the derivative of the overall Lyapunov function can be obtained by equations (34), (43) and (45), i.e.:

[0183]

[0184] where, and

[0185]

[0186] Then this embodiment sets the

[0187] The uniform performance of the system can be expressed as equation (48):

[0188]

[0189] Further, the uniform ultimate bounded performance of the system can be expressed as:

[0190]

[0191]

[0192] Thus, the proof is complete.

[0193] The successful proof of the uniform bounded and uniform ultimate bounded performance of the system shows that even if equation (5) is affected by the initial bias and uncertainty, the control error can still converge to and remain in a small neighborhood around 0, so that the system eventually reaches a stable state.

[0194] Finally, it should be pointed out that the above embodiments are only used to illustrate the technical solutions of the present application, and are not intended to limit the same. Those skilled in the art should understand that the technical solutions described in the foregoing embodiments can be modified, or some technical features thereof can be replaced by equivalent ones; these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A path tracking control method of a four-wheel independent steering vehicle, characterized by, Comprising: obtaining a current vehicle state; according to the input vehicle state, the upper controller combines a four-wheel independent steering vehicle kinematics model to calculate a steering radius; according to the calculated steering radius, the lower controller combines the steering dynamics model with uncertainty of the four-wheel independent steering vehicle, and converts the steering angle consistent coordination control target meeting the steering radius and Ackerman steering relationship into a coupling constraint between the steering angles, which is used to calculate the torque control output; The four-wheel independent steering vehicle kinematics model is described as formula (3): In the formula, X and Y are the lateral and longitudinal coordinates of the vehicle mass center in the earth coordinate system, v, θ, R, δ1, L and B represent the longitudinal speed, heading angle, steering radius, steering angle of the left front wheel, front and rear wheelbase and left and right wheelbase of the vehicle respectively; The steering dynamics model with uncertainty of the four-wheel independent steering vehicle is described as formula (5): In the formula, B represents a control coefficient matrix, σ represents a p-dimensional uncertain parameter containing multi-source uncertainty, U = [T e1 , e2 , e3 , e4 ] represents a steering control vector, T e1 , e2 , e3 , e4 respectively represent the output torques of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel of the vehicle, q = [δ1, δ2, δ3, δ4] represents a steering angle vector, δ1, δ2, δ3, δ4 respectively represent the steering angles of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel of the vehicle, respectively represent the first and second derivatives of q, C = diag(B m1 , m2 , m3 , m4 ) represents a viscous friction resistance coefficient matrix of the vehicle, B m1 , m2 , m3 , m4 respectively represent the viscous friction resistance coefficients of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel of the vehicle, g = [T L1 , L2 , L3 , L4 ] T represents a load torque matrix of the vehicle, T L1 , L2 , L3 , L4 respectively represent the load torques of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel of the vehicle; M, C, g, B are respectively set as including a nominal part and a corresponding bounded uncertain part ΔM, ΔC, Δg, ΔB, described as formula (6):

2. The path tracking control method of a four-wheel independent steering vehicle according to claim 1, characterized by, The coupling constraint includes formula (13) or formula (16): Wherein, In the formula, A represents the state constraint matrix, c represents the first-order constraint vector, R, δ1, L and B represent the steering radius, steering angle of the left front wheel, front and rear wheelbase and left and right wheelbase of the vehicle respectively, h1, h2, h3, h4 are all scalar constants greater than 0, e1, e2, e3, e4 represent Ackerman steering angle error of the left front wheel, right front wheel, left rear wheel and right rear wheel of the vehicle respectively; Wherein, In the formula, A represents a state constraint matrix, c represents a first-order constraint vector, b represents a second-order constraint vector, b1 and b2 are both intermediate parameters for simplifying the formula, R, δ1, L and B represent a turning radius of the vehicle, a steering angle of the left front wheel, a front-rear wheelbase and a left-right wheel track respectively, h1, h2, h3 and h4 are all scalar constants greater than 0, respectively represent first-order derivatives of Ackerman steering angle errors of the left front wheel, the right front wheel, the left rear wheel and the right rear wheel of the vehicle.

3. The path tracking control method of a four-wheel independent steering vehicle according to claim 2, characterized by, The coupling constraint also includes the Ackerman steering principle constraint error β defined by formula (19):

4. The path tracking control method of a four-wheel independent steering vehicle according to claim 3, characterized by, The torque control output U is described as formula (32): Wherein, where p1and p2both represent the control law of the nominal part of the kinetic system, p3represents the robust control law, denotes the estimate of the unknown vector a, κ > 0 denotes an adjustable parameter, P is a given matrix, P e R 4×4 and P > 0, γ denotes a selection function, μ denotes a function with respect to the constraint error, is a known function.

5. A path tracking control device for a four-wheel independent steering vehicle, characterized in that: Comprising: an upper controller, which is used to combine a four-wheel independent steering vehicle kinematics model according to an input vehicle state, and calculate a steering radius; a lower controller, which is used to combine a steering dynamics model with uncertainty of the four-wheel independent steering vehicle according to the calculated steering radius, and convert a steering angle consistent coordination control target meeting the steering radius and Ackerman steering relationship into a coupling constraint between the steering angles, which is used to calculate a torque control output; The four-wheel independent steering vehicle kinematics model is described as formula (3): In the formula, X and Y are the lateral and longitudinal coordinates of the vehicle mass center in the earth coordinate system, v, θ, R, δ1, L and B represent the longitudinal speed, heading angle, steering radius, steering angle of the left front wheel, front and rear wheelbase and left and right wheelbase of the vehicle respectively; The steering dynamics model with uncertainty of the four-wheel independent steering vehicle is described as formula (5): where B represents a control coefficient matrix, σ represents a p-dimensional uncertain parameter including multi-source uncertainty, U = [T e1 ,T e2 ,T e3 ,T e4 ] represents a steering control vector, T e1 ,T e2 ,T e3 ,T e4 represent output torques of the left front wheel, the right front wheel, the left rear wheel, and the right rear wheel of the vehicle, respectively, q = [δ1, δ2, δ3, δ4] represents a steering angle vector, δ1, δ2, δ3, δ4 represent steering angles of the left front wheel, the right front wheel, the left rear wheel, and the right rear wheel of the vehicle, respectively, represent first and second derivatives of q, respectively, C = diag(B m1 ,B m2 ,B m3 ,B m4 ) represents a viscous friction resistance coefficient matrix of the vehicle, B m1 ,B m2 ,B m3 ,B m4 represent viscous friction resistance coefficients of the left front wheel, the right front wheel, the left rear wheel, and the right rear wheel of the vehicle, respectively, g = [T L1 ,T L2 ,T L3 ,T L4 ] T represents a load torque matrix of the vehicle, T L1 ,T L2 ,T L3 ,T L4 represent load torques of the left front wheel, the right front wheel, the left rear wheel, and the right rear wheel of the vehicle, respectively; M, C, g, B are set to include nominal parts and corresponding bounded uncertain parts ΔM, ΔC, Δg, ΔB, respectively, and are described as formula (6):

6. The path tracking control device of a four-wheel independent steering vehicle according to claim 5, characterized by The torque control output is described as formula (32): Wherein, where p1and p2both represent the control law of the nominal part of the kinetic system, p3represents the robust control law, represents the estimate of the unknown vector a, κ > 0 represents an adjustable parameter, P is a given matrix, P e R 4×4 , P > 0, γ represents a selection function, μ represents a function with respect to the constraint error.

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