An adaptive steering mode switching control method for a multi-axis chassis

Abstract

The application provides an adaptive steering mode switching control method for a multi-axle chassis, comprising the following steps: step S1: establishing a kinematics model of the multi-axle chassis to describe the kinematics state during low-speed driving; step S2: considering external bounded random disturbance and parameter uncertainty, regarding the chassis steering mode as an optional subsystem, and constructing a unified switching model with the state of each steering mode interconnected; step S3: based on the state error of the multi-axle chassis, constructing an internal coupling sliding surface and designing a modified approaching law, establishing an improved internal coupling sliding surface controller ICSMC, and optimizing the continuous control input of each subsystem; step S4: establishing a supervision criterion describing the energy attenuation law of the system, constructing an evaluation rule for identifying the mismatched sub-controller, realizing the autonomous switching of each subsystem, optimizing the selection of the controller parameters, and ensuring the global stability and H performance of the system; and the application is beneficial to improving the flexibility and tracking control performance of the multi-axle chassis.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of multi-axis by-wire chassis steering mode switching control, and particularly relates to an adaptive steering mode switching control method for a multi-axis by-wire chassis. BACKGROUND

[0002] Safety, comfort, energy saving, and environmental protection are the development direction and eternal theme of vehicles, and by-wire chassis technology provides strong technical support for the intelligentization of vehicles. The steering system of a multi-axis by-wire chassis discards the complex mechanical structure of a traditional steering system, adjusts the driving and braking torque on each wheel by using a hub motor, and can realize the switching control of multiple steering modes, including front-wheel steering, rear-wheel steering, zero-radius steering, Ackerman steering, and the like, thereby effectively improving the flexibility of a vehicle in a complex environment.

[0003] The existing steering mode switching control methods for vehicles, such as the design method for steering mode switching of a four-wheel independent driving steering mobile platform proposed in reference patent CN 117644776A, identify the state of the platform by using a vehicle controller, determine whether the switching condition is met, and calculate the expected tire turning angle of the driving wheel to perform steering mode switching. For example, the four-wheel steering mode dynamic switching control system proposed in reference patent CN 117584940A includes a vehicle parameter acquisition module, a target steering mode wheel turning angle calculation module, a steering mode dynamic switching control module, and a steering mode dynamic switching execution module, and realizes the autonomous switching of the steering mode of a vehicle in various driving states. These switching control methods improve the steering flexibility of a multi-axis by-wire chassis. However, there are still some deficiencies and limitations, mainly including:

[0004] (1) The multi-axis by-wire chassis is prone to nonlinear correlation in multiple steering modes, which leads to system instability. The tracking control performance of the traditional sliding mode control strategy based on decoupling of the state variable according to the control input decreases under the condition of bounded random disturbance and parameter uncertainty, and is usually accompanied by chattering. At the same time, the traditional reaching law faces the dilemma between improving the control robustness near the sliding surface and shortening the reaching time.

[0005] (2) The traditional multi-steering mode switching strategy generally requires the vehicle to be in a stationary or extremely low-speed state. This control method not only has a complex process and a long switching time, but also requires a large steering torque and steering power, which leads to tire wear, greatly limits the flexibility and trajectory tracking performance of the vehicle, and hinders the intelligent development of the vehicle. SUMMARY

[0006] The present application provides an adaptive steering mode switching control method for a multi-axis by-wire chassis, which is beneficial to improve the flexibility and tracking control performance of the multi-axis by-wire chassis.

[0007] The application adopts the following technical solutions.

[0008] An adaptive steering mode switching control method for a multi-axle chassis, comprising the following steps:

[0009] Step S1: establishing a kinematic model of the multi-axle chassis to describe the kinematic state of the vehicle when driving at low speed;

[0010] Step S2: considering the external bounded random disturbance and parameter uncertainty, regarding the steering mode of the multi-axle chassis as an optional subsystem, constructing a unified switching model with the state interconnection of each steering mode;

[0011] Step S3: constructing an internal coupling sliding surface based on the state error of the multi-axle chassis and designing a modified reaching law to establish an improved internal coupling sliding mode controller ICSMC for optimizing the continuous control input of each subsystem;

[0012] Step S4: establishing a supervision criterion describing the energy attenuation law of the system, constructing an evaluation rule for identifying the mismatched sub-controller to realize the autonomous switching of each subsystem and optimize the selection of the controller parameters, and ensuring the global stability and H performance of the system.

[0013] In step S1, the kinematic model of the multi-axle chassis describes the motion law of its pose in space changing with time from a geometric perspective; the implementation method of step S1 is as follows:

[0014] When studying the motion control problem of the multi-axle chassis based on the kinematic model, it is assumed that the vehicle drives at a low speed, only pure rolling without sliding occurs between the tire and the ground, and there is no side slip in steering, i.e., the center of mass side slip angle is 0, satisfying the nonholonomic constraint condition,

[0015] From the geometric relationship, we can get:

[0016]

[0017] The instantaneous turning radius R can be derived as follows:

[0018]

[0019] The yaw rate ω of the multi-axle chassis can be determined from the turning radius R and the center of mass velocity v:

[0020]

[0021] The velocity components of the multi-axle chassis on the X-axis and Y-axis:

[0022]

[0023] The multi-axle chassis kinematic model in the coordinate system XOY is represented as:

[0024]

[0025] where (x, y) are the coordinates of the center of mass P, v is the velocity of the center of mass, θ is the angle between the center of mass and the X-axis, i.e., the heading angle, L1 and L n are the distances from the center of mass to the first and nth axles, respectively, and are the steering angles of the virtual first and nth axle tires, respectively, and all other variables are functions of time t, except for the wheelbase L.

[0026] For continuous subsystems and discrete switching signals, the hybrid switching control system of the adaptive steering mode is represented as:

[0027]

[0028] where x(t) represents the system state, f σ(t) is a collection of n different functions, σ(t) is the switching signal that determines which f σ(t) function controls the system behavior at time t, represents the number of subsystems, and the solution of the system is a pair {x(t), σ(t)} that provides the optimal system state x(t) and switching signal σ(t); σ(t) is classified as state-dependent or time-dependent by determining whether the switching depends on the system state x(t) or time t;

[0029] By using the virtual front axle and the real axles, the motion state of the multi-axle chassis is represented as a single-track model.

[0030] q is represented as the state, (x, y) represents the center of mass planar position, θ and represent the heading angle and front wheel steering angle, respectively. The following derivation relates to the kinematic state of the alternative steering modes of the multi-axle chassis.

[0031] 1) Zero-radius steering mode: This mode is applied to achieve a pivot steering by setting the left and right wheels in opposite directions, while avoiding position deviation or skidding / sideslip; in this way, the multi-axle chassis is flexibly adjusted for yaw moment and rotation speed. The kinematics of this mode are determined by the following equation:

[0032]

[0033] where L f is the distance from the front wheel to the virtual center of the multi-axle chassis, and ω is the rotation rate of the multi-axle chassis.

[0034] q e is represented as the state error, and the desired state vector and The following can be obtained:

[0035]

[0036] Tracking error θ e The dynamic form is:

[0037]

[0038] 2) Diagonal movement mode: the multi-axle chassis moves diagonally or even laterally without yaw adjustment to achieve direct and fast movement from one point to another, thereby improving efficiency and accuracy; when v is the driving speed, the motion dynamics is

[0039]

[0040] For this mode, the reference and the reference control input u r = (v r , ω r ) T The motion error vector q e is given by:

[0041]

[0042] 3) Variable Ackerman mode: by flexibly adjusting the steering angles of the front and rear wheels, the multi-axle chassis can adjust the steering radius to obtain higher maneuverability to adapt to various environments or operating conditions; the kinematics equation is as follows:

[0043]

[0044] where L represents the distance from the first axis to the nth axis, and k1 and k2 represent configuration parameters. Specifically, where is the steering angle of the front wheel, is the steering angle of the rear wheel. When k1 = 0 and k2 = 1, the traditional Ackerman steering mode is adopted, which realizes fast steering only by steering the front wheel; when k1 = 1 and k2 = 0, the double Ackerman steering mode is adopted, the steering angles of the front and rear wheels are the same, and fast yaw response is obtained by reducing the turning radius; using the modified control input vector [v′, ω′] T , the above equation is simplified as:

[0045]

[0046] where, v′ is the longitudinal speed of the multi-axle chassis;

[0047] By defining an intermediate variable z, it is derived that when the multi-axle chassis is in diagonal movement mode, and when z = θ, the multi-axle chassis is in zero-radius turning mode or variable Ackerman mode. The following unified model is obtained:

[0048]

[0049] wherein, and represent the relevant reference control inputs in different steering modes.

[0050] In step S2, the multiple steering modes of the multi-axle chassis are all regarded as optional subsystems; the implementation method of step S2 is as follows:

[0051] Considering external bounded random disturbance and parameter uncertainty, a unified switching model containing multiple subsystems and switching signals is established:

[0052]

[0053] u(t) = [v σ ω σ ] T Formula three;

[0054] wherein, q e = [x e y e z e ] T is the error state vector of the multi-axle chassis, q r = [x r y r z r ] T is the desired state vector, f σ is a nonlinear set of M different functions, representing the selected subsystem, M ∈ N+ represents the number of optional steering modes of the system, i.e., the subsystem set, the switching signal σ: [0, ∞) → i = {1, 2,..., M} is a piecewise constant function, which determines the preferred subsystem of the current system; (x, y) is the planar coordinate position of the multi-axle chassis, z is an intermediate variable, which is used to determine the steering mode of the multi-axle chassis; u(t) is the control input, v σ is the longitudinal speed of the multi-axle chassis, and ω σ is the rotation rate of the multi-axle chassis. is an unknown bounded disturbance, and in this step, it is assumed that there is no jump in the system state of the multi-axle chassis at each switching time.

[0055] The unknown bounded disturbance includes external bounded random disturbance, modeled or unstructured uncertainty, and parameter vibration.

[0056] The implementation method of step S3 is: assuming that the output dimension of the multi-axle chassis is three (i.e., x e , y e , and z e ) and the input dimension is two (i.e., v σ and ω σ ), then the state error q e (t) of the multi-axle chassis is based on e x e y e z T Design new internal coupling sliding surface s 1σ and s 2σ :

[0057]

[0058] wherein k iσ (i=0, 1, 2) is a defined normal number, tanh(*) represents a hyperbolic tangent function, represents a scalar ensuring ;

[0059] For the designed internal coupling sliding surface, the following control law is adopted:

[0060]

[0061] The equivalent control law is that v and ω slide ; the non-chattering approaching law is that v switch and ω switch , which is expressed by the following formula:

[0062]

[0063] wherein p iσ >0, β iσ >0, α iσ ∈[0, 1] and β iσ ∈[0, 1] (i=1, 2) represent normal constants, and the tracking error of each subsystem will approach the equilibrium state.

[0064] The tracking error of each subsystem will approach the equilibrium state, which means that the proposed ICSMC method makes the state error of each subsystem of the multi-axle chassis tend to be stable.

[0065] The implementation method of step S4 is: assuming that it is not known in advance which sub-controller is most suitable for the multi-axle chassis for tracking the current reference trajectory, then any one of the sub-controllers is initially activated as the current controller; the supervision criterion ζ(t) is constructed for the current steering mode, i.e., the i-th subsystem, and is expressed by the following formula:

[0066]

[0067] where ε > 0 is a small positive number, are switching instants on the interval [t0, T], V(s(t i )) is a Lyapunov function with s(t i ) = [s 1σ (t i ) s 2σ (t i )], where 0 < γ i < λ i < λ i denotes the energy decay rate of the system;

[0068] The energy decay rate is derived as follows:

[0069]

[0070] According to the construction of the supervisory criterion ζ(t), if the compensation tracking error increases, V(s(t i )) > ζ(t), the exponential convergence is no longer valid, and the LCB system needs to change the existing steering mode to a better one to maintain the tracking performance and global convergence.

[0071] Based on the construction of the supervisory criterion ζ(t), the rule of evaluation excludes the mismatched subsystems and sub-controllers of the multi-axle LCB system under the current running condition; if the switching speed is slow enough, it is directly considered that the subsystem remains stable, and the time consumed by asynchronous switching needs to meet the mode-dependent average dwell time (MDADT) condition, i.e.,

[0072]

[0073] where μ is the increase coefficient of the Lyapunov function of each activated subsystem at the switching instant;

[0074] Under the MDADT condition, the switching signal σ is generated by periodically applying the following evaluation rules:

[0075] Evaluation rule a) if V σ (s(t)) < ζ(t), the multi-axle LCB system maintains the current steering mode, i.e.

[0076] Evaluation rule b) if V σ (s(t)) = ζ(t), the LCB system will switch to the next subsystem, i.e.

[0077] Evaluation rule c) if V σIf s(t) = z(t) and sigma = M, then the clockwise sequence of switching signal sigma will return to the initial value.

[0078] The supervision criterion z(t) is derived from The initial value is Where sigma(t0) is in N + Is a positive integer, once the adopted steering mode violates the supervision criterion z(t), the multi-axle chassis system will autonomously and adaptively switch the subsystem and the sub-controller.

[0079] The present application is directed to the system tracking control problem under external bounded random disturbance and parameter uncertainty, and proposes an adaptive steering mode switching control method for a multi-axle chassis, which can realize the steering mode switching control of the multi-axle chassis in a narrow space, and improve the flexibility and tracking control performance of the multi-axle chassis.

[0080] Compared with the prior art, the present application has the following beneficial effects:

[0081] (1) The present application is directed to the problem of system instability caused by nonlinear correlation of the multi-axle chassis in multiple steering modes, and constructs a unified switching model considering external bounded random disturbance and parameter uncertainty, and optimizes the continuous control input of each subsystem by designing an improved internal coupling sliding film controller, so that the controller adaptive law is continuous and has no chattering state in the sliding stage and the reaching stage. Through the optimization of the control input, the control accuracy and system robustness can be improved.

[0082] (2) The present application is directed to the problem that it is difficult to realize robust tracking control in a single steering mode in a cluttered environment or a limited space of the multi-axle chassis, and designs a hierarchical switching law fused with expected trajectory information, establishes a supervision criterion describing the energy decay law of the system, defines a delay time parameter for asynchronous switching, constructs an evaluation rule for identifying mismatched sub-controllers, realizes autonomous steering mode switching of the multi-axle chassis system without stopping, and guarantees the global stability and H performance of the system. BRIEF DESCRIPTION OF DRAWINGS

[0083] The present application will be further described in detail below in combination with the drawings and specific embodiments:

[0084] The attached Figure 1 is the method implementation flowchart of the embodiment of the present application;

[0085] The attached Figure 2 is the implementation principle diagram for controlling the multi-axle chassis in the embodiment of the present application;

[0086] The attached Figure 3 is the kinematic model of the multi-axle chassis in the embodiment of the present application;

[0087] The attachedFigure 4 Structure diagram of a multi-axle chassis in an embodiment of the present application;

[0088] Figure 2 is a schematic diagram of a multi-axle chassis in an embodiment of the present application; Figure 5 Figure 3 is a schematic diagram of a plurality of steering modes of a multi-axle chassis in an embodiment of the present application. DETAILED DESCRIPTION

[0089] The present application will be further described below with reference to the accompanying drawings and embodiments.

[0090] It should be noted that the following detailed description is exemplary in nature and is intended to provide further description of the present application. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.

[0091] It is to be understood that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments in accordance with the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and / or "comprising," when used in this specification, specify the presence of stated features, steps, operations, elements, components, and / or groups thereof, but do not preclude the presence or addition of one or more other features, steps, operations, elements, components, and / or groups thereof.

[0092] As shown in Figure 1, a method for adaptive steering mode switching control of a multi-axle chassis includes the following steps: Figure 1

[0093] Step S1: Establish a kinematic model of the multi-axle chassis to describe the kinematic state of the vehicle when driving at low speed;

[0094] Step S2: Considering the external bounded random disturbance and parameter uncertainty, the steering mode of the multi-axle chassis is regarded as a selectable subsystem, and a unified switching model is constructed for the state interconnection of each steering mode;

[0095] Step S3: Based on the state error of the multi-axle chassis, an internal coupling sliding surface is constructed and a modified approaching law is designed, and an improved internal coupling sliding mode controller ICSMC is established for optimizing the continuous control input of each subsystem;

[0096] Step S4: A supervision criterion is established to describe the energy attenuation law of the system, and an evaluation rule is constructed to identify the mismatched sub-controller, so as to realize the autonomous switching of each subsystem and optimize the selection of the controller parameters, and ensure the global stability and H performance of the system.

[0097] The implementation principle of the method provided in the present example for switching control of the multi-axle chassis is as shown in Figure 2. Figure 2 ​The kinematic model of the multi-axle chassis is first established, the steering mode of the multi-axle chassis is regarded as a selectable subsystem, the bounded random disturbance and parameter uncertainty are considered, and a unified switching model of the state interconnection of each steering mode is constructed; then, the internal coupling sliding surface and the modified reaching law are constructed based on the state error of the multi-axle chassis, and an improved internal coupling sliding mode controller (ICSMC) without chattering is established; finally, the supervision criterion describing the energy attenuation law is established, the evaluation rule for identifying the mismatched sub-controller is constructed, and the autonomous switching of each subsystem and the optimization of the controller parameters are realized.

[0098] Figure 3 The kinematic model of the multi-axle chassis is first established, the steering mode of the multi-axle chassis is regarded as a selectable subsystem, the bounded random disturbance and parameter uncertainty are considered, and a unified switching model of the state interconnection of each steering mode is constructed; then, the internal coupling sliding surface and the modified reaching law are constructed based on the state error of the multi-axle chassis, and an improved internal coupling sliding mode controller (ICSMC) without chattering is established; finally, the supervision criterion describing the energy attenuation law is established, the evaluation rule for identifying the mismatched sub-controller is constructed, and the autonomous switching of each subsystem and the optimization of the controller parameters are realized.

[0099] Figure 4 The kinematic model of the multi-axle chassis is first established, the steering mode of the multi-axle chassis is regarded as a selectable subsystem, the bounded random disturbance and parameter uncertainty are considered, and a unified switching model of the state interconnection of each steering mode is constructed; then, the internal coupling sliding surface and the modified reaching law are constructed based on the state error of the multi-axle chassis, and an improved internal coupling sliding mode controller (ICSMC) without chattering is established; finally, the supervision criterion describing the energy attenuation law is established, the evaluation rule for identifying the mismatched sub-controller is constructed, and the autonomous switching of each subsystem and the optimization of the controller parameters are realized.

[0100] Figure 5 The kinematic model of the multi-axle chassis is first established, the steering mode of the multi-axle chassis is regarded as a selectable subsystem, the bounded random disturbance and parameter uncertainty are considered, and a unified switching model of the state interconnection of each steering mode is constructed; then, the internal coupling sliding surface and the modified reaching law are constructed based on the state error of the multi-axle chassis, and an improved internal coupling sliding mode controller (ICSMC) without chattering is established; finally, the supervision criterion describing the energy attenuation law is established, the evaluation rule for identifying the mismatched sub-controller is constructed, and the autonomous switching of each subsystem and the optimization of the controller parameters are realized.

[0101] In step S1, the kinematic model of the multi-axle chassis describes the motion law of the spatial pose of the multi-axle chassis changing with time from a geometric perspective; the implementation method of step S1 is as follows:

[0102] When the kinematic model is used to study the motion control problem of the multi-axle chassis, it is assumed that the vehicle travels at a low speed, only pure rolling without sliding occurs between the tire and the ground, the mechanical factors such as tire force, roll force and friction force of the vehicle are ignored, the steering does not exist side slip, that is, the center of mass side slip angle is 0, and the non-complete constraint condition is satisfied,

[0103] From the geometric relationship, the following can be obtained:

[0104]

[0105] The instantaneous turning radius R can be derived as follows:

[0106]

[0107] The yaw angular velocity ω of the multi-axle chassis can be determined from the turning radius R and the center of mass velocity v:

[0108]

[0109] The velocity components of the multi-axle chassis on the X-axis and the Y-axis are as follows:

[0110]

[0111] The multi-axle chassis kinematic model in the coordinate system XOY is represented as:

[0112]

[0113] where (x, y) are the coordinates of the center of mass P, v is the velocity of the center of mass, θ is the angle between the center of mass and the X-axis, i.e., the heading angle, L1 and L n are the distances from the center of mass to the first and nth axles, respectively, and are the steering angles of the virtual first and nth axle tires, respectively, and all other variables are functions of time t, except for the wheelbase L.

[0114] For continuous subsystems and discrete switching signals, the hybrid switching control system of the adaptive steering mode is represented as:

[0115]

[0116] where x(t) represents the system state, f σ(t) is a collection of n different functions, and σ(t) is the switching signal that determines which f σ(t) function controls the system behavior at time t, represents the number of subsystems, and the solution of the system is a pair {x(t), σ(t)} that provides the optimal system state x(t) and switching signal σ(t); σ(t) is classified as state-dependent or time-dependent by determining whether the switching depends on the system state x(t) or time t;

[0117] By using the virtual front axle and the real axles, the motion state of the multi-axle chassis is represented as a single-track model.

[0118] q is represented as the state, (x, y) represents the center of mass planar position, θ and represent the heading angle and front wheel steering angle, respectively. The following derivation relates to the kinematic state of the alternative steering modes of the multi-axle chassis.

[0119] 1) Zero-radius steering mode: This mode is applied to achieve a pivot steering by setting the left and right wheels in opposite directions, while avoiding position deviation or skidding / slip; in this way, the multi-axle chassis is flexibly adjusted for yaw moment and rotation speed. The kinematics of this mode are determined by the following equation:

[0120]

[0121] where L f is the distance from the front wheel to the virtual center of the multi-axle chassis, and ω is the rotation rate of the multi-axle chassis.

[0122] q e is represented as the state error, and the desired state vector and The following can be obtained:

[0123]

[0124] Tracking error θ e The dynamic form is:

[0125]

[0126] 2) Diagonal movement mode: the multi-axle chassis moves diagonally or even laterally without yaw adjustment to achieve direct and fast movement from one point to another, thereby improving efficiency and accuracy; when v is the driving speed, the motion dynamics is

[0127]

[0128] For this mode, the reference and the reference control input u r = (v r , ω r ) T The motion error vector q e is given by:

[0129]

[0130] 3) Variable Ackerman mode: by flexibly adjusting the steering angles of the front and rear wheels, the multi-axle chassis can adjust the steering radius to obtain higher maneuverability to adapt to various environments or operating conditions; the kinematics equation is as follows:

[0131]

[0132] where L represents the distance from the first axis to the nth axis, and k1 and k2 represent configuration parameters. Specifically, where is the steering angle of the front wheel, is the steering angle of the rear wheel. When k1 = 0 and k2 = 1, the traditional Ackerman steering mode is adopted, and fast steering is achieved only by steering the front wheel; when k1 = 1 and k2 = 0, the double Ackerman steering mode is adopted, and the steering angles of the front and rear wheels are the same, and fast yaw response is obtained by reducing the turning radius; using the modified control input vector [v′, ω′] T , the above equation is simplified as:

[0133]

[0134] where, v′ is the longitudinal speed of the multi-axle chassis;

[0135] By defining an intermediate variable z, it is derived that when the multi-axle chassis is in diagonal movement mode, and when z = θ, the multi-axle chassis is in zero-radius turning mode or variable Ackerman mode. The following unified model is obtained:

[0136]

[0137] wherein and represent the relevant reference control inputs in different steering modes.

[0138] In step S2, the multiple steering modes of the multi-axle chassis are all regarded as optional subsystems; the implementation method of step S2 is as follows:

[0139] Considering external bounded random disturbances and parameter uncertainties, a unified switching model of the multi-axle chassis containing multiple subsystems and switching signals is established:

[0140]

[0141] u(t) = [v σ ω σ ] T Equation three;

[0142] wherein q e = [x e y e z e ] T is an error state vector of the multi-axle chassis, q r = [x r y r z r ] T is a desired state vector, f σ is a nonlinear set of M different functions, representing the selected subsystem, M ∈ N+ represents the number of optional steering modes of the system, i.e., the subsystem set, the switching signal σ: [0, ∞) → i = {1, 2,..., M} is a piecewise constant function, which determines the preferred subsystem of the current system; (x, y) is the planar coordinate position of the multi-axle chassis, z is an intermediate variable, which is used to determine the steering mode of the multi-axle chassis; u(t) is the control input, v σ is the longitudinal speed of the multi-axle chassis, and ω σ is the rotation rate of the multi-axle chassis. is an unknown bounded disturbance, and in this step, it is assumed that there is no jump in the system state of the multi-axle chassis at each switching time, necessary assumptions and lemmas are provided here.

[0143] Assumption 1: For a given period T funder the constraint condition is lower bounded.

[0144] Lemma 1: Given a certain switching signal σ and an arbitrary initial state x(t0), if there exist constants α > 0 and δ > 0 such that

[0145]

[0146] then: the equilibrium state x(t) = 0 (t→∞) of the switched model is globally exponentially stable.

[0147] Lemma 2: If the following conditions are met:

[0148] 1) the system is exponentially stable in the absence of disturbances;

[0149] 2) the response z satisfies

[0150]

[0151] where T i (t0,t) is the total running time of the ith subsystem in the interval [t0,t), and α i > 0 is a positive scalar, then: the system has exponential H∞ regulation performance at a given disturbance rejection level η.

[0152] The unknown bounded disturbance includes external bounded random disturbance, modelized or unstructured uncertainty, and parameter vibration.

[0153] The implementation method of step S3 is: assuming that the output dimension of the multi-axle chassis is three (i.e., x e , y e and z e ) and the input dimension is two (i.e., v σ and ω σ ), a state error q e (t) = [x e y e z e ] T is designed based on the multi-axle chassis, and new internal coupling sliding surfaces s 1σ and s 2σ are designed:

[0154]

[0155] where k iσ (i = 0, 1, 2) is a defined normal number, tanh(*) represents a hyperbolic tangent function, and represents a scalar that guarantees ;

[0156] Theorem 1: For the designed internal coupling sliding surface, the following control law is adopted:

[0157]

[0158] The equivalent control law is and slide The chattering-free approaching law is switch and switch which is expressed as

[0159]

[0160]

[0161] where p iσ > 0, β iσ > 0, α iσ ∈ [0, 1] and β iσ ∈ [0, 1] (i = 1, 2) are the norm constants, and the tracking error of each subsystem will approach the equilibrium state.

[0162] The tracking error of each subsystem will approach the equilibrium state means that the proposed ICSMC method makes the state error of each subsystem of the multi-axle controlled chassis tend to be stable.

[0163] The proof of Theorem 1 should satisfy the sufficient conditions for the finite-time reaching and asymptotic stability of the obtained ICSMC method under the desired sliding surface. We give the following three parts.

[0164] Part 1 (Lyapunov function): A Lyapunov candidate function is chosen as follows:

[0165] V(s(t)) = 0.5s T s,s = [s 1σ s 2σ ] T

[0166] Taking the derivative of it gives:

[0167]

[0168] The derivative of the proposed coupling sliding surface is:

[0169]

[0170] Substituting the derivative of the coupling sliding surface and the control law into the derivative of the Lyapunov function gives:

[0171]

[0172] Based on this, the integral coefficients are chosen to ensure that is semi-negative definite, i.e. According to Lyapunov principle, the closed-loop stability of each subsystem is guaranteed.

[0173] Part 2 (finite-time reaching condition): Combining the reaching law between 0 and , we have

[0174]

[0175] Let Then:

[0176]

[0177] If the initial condition of the sliding surface satisfies Assume We have:

[0178]

[0179] Similarly, consider and We have:

[0180]

[0181] The reaching time is expressed as:

[0182]

[0183] For s 2σ , the related reaching time and have the same structure. Therefore, under any initial condition, we can guarantee that the desired sliding surface reaches in finite time.

[0184] Part 3 (state error convergence): When reaching the sliding surface, considering s = 0, we have:

[0185]

[0186] From s 1σ and k 1σ > 0, we can conclude that when x e converges to 0. In addition, if s 2σ converges to 0, the steady state means:

[0187]

[0188] Note that x e is defined to asymptotically approach the origin, and is positive and bounded. Then when k 0σ > 0 and k 2σ > 0, we get:

[0189]

[0190] y e The asymptotic convergence of s 2σ The internal coupling of y e and z e results in the asymptotic convergence of s and z e Therefore, q e is bounded and asymptotically convergent to the origin, i.e., the output state tracks the reference signal, and the proposed ICSMC method makes the multi-axle controlled chassis system continuous stable.

[0191] Note: For the zero-radius steering mode, since the tracking error is only related to the steering angle, the sliding surface where k 3σ > 0 is a positive constant, the robust control law for steering regulation can be obtained as follows:

[0192]

[0193] where p 3σ , q 3σ , β 3σ and a 3σ ∈ [0, 1] are positive coefficients, and the proven stability and convergence can be extended here.

[0194] In the upper layer switching allocation mechanism, the steering mode is regarded as an optional subsystem, including the diagonal moving steering mode, the zero-radius steering mode, and the variable Ackerman steering mode. Considering the tracking control ability of the selected steering mode, the desired trajectory information is integrated into the switching mechanism, which is called the hierarchical switching law. For example, the zero-radius steering mode can achieve efficient pivot steering, flexibly adjust the direction when entering the transition zone within the radius, suppress the tracking overshoot in the presence of sharp corners, and is conducive to handling the scene of sharp turns. It can also provide more comfortable distance to safely move in narrow environments or limited space. Once the sharp tuning problem is solved, the multi-axle controlled chassis system will switch to the trajectory tracking control in an autonomous manner.

[0195] Since it is not known in advance which sub-controller (such as the diagonal moving steering mode or the Ackerman steering mode) is most suitable for the multi-axle controlled chassis to track the current reference trajectory, any one of the sub-controllers can be activated as the current controller initially, and then an autonomous switching rule for controlling the optional steering mode is developed.

[0196] The implementation method of step S4 is: if it is not known in advance which sub-controller is most suitable for the multi-axle chassis for tracking the current reference trajectory, then any one sub-controller is activated as the current controller at the beginning; a supervision criterion ζ(t) is constructed for the current steering mode, i.e., the ith subsystem, which is expressed in formula as:

[0197]

[0198] wherein ε>0 represents a small positive number, is the switching time on the interval [t0, T], V(s(t i )) is a Lyapunov function with s(t i ) = [s 1σ (t i )s 2σ (t i )], wherein 0<γ i <λ i , and λ i represents the energy decay rate of the system;

[0199] In an ideal case, the optimal controller synchronously and autonomously switches between the selectable subsystems associated with the multi-axle chassis system. Since the system inevitably needs additional time to identify the currently used controller, the time of switching to the optimal controller is not consistent with the time of activating the subsystem, resulting in an asynchronous switching action. Considering that the selected subsystem cannot be matched with the optimal controller in a short time, a mismatch time, i.e., a delay time, Δ i ≤τ i = t i+1 -t i (i = 0, 1, 2,...), is defined, and the control switching time is expressed as t i + Δ i , and let and When the activated subsystem is matched to the optimal controller, i.e., By setting β1 and β2 to ensure tanh(β 1σ s 1σ ) ≥ s 1σ and tanh(β 2σ s 2σ ) ≥ s 2σ , the following can be obtained:

[0200]

[0201] The energy decay rate is derived by the following formula:

[0202]

[0203] According to the construction of the supervision criterion ζ(t), if the compensation tracking error increases, V(s(t i ))>ζ(t), the exponential convergence is no longer valid, and the steer-by-wire chassis system needs to change the existing steering mode to a better steering mode to maintain tracking performance and global convergence.

[0204] According to the construction of the supervision criterion ζ(t), the rule of evaluation excludes the mismatched subsystems and sub-controllers of the multi-axle steer-by-wire chassis system under the current running condition; if the switching speed is slow enough, it is directly considered that the subsystem remains stable, and the time consumed by asynchronous switching needs to meet the mode-dependent average dwell time MDADT condition, that is:

[0205]

[0206] wherein μ is the increase coefficient of the Lyapunov function of each activated subsystem at the switching moment;

[0207] Under the MDADT condition, the switching signal σ is generated by periodically applying the following evaluation rules:

[0208] The evaluation rule a) if V σ (s(t))<ζ(t), the multi-axle steer-by-wire chassis system maintains the current steering mode, that is

[0209] The evaluation rule b) if V σ (s(t))=ζ(t), the steer-by-wire chassis system will switch to the next subsystem, that is

[0210] The evaluation rule c) if V σ (s(t))=ζ(t) and σ=M, the clockwise sequence of the switching signal σ will return to the initial value.

[0211] Note that the supervision criterion is not a priori knowledge or offline tuning, and the supervision criterion ζ(t) is derived from , and the initial value is wherein σ(t0)∈N + is a positive integer, and once the adopted steering mode violates the supervision criterion ζ(t), the multi-axle steer-by-wire chassis system will autonomously and adaptively switch the subsystems and sub-controllers.

[0212] The example proposes an adaptive steering mode switching control method for a multi-axle steer-by-wire chassis for the system tracking control problem under external bounded random disturbances and parameter uncertainties, which can realize the steering mode switching control of the multi-axle steer-by-wire chassis in a narrow space and improve the flexibility and tracking control performance of the multi-axle steer-by-wire chassis.

[0213] Those skilled in the art will appreciate that embodiments of the application can be readily used as software, hardware, or a combination of software and hardware. In one

[0214] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 one or more flowcharts and / or blocks in the flowcharts and / or a combination thereof. These computer program instructions can also be stored in a computer readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer readable memory produce an article of manufacture including instructions which implement the function specified in the flowchart block or blocks. Figure 1 an apparatus to perform functions specified in the flowchart block or blocks.

[0215] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 one or more flowcharts and / or blocks in the flowcharts and / or a combination thereof. These computer program instructions can also be stored in a computer readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer readable memory produce an article of manufacture including instructions which implement the function specified in the flowchart block or blocks. Figure 1 an apparatus to perform functions specified in the flowchart block or blocks.

[0216] The computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 one or more flowcharts and / or blocks in the flowcharts and / or a combination thereof. These computer program instructions can also be stored in a computer readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer readable memory produce an article of manufacture including instructions which implement the function specified in the flowchart block or blocks. Figure 1 an apparatus to perform functions specified in the flowchart block or blocks.

[0217] The above descriptions are only preferred embodiments of the present application, and are not intended to limit the present application to other forms. Any person skilled in the art can make modifications or alterations to the above-described embodiments without departing from the technical scope of the present application. Any simple modifications, equivalent changes and alterations made to the above-described embodiments based on the technical essence of the present application shall fall within the scope of protection of the present application.

Claims

1. An adaptive steering mode switching control method for a multi-axle chassis, characterized by: Comprising the following steps; Step S1: establishing a kinematic model of the multi-axle chassis to describe the kinematic state of the vehicle when driving at low speed; Step S2: considering the external bounded random disturbance and parameter uncertainty, regarding the steering mode of the multi-axle chassis as an optional subsystem, constructing a unified switching model of the state interconnection of each steering mode; Step S3: based on the state error of the multi-axle chassis, constructing an internal coupling sliding surface and designing a modified approaching law to establish an improved internal coupling sliding surface controller ICSMC for optimizing the continuous control input of each subsystem; Step S4: establishing a supervision criterion describing the energy attenuation law of the system, constructing an evaluation rule for identifying the mismatched sub-controller to realize the autonomous switching of each subsystem and optimize the selection of the controller parameters, and ensuring the global stability and H performance of the system; In step S1, the kinematic model of the multi-axle chassis describes the motion law of its spatial pose changing with time from a geometric perspective; the implementation method of step S1 is as follows: When studying the motion control problem of the multi-axle chassis based on the kinematic model, it is assumed that the vehicle is driving at a low speed, and only pure rolling without sliding occurs between the tire and the ground, and there is no side slip in steering, i.e. the center of mass side slip angle is 0, which satisfies the nonholonomic constraint condition, From the geometric relationship, we have: The instantaneous turning radius R is derived as follows: The yaw rate ω of the multi-axle chassis is determined by the turning radius R and the center of mass velocity v: The velocity components of the multi-axle chassis on the X and Y axes are: Then the kinematic model of the multi-axle chassis in the coordinate system XOY is represented as: wherein the coordinates of the center of mass P are (x, y), v is the velocity of the center of mass, Θ is the angle of the center of mass with the X axis, i.e. the direction angle, L1 and L n are the distances of the first and n-th axis, respectively, from the center of mass, and are the steering angles of the virtual first and n-th axis tires, respectively, and all variables except the wheel base L are functions of time t. For continuous subsystems and discrete switching signals, the hybrid switching control system of adaptive steering mode is represented as: where x(t) represents the system state, f σ(t) is a collection of n different functions, σ(t) is a switching signal that determines which f σ(t) function controls the system behavior at time t, represents the number of subsystems, the solution of the system is a pair {x(t), σ(t)} that provides the optimal system state x(t) and switching signal σ(t); σ(t) is classified as state-dependent or time-dependent by determining whether the switching depends on the system state x(t) or time t; By using the virtual front axle and the real axle, the motion state of the multi-axle chassis is represented as a single-track model; q denotes the state, (x, y) denotes the center of mass planar position, θ and respectively denote the heading angle and the front wheel steering angle; the following derivation relates to the kinematic state of the alternative steering mode of the multi-axle chassis; 1) Zero-radius steering mode: This mode is applied to achieve pivot steering by setting the left and right wheels in opposite directions, while avoiding position deviation or skidding / sideslip; in this way, the multi-axle chassis can flexibly adjust the yaw moment and rotation speed; the kinematics of this mode is determined by the following formula: where L f is the distance from the front wheel to the virtual center of the multi-axle chassis, and ω is the rotation rate of the multi-axle chassis. q e is expressed as a state error, combined with a desired state vector and It can be obtained: Tracking error θ e The dynamic form of the equation is: 2) Diagonal movement mode: The multi-axle chassis moves diagonally or even laterally without yaw adjustment to achieve direct and fast movement from one point to another, thereby improving efficiency and accuracy; when v is the driving speed, the motion dynamics is For this mode, the reference and the reference control input u r = (v r , ω r ) T The motion error vector q e is given by 3) Variable Ackerman mode: By flexibly adjusting the steering angles of the front and rear wheels, the multi-axle chassis can adjust the steering radius to obtain higher maneuverability to adapt to various environments or operating conditions; the kinematic equation is as follows: wherein L denotes the distance from the first axis to the n-th axis, and k1 and k2 denote configuration parameters; in particular, wherein is the steering angle of the front wheels, is the steering angle of the rear wheels; when k1 = 0 and k2 = 1, a conventional Ackermann steering mode is adopted, in which only the front wheels are steered for fast steering; when k1 = 1 and k2 = 0, a double Ackermann steering mode is adopted, in which the steering angles of the front and rear wheels are the same, and fast yaw response is obtained by reducing the turning radius; using a modified control input vector [v', ω'] T simplifies to: wherein, v' is the longitudinal speed of the multi-axle chassis; By defining an intermediate variable z, it is derived that when the multi-axle chassis is in diagonal movement mode, and when z = θ, the multi-axle chassis is in zero-radius turning mode or variable Ackerman mode; the following unified model is obtained: wherein, and represent the relevant reference control inputs for different steering modes. In step S2, the multiple steering modes of the multi-axle chassis are regarded as optional subsystems; the implementation method of step S2 is as follows: Considering the external bounded random disturbance and parameter uncertainty, a unified switching model containing multiple subsystems and switching signals is established: u(t) = [v σ ω σ ] T Equation Three; where q e = [x e y e z e ] T is the error state vector of the multi-axle chassis, q r = [x r y r z r ] T is the desired state vector, f σ is a nonlinear set of M different functions representing the selected subsystems, M e N+ represents the number of selectable steering modes of the system, i.e. the subsystem set, the switching signal s: [0,∞)→ i = {1,2,...,M} is a piecewise constant function that determines the currently preferred subsystem of the system; (x,y) is the planar coordinate position of the multi-axle chassis, z is an intermediate variable used to determine the steering mode of the multi-axle chassis; u(t) is the control input, v σ is the longitudinal velocity of the multi-axle chassis, ω σ is the rotational rate of the multi-axle chassis; is an unknown bounded disturbance, while in this step it is assumed that there are no jumps in the system state of the multi-axle chassis at each switching instant.

2. The adaptive steering mode switching control method for a multi-axle chassis according to claim 1, characterized in that: The unknown bounded disturbance includes external bounded random disturbance, modelized or unstructured uncertainty, and parameter vibration.

3. The adaptive steering mode switching control method for a multi-axle chassis according to claim 1, characterized in that: The implementation method of step S3 is: assuming that the output dimension of the multi-axle chassis is three (i.e., x e , y e and z e ) and the input dimension is two (i.e., v σ and ω σ ), then the state error q e (t) of the multi-axle chassis is based on e x e y e z T Design new internal coupling sliding film surfaces s 1σ and s 2σ : wherein k iσ (i = 0, 1, 2) are defined normal numbers, tanh(*) represents the hyperbolic tangent function, denotes a scalar that ensures that For the designed internal coupling sliding surface, the following control law is adopted: The equivalent control law is and ω slide ; the chattering-free approaching law is v switch and ω switch , which is expressed by the following formula: where p iσ > 0, β iσ > 0, a iσ ∈ [0, 1] and β iσ ∈ [0, 1] (i = 1, 2) represent the norm constants, and the tracking error of each subsystem will tend to the equilibrium state.

4. The adaptive steering mode switching control method for a multi-axle chassis according to claim 1, characterized by: The tracking error of each subsystem will tend to be balanced, which means that the proposed ICSMC method makes the state error of each subsystem of the multi-axle chassis tend to be stable.

5. The adaptive steering mode switching control method for a multi-axle chassis according to claim 1, characterized in that: The implementation method of step S4 is: assuming that it is not known in advance which sub-controller is most suitable for the multi-axle-by-wire chassis for tracking the current reference trajectory, any one sub-controller is activated as the current controller at the beginning; a supervision criterion ζ(t) is constructed for the current steering mode, i.e. the i-th subsystem, which is expressed in formula as: where ε > 0 is a small positive number, t∈[t i ,t i+1 ) is the switching time interval on [t0, T], V(s(t i )) is a Lyapunov function with s(t i ) = [s 1σ (t i ) s 2σ (t i )] where 0 < γ i < λ i < 1, and λ i denotes the energy decay rate of the system.

6. The adaptive steering mode switching control method for a multi-axle chassis according to claim 5, characterized in that: The energy decay rate is derived by the following formula: According to the construction of the supervision criterion ζ(t), the evaluation rule is that if the compensation tracking error increases, V(s(t i )) > ζ(t), then the exponential convergence is no longer valid, and the steer-by-wire chassis system needs to change the existing steering mode and switch to a better steering mode to maintain tracking performance and global convergence.

7. The adaptive steering mode switching control method for a multi-axle chassis according to claim 6, characterized in that: Based on the construction of the supervision criterion ζ(t), the evaluation rule is constructed to exclude the mismatched subsystems and sub-controllers of the multi-axle-by-wire chassis system under the current operating condition; if the switching speed is slow enough, it is directly considered that the subsystem remains stable, and the time consumed by asynchronous switching needs to meet the mode-dependent average dwell time MDADT condition, i.e. Wherein μ is the increase coefficient of the Lyapunov function of each activated subsystem at the switching moment; Under MDADT conditions, the switching signal σ is generated by periodically applying the following evaluation rules, which are specified as evaluation rule a) if V σ (s(t)) < ζ(t), the multi-axle chassis system remains in the current steering mode, i.e. Evaluation rule b) if V σ (s(t)) = ζ(t), the drive-by-wire chassis system will switch to the next subsystem, i.e. Evaluation rule c) if V σ (s(t)) = ζ(t) and σ = M, the clockwise sequence of the switching signal σ will return to the initial value.

8. The adaptive steering mode switching control method for a multi-axle chassis according to claim 7, characterized in that: The supervision criterion ζ(t) is derived from with initial value where σ(t0) ∈ N + is a positive integer, the multi-axle chassis system will autonomously and adaptively switch subsystems and sub-controllers once the steering mode employed violates the supervision criterion ζ(t).

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