A double closed-loop finite-time control method for disturbed wheeled mobile robots

Abstract

The embodiment of the present invention provides a dual closed-loop finite-time control method for a disturbed wheeled mobile robot. The method includes: establishing a kinematic model and a dynamic model of the wheeled mobile robot; using the kinematic model to derive a kinematic attitude tracking error model of the wheeled mobile robot, and decomposing it into a position subsystem and an attitude subsystem; designing a non-singular terminal sliding mode linear velocity controller for the attitude subsystem; using a fixed-time integral sliding surface to design a finite-time convergent extended state observer and a fixed-time dynamic loop velocity tracking controller for the dynamic model of the disturbed wheeled mobile robot; using the observer and the controller to control the disturbed wheeled mobile robot to track the desired trajectory within a finite time, thereby realizing trajectory tracking control. The method of the present invention effectively solves the problems of changeable conditions, fast output response, and high control accuracy requirements in the trajectory tracking control process. It has strong operability and is conducive to improving economic benefits.

Description

Technical Field

[0001] The invention relates to the technical field of mobile robots, and in particular to a double closed-loop finite-time control method for a disturbed wheeled mobile robot. Background Art

[0002] The three-wheeled mobile robot is the basic mobile structure of the wheeled mobile robot. This structure has the characteristics of stable motion, high energy utilization, and simple structure. Its driving forms mainly include differential drive and synchronous drive. Due to its special under-actuated structure, the trajectory tracking control problem of the differential drive wheeled mobile robot is a research direction that has attracted attention today.

[0003] As people's requirements for robot trajectory tracking control accuracy and response speed are getting higher and higher, finite time control technology and disturbance observation technology have attracted widespread attention from scholars. Finite time control is a control strategy that can greatly improve the response speed. For complex nonlinear systems such as wheeled mobile robots, observer technology is usually used to feedforward offset complex disturbances and construct terminal sliding membranes to achieve finite time control goals.

[0004] Based on the above analysis, there are relatively few studies on finite-time trajectory tracking of wheeled mobile robots at home and abroad. Summary of the invention

[0005] An embodiment of the present invention provides a double closed-loop finite-time control method for a disturbed wheeled mobile robot, so as to effectively perform a trajectory tracking control process on the wheeled mobile robot.

[0006] In order to achieve the above object, the present invention adopts the following technical scheme.

[0007] A double closed-loop finite-time control method for a disturbed wheeled mobile robot, comprising:

[0008] A kinematic model is established for the under-actuated motion mode unique to wheeled mobile robots, the external disturbance forces on the wheeled mobile robots are analyzed, and a dynamic model is established;

[0009] The desired position and posture information of the wheeled mobile robot is obtained by decoupling the kinematic model, a kinematic posture tracking error model of the wheeled mobile robot is derived, and the kinematic posture tracking error model is decomposed into a position subsystem and a posture subsystem using a cascade control method;

[0010] Constructing a non-singular terminal sliding surface with the position subsystem error in the kinematic attitude tracking error model as the sliding mode, and constructing a fixed time integral sliding surface with the dynamic velocity deviation as the sliding mode;

[0011] A finite-time angular velocity controller is designed for the position subsystem, and a non-singular terminal sliding mode linear velocity controller is designed for the attitude subsystem;

[0012] For the dynamic model of a disturbed wheeled mobile robot, a finite-time convergent extended state observer and a fixed-time dynamic loop speed tracking controller are designed using the fixed-time integral sliding surface;

[0013] The observer and the controller are used to control the disturbed wheeled mobile robot to track a desired trajectory within a limited time, thereby realizing trajectory tracking control of the disturbed wheeled mobile robot.

[0014] Preferably, the kinematic model is established for the under-actuated motion mode unique to the wheeled mobile robot, the external disturbance force on the wheeled mobile robot is analyzed, and the dynamic model is established, including:

[0015] The non-holonomic constrained motion of the wheeled mobile robot in the local coordinate system is analyzed, and the kinematic equations at the posture and velocity levels are established:

[0016]

[0017] Where v and w represent the linear velocity and angular velocity of the robot, respectively, and the posture q = (x, y, θ) represents the position and angle of the robot in the global coordinate system;

[0018] The Euler-Lagrange method is used to establish the dynamic equation with the overall speed of the wheeled mobile robot as the output and the torque of the two driving wheels as the output:

[0019]

[0020] Where M is the inertia matrix of the system, are the centrifugal force and Coriolis force related to the position and velocity of the system, G(q), are the gravity term and friction term of the system, τ d is the external disturbance term, B(q) is the input transformation matrix, A T (q) is the Pfafian constraint matrix, m is the mass of the mobile robot, I is the moment of inertia, and the distance between the center of mass and the centroid of the car is d.

[0021] The specific expressions of each parameter matrix are as follows:

[0022]

[0023] In order to obtain the relationship between the output torque and the real-time speed of the robot, the kinematic model is used to eliminate the incomplete constraint matrix in the dynamic model, and the simplified dynamic model of the wheeled mobile robot is obtained:

[0024]

[0025]

[0026]

[0027] Without loss of generality, it is assumed that the wheels of the wheeled mobile robot obey pure rolling without sliding on the running surface during movement and the wheels always maintain point contact with the moving surface.

[0028] Preferably, the kinematic model is decoupled to obtain the desired position and posture information of the wheeled mobile robot, a kinematic posture tracking error model of the wheeled mobile robot is derived, and a cascade control method is used to decompose the kinematic posture tracking error model into a position subsystem and a posture subsystem, including:

[0029] The expected trajectory z of a wheeled mobile robot is obtained using the differential flatness technique. r =(x r ,y r ) is used for planning, and the desired posture information of the wheeled mobile robot is obtained after decoupling the kinematic model, and the desired posture information includes the desired posture angle θ r , expected linear velocity v r and the desired angular velocity w r ;

[0030]

[0031] Taking the robot reference system as the local coordinate system, the kinematic posture tracking error model of the wheeled mobile robot in the local coordinate system is derived. The kinematic posture tracking error model is expressed as:

[0032]

[0033] The trajectory tracking control problem of the wheeled mobile robot at the kinematic level is transformed into controlling the actual robot motion speed V, so that the wheeled mobile robot can track the reference speed V of the reference trajectory in real time. r =[v r ,w r ] T , pose q r =(x r ,y r ,θ r ) T

[0034] The trajectory error differential equation of the mobile robot is obtained by derivation of the kinematic posture tracking error model:

[0035]

[0036] The kinematic attitude tracking error model is decomposed into a position subsystem and an attitude subsystem in the form of an integral chain using a cascade control method.

[0037] The underactuated system of the disturbed wheeled mobile robot with underactuated motion is decoupled according to its structural characteristics. The system is used as an interference subsystem. θ As a cascade intermediate term, the trajectory error differential equation of the mobile robot is decomposed into a first-order posture subsystem and an integral chain second-order position subsystem.

[0038] Preferably, the construction of a non-singular terminal sliding surface with the position subsystem error in the kinematic posture tracking error model as the sliding mode and the construction of a fixed time integral sliding surface with the dynamic velocity deviation as the sliding mode include:

[0039] The coordinate transformation of the attitude subsystem state in the kinematic attitude tracking error model is performed. When the transformed state converges, it is easy to obtain that the original system's x and y direction errors also converge to zero:

[0040]

[0041] After the coordinate transformation, the original attitude subsystem is decoupled into an integral chain form, with two states z1 and z2 respectively;

[0042] Construct a non-singular terminal sliding mode surface with the position subsystem error in the kinematic attitude tracking error model as the sliding mode:

[0043]

[0044] where β kinematic is a positive number, p, q are positive odd numbers and 1<p / q<2;

[0045] The control objective of the dynamic model is that the model output speed can track the virtual control law output by the kinematic controller. The speed tracking error of the dynamic model is defined as:

[0046] e dynamic =V d -V (12)

[0047] Where V d =[v d ,w d ] is the kinematic controller output, and a fixed time integral sliding mode surface with dynamic velocity deviation as the sliding mode is constructed:

[0048]

[0049] where β dynamicare the parameters to be designed of the fixed time integral sliding surface.

[0050] Preferably, the design of a finite-time angular velocity controller for the position subsystem and the design of a non-singular terminal sliding mode linear velocity controller for the attitude subsystem include:

[0051] A finite-time angular velocity controller is designed for the position subsystem in the kinematic attitude tracking error model:

[0052]

[0053] Among them, α0, β0, m0, n0, p0, q0 are the fixed time controller design parameters respectively;

[0054] A non-singular terminal sliding mode linear velocity controller is designed for the attitude subsystem in the kinematic attitude tracking error model:

[0055]

[0056] Where 0<α<1, k1, k2 are suitable positive constants and k1≤k2; where w r ,v r are the reference linear velocity and angular velocity, β kinematic are the parameters of the sliding surface designed above, z1, z2 are the integral chain states, p, q are positive odd numbers and 1<p / q<2; Substitute the controller and sliding surface parameters into formulas (16) and (17) to obtain the closed-loop system of kinematic attitude error;

[0057]

[0058]

[0059] α0, β0, m0, n0, p0, q0 are the fixed time controller design parameters in equation (14), w r ,v r are the reference linear velocity and angular velocity, β kinematic are the parameters of the sliding surface designed above, z1, z2 are the integral chain states, p, q are positive odd numbers and 1<p / q<2e x ,e y ,e θ is the error state in equation (8).

[0060] Preferably, the dynamic model for the disturbed wheeled mobile robot uses the fixed-time integral sliding surface to design a finite-time convergent extended state observer and a fixed-time dynamic loop speed tracking controller, including:

[0061] For the dynamic model of a disturbed wheeled mobile robot, the fixed-time integral sliding surface is used to design an extended state observer with finite-time convergence:

[0062]

[0063] in is an estimate of the output velocity of the dynamics model, is the estimate of the lumped disturbance of the dynamic model, θ is the bandwidth of the observer to be designed, k3, k4 are the observer parameters to be designed, It's a signal The output after the low-pass filter;

[0064] Designing a fixed-time dynamic loop speed tracking controller using the fixed-time integral sliding surface;

[0065]

[0066] where β dynamic ,a,λ,μ,α2,γ2 are the parameters to be designed for the sliding film controller, satisfying α2>1,1>γ2>0;

[0067] Substituting the controller, observer, and sliding surface parameters into formula (20), we can obtain the closed-loop system of dynamic speed tracking error:

[0068]

[0069] where e dynamic is the deviation between the virtual speed control law and the dynamic speed output, a,α2,λ,μ,γ2,β dynamic are the design parameters of the integral sliding surface, satisfying λ,μ>0,

[0070] Preferably, the method further comprises:

[0071] The finite time angular velocity controller and the non-singular terminal sliding mode linear velocity controller constitute a closed loop system of kinematic attitude error, and the extended state observer and the fixed time dynamic loop velocity tracking controller constitute a closed loop system of dynamic velocity tracking error;

[0072] The Lyapunov function is constructed to prove the fixed-time stability of the closed-loop system of the kinematic degree posture error:

[0073]

[0074] Analyze and organize The kinematic loop posture subsystem converges asymptotically to zero in a fixed time;

[0075] The Lyapunov function is constructed to prove the finite-time stability of the closed-loop system of the dynamic velocity tracking error:

[0076]

[0077] Analyze and organize And the sliding mode on the sliding surface approaches the origin in a finite time, and the closed-loop system of the dynamic speed tracking error converges asymptotically in a finite time;

[0078] E θ As cascade items, through the knowledge of cascade control technology, the attitude subsystem can be regarded as the driven subsystem, and the position subsystem can be regarded as the driving subsystem, so as to obtain the finite time stabilization of the attitude error of the entire kinematic loop;

[0079] Construct Lyapunov function to prove the fixed-time stability of dynamic loop:

[0080]

[0081] Analyze and organize That is, any tracking error state reaches the sliding mode at a fixed time, and then the derivative of both sides of the sliding membrane surface is obtained:

[0082]

[0083] The state on the synovial surface S2 is fixed at a fixed time The designed torque controller can make the speed tracking error of the dynamic model converge to 0 in a fixed time.

[0084] It can be seen from the technical solutions provided by the above embodiments of the present invention that the present invention proposes a double closed-loop finite-time sliding film control strategy for this situation, which effectively solves the problems of variable conditions, fast output response and high control accuracy requirements during trajectory tracking control. It has strong operability and is conducive to improving economic benefits.

[0085] Additional aspects and advantages of the present invention will be given in part in the following description, which will become obvious from the following description, or may be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0087] Figure 1A flow chart of a finite-time sliding film trajectory tracking control of a disturbed wheeled mobile robot based on a double closed-loop structure provided by an embodiment of the present invention;

[0088] Figure 2 A schematic diagram of the basic structure of a wheeled mobile robot provided by an embodiment of the present invention;

[0089] Figure 3 A structural diagram of a trajectory tracking control system for a disturbed wheeled mobile robot based on a double closed-loop structure provided by an embodiment of the present invention;

[0090] Figure 4 A schematic diagram of trajectory tracking posture error of a wheeled mobile robot in a local coordinate system provided by an embodiment of the present invention;

[0091] Figure 5 A schematic diagram of a cascade control algorithm structure of a kinematic model provided by an embodiment of the present invention;

[0092] Figure 6 An actual trajectory curve of a disturbed wheeled mobile robot tracking a circular reference trajectory provided by an embodiment of the present invention;

[0093] Figure 7 A posture error variation curve of a disturbed wheeled mobile robot tracking a circular reference trajectory provided by an embodiment of the present invention;

[0094] Figure 8 A schematic diagram of a curve showing the output speed of a kinematic controller based on a cascade control structure and the desired speed planned by the trajectory provided by an embodiment of the present invention;

[0095] Fig. 9 A schematic diagram of an estimation curve of a lumped disturbance in a system by a finite-time extended state observer provided in an embodiment of the present invention;

[0096] Fig.10 A schematic diagram of a curve of a dynamic model tracking a virtual speed under the control of a fixed-time integral sliding film controller based on a finite-time extended state observer provided in an embodiment of the present invention;

[0097] Fig.11 A schematic diagram of the two-wheel torque output of a dynamic loop controller of a disturbed wheeled mobile robot provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0098] The embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be interpreted as limiting the present invention.

[0099] It will be understood by those skilled in the art that, unless expressly stated, the singular forms "one", "said", and "the" used herein may also include plural forms. It should be further understood that the term "comprising" used in the specification of the present invention refers to the presence of the features, integers, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or groups thereof. It should be understood that when we refer to an element as being "connected" or "coupled" to another element, it may be directly connected or coupled to the other element, or there may be intermediate elements. In addition, the "connection" or "coupling" used herein may include wireless connection or coupling. The term "and / or" used herein includes any unit and all combinations of one or more associated listed items.

[0100] It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as those generally understood by those skilled in the art in the art to which the present invention belongs. It should also be understood that terms such as those defined in common dictionaries should be understood to have meanings consistent with the meanings in the context of the prior art, and will not be interpreted with idealized or overly formal meanings unless defined as herein.

[0101] To facilitate understanding of the embodiments of the present invention, several specific embodiments will be further explained below with reference to the accompanying drawings, and each embodiment does not constitute a limitation on the embodiments of the present invention.

[0102] The non-singular terminal synovial control method based on the double closed-loop control structure provided by the embodiment of the present invention can be used for trajectory tracking control of a wheeled mobile robot under complex working conditions. The processing flow of the method is as follows: Figure 1 As shown, the following steps are included:

[0103] Step S1, establishing a kinematic model for the under-actuated motion mode unique to the wheeled mobile robot, and establishing a dynamic model for analyzing the external disturbance force on the wheeled mobile robot;

[0104] Establishing kinematic equations for the incomplete constraints of the wheeled mobile robot can solve the control problem of posture (or position) at the speed level (steps 3 and 4 are the design of kinematic controllers). Kinematics is the most basic study of how mechanical systems operate, and a virtual speed control law that can converge the posture error to zero is obtained; then the Euler-Lagrange equation (EL equation) is used to model the dynamics of the system. The dynamics model not only includes the relationship between the robot's spatial coordinates and speed, but also describes the influence of external interference forces on the robot's speed control and spatial posture. Therefore, establishing a dynamics model is the most fundamental and comprehensive analysis and description of the robot system. (Step 5 is the design of the controller for the dynamics model).

[0105] The connection between the kinematic model and the dynamic model is: because the wheeled mobile robot is a typical under-actuated constraint, its movement process is restricted by non-complete constraints, that is, it can only be steered by differential speed of the two wheels and cannot be directly translated. In the dynamic model, the elimination method should be used to eliminate the non-independent generalized coordinate integral terms in the dynamic equation. Therefore, in step 1, the dynamic model of the wheeled mobile robot will be derived and simplified in combination with the kinematic model to obtain a simplified analytical dynamic model of the local speed of the wheeled mobile robot and the output torque of the two wheels.

[0106] Step S2, use the differential flatness technology to plan the desired trajectory of the wheeled mobile robot, obtain the desired posture information after decoupling the above-mentioned kinematic model, derive the kinematic degree posture tracking error model of the wheeled mobile robot in the local coordinate system, and use the cascade control method to decompose the kinematic degree posture tracking error model into a position subsystem and an attitude subsystem in the form of an integral chain.

[0107] Step S3: construct a non-singular terminal sliding surface with the position subsystem error in the kinematic attitude tracking error model as the sliding mode, and construct a fixed time integral sliding surface with the dynamic velocity deviation as the sliding mode.

[0108] First, a non-singular terminal sliding surface with position error as the state variable is designed for the position subsystem of the kinematic model; then, for the simplified dynamic model obtained in step S1, a fixed-time integral sliding surface with velocity deviation as the state variable of the sliding mode is designed.

[0109] Step S4, designing a finite time angular velocity controller and a non-singular terminal sliding mode linear velocity controller respectively according to the two subsystems of the kinematic attitude tracking error model after dimensionality reduction;

[0110] Step S5: for the dynamic model of the disturbed wheeled mobile robot, use the fixed-time integral sliding surface to design a finite-time convergent extended state observer and a fixed-time dynamic loop speed tracking controller;

[0111] Step S6, the finite-time angular velocity controller and the non-singular terminal sliding mode linear velocity controller for the kinematic model, and the extended state observer and the fixed-time dynamic loop velocity tracking controller for the dynamic model form a double closed-loop control structure.

[0112] The appropriate Lyapunov function is selected to prove the stability of the double closed-loop control structure, and then the designed observer and controller are used to control the disturbed wheeled mobile robot to track the desired trajectory within a finite time. The control method ultimately achieves trajectory tracking control of the robot by controlling the torque of the motors on the two driving wheels.

[0113] Wherein, step S1 includes the following sub-processes:

[0114] S1.1. Analyze the nonholonomic constrained motion of the wheeled mobile robot in the local coordinate system and establish the kinematic equations at the level of posture and velocity:

[0115]

[0116] Where v and w represent the linear velocity and angular velocity of the robot respectively, and the posture q = (x, y, θ) represents the position and angle of the robot in the global coordinate system.

[0117] S1.2. Considering the influence of system mass, moment of inertia, friction torque and other parameters on the robot, the Euler-Lagrange method can be used to establish the dynamic equation with the overall speed of the wheeled mobile robot as the output and the torque of the two driving wheels as the output:

[0118]

[0119] Where M is the inertia matrix of the system, are the centrifugal force and Coriolis force related to the position and velocity of the system, G(q), are the gravity term and friction term of the system, τ d is the external disturbance term, B(q) is the input transformation matrix, A T (q) is the Pfafian constraint matrix, m is the mass of the mobile robot, I is the moment of inertia, and the specific expressions of each parameter matrix are as follows:

[0120]

[0121] In order to obtain the relationship between the output torque and the real-time speed of the robot, the kinematic model is used to eliminate the incomplete constraint matrix in the dynamic model, and the simplified mathematical model of the wheeled mobile robot is obtained:

[0122]

[0123]

[0124]

[0125] Without loss of generality, it is assumed that the wheels of the wheeled mobile robot obey pure rolling without sliding on the running surface during movement and the wheels always maintain point contact with the moving surface.

[0126] Step S2 includes the following sub-steps:

[0127] S2.1. Candidate z r =(x r ,y r ) is the differential flat output of the desired trajectory, and the differential flat technique is used. The desired posture angle θ under the desired trajectory can be solved r , expected linear velocity v r and the desired angular velocity w r :

[0128]

[0129] S2.2, the pose error with the robot reference system as the local coordinate system can be expressed as:

[0130]

[0131] The trajectory tracking control problem of the mobile robot at the kinematic level can be transformed into controlling the actual robot motion speed V so that it can track the reference speed V of the reference trajectory in real time. r =[v r ,w r ] T , pose q r =(x r ,y r ,θ r ) T

[0132] S2.3 The trajectory error differential equation of the mobile robot is obtained by derivation of the posture error model:

[0133]

[0134] The above underdriven system is decoupled according to its structural characteristics. The system is used as an interference subsystem. θAs a cascade intermediate term, the error state equation is decomposed into a first-order attitude subsystem and an integral chain second-order position subsystem.

[0135] Step S3 further includes the following sub-steps:

[0136] S3.1 performs coordinate transformation on the state of the kinematic loop attitude error subsystem. When the transformed state converges, it is easy to obtain that the original system's x and y direction errors also converge to zero:

[0137]

[0138] Design a novel non-singular terminal sliding surface:

[0139]

[0140] where β kinematic is a positive number, p, q are positive odd numbers and 1<p / q<2. The specific parameters of the sliding surface will be designed later.

[0141] S3.2, the control objective of the dynamic loop design is: the model output speed can track the virtual control law output by the kinematic controller, and its speed tracking error is defined as:

[0142] e dynamic =V d -V (12)

[0143] Where V d =[v d ,w d ] is the kinematic controller output, and a novel non-singular fixed-time integral sliding membrane surface is designed:

[0144]

[0145] where β dynamic are the parameters to be designed of the fixed time integral sliding surface.

[0146] Step S4 further includes the following sub-steps:

[0147] S4.1. Design a finite-time angular velocity controller for the attitude subsystem in the kinematic attitude tracking error model.

[0148]

[0149] Among them, α0, β0, m0, n0, p0, and q0 are the fixed-time controller design parameters.

[0150] S4.2. Design a non-singular terminal sliding mode linear velocity controller for the attitude subsystem in the kinematic attitude tracking error model:

[0151]

[0152] Where 0<α<1, k1, k2 are suitable positive constants and k1≤k2; where w r ,v r are the reference linear velocity and angular velocity, β kinematic are the parameters of the sliding surface designed above, z1, z2 are the integral chain states, p, q are positive odd numbers and 1<p / q<2;

[0153] S4.3. Substitute the controller and sliding surface parameters into formulas (16) and (17) to obtain the closed-loop system of kinematic attitude error:

[0154]

[0155]

[0156] α0, β0, m0, n0, p0, q0 are the fixed time controller design parameters in equation (14), w r ,v r are the reference linear velocity and angular velocity, β kinematic are the parameters of the sliding surface designed above, z1, z2 are the integral chain states, p, q are positive odd numbers and 1<p / q<2e x ,e y ,e θ is the error state in equation (8).

[0157] Step S5 further includes the following sub-steps:

[0158] S5.1. Design of finite-time extended state observer:

[0159]

[0160] in is an estimate of the output velocity of the dynamics model, is the estimate of the lumped disturbance of the dynamic model, θ is the bandwidth of the observer to be designed, k3, k4 are the observer parameters to be designed, It's a signal The output of the low pass filter.

[0161] S5.2. Design a fixed-time dynamic loop speed tracking controller:

[0162]

[0163] Among them, β dynamic ,a,λ,μ,α2,γ2 are the parameters to be designed for the sliding film controller, satisfying α2>1,1>γ2>0.

[0164] S5.3. Substitute the controller, observer, and sliding surface parameters into the formula to obtain the closed-loop system of dynamic speed tracking error:

[0165]

[0166] where e dynamic is the deviation between the virtual speed control law and the dynamic speed output, a,α2,λ,μ,γ2,β dynamic are the design parameters of the integral sliding surface, satisfying λ,μ>0,

[0167] Step S6 further includes the following sub-steps:

[0168] S6.1 Construct Lyapunov function to prove the fixed-time stability of the kinematic loop attitude subsystem:

[0169]

[0170] Analyze and organize Therefore, the kinematic loop pose subsystem converges asymptotically to zero in a fixed time.

[0171] S6.2. Construct Lyapunov function to prove the finite-time stability of the kinematic loop position subsystem:

[0172]

[0173] Analyze and organize And the sliding mode on the sliding surface approaches the origin in a finite time, so the kinematic loop position subsystem converges asymptotically in a finite time. θ As cascade items, through the knowledge of cascade control technology, the attitude subsystem can be regarded as the driven subsystem, and the position subsystem can be regarded as the driving subsystem, then the finite time stabilization of the attitude error of the entire kinematic loop can be obtained.

[0174] S6.3. Construct Lyapunov function to prove the fixed-time stability of dynamic loop:

[0175]

[0176] Analyze and organize That is, any tracking error state reaches the sliding mode at a fixed time, and then the derivative of both sides of the sliding membrane surface is obtained:

[0177]

[0178] The state on the synovial surface S2 is fixed at a fixed time It converges to the origin, that is, the designed torque controller can make the speed tracking error of the dynamic model converge to 0 in a fixed time; therefore, the trajectory tracking controller with a double closed-loop structure designed in this patent can make all signals of the closed-loop system bounded, and the system's posture tracking error and speed tracking error converge to zero in a finite time, that is, the system trajectory tracking response is fast and the accuracy is high.

[0179] Next, in order to verify the effectiveness of the finite time trajectory tracking control method based on the dual-loop structure provided in this embodiment, a simulation experiment is carried out using MATLAB and a detailed description is given.

[0180] The dual-wheel differential mobile robot model provided in this embodiment comprehensively considers the unique under-driven motion mode of wheeled robots and the influence of friction and unknown interference torque on tracking performance in unknown trajectory tracking control tasks. A dual closed-loop control structure of kinematic loop and dynamic loop is adopted, and non-singular terminal sliding film control is used for the kinematic loop to make the position error subsystem finite time stable; a fixed-time integral sliding mode controller is used for the dynamic loop so that the speed of the dynamic model can keep up with the virtual speed generated by the kinematic controller within a fixed time, and an extended state observer is used to estimate and feedforward offset the uncertainty and interference in the model, so that the designed control algorithm has good position and speed tracking performance, and has good suppression of unknown interference.

[0181] In the simulation experiment, the initial position of the wheeled mobile robot is q = (1, 1, 0) T , the robot mass is m = 10kg, and the moment of inertia is J = 5kg*m 2 , the wheel radius is r = 0.05m, the width of the trolley is b = 0.22m, and the friction force in the tracking task is f = (v + w + 0.2, v + w + 0.2, v + w + 0.2) T , the unknown interference torque received is τ d =(sin(10t),sin(8t),sin(10t)+cos(5t) T ,The expected trajectory of the robot to be tracked is:

[0182]

[0183] During the simulation, the virtual speed control law of the kinematic output needs to be regarded as the reference input, so the derivative of the virtual speed control law needs to be obtained. To simplify the calculation and ensure the signal is smooth, the following mixed differentiator is used to estimate the derivative of the virtual speed control law:

[0184]

[0185] Based on the above parameters and the desired trajectory shown in equation (25).

[0186] Figure 6 It is demonstrated that the wheeled mobile robot can track the desired trajectory from any position with a good fitting degree under the method of the present invention; Figure 7 The tracking error curve of the mobile robot posture level is shown. Figure 8 The virtual control law and the desired velocity curve output by the kinematic controller are shown. Fig. 9 The trajectory effect curve of the designed finite-time extended state observer on the system lumped disturbance is shown. Fig.10 The effect curve of the mobile robot tracking the virtual speed control law at the dynamic level is shown. It can be observed that the posture error and speed error of the robot system tend to zero within a finite time. Fig.11 The output torque of the two-wheel motors output by the dynamic controller shows that the control quantity of the proposed method will not have any singular values. That is, the proposed control algorithm can be used in trajectory tracking control tasks, and the system has a faster response speed and control accuracy under this control algorithm.

[0187] The above analysis proves the effectiveness of the finite-time control strategy for the wheeled mobile robot based on the double closed-loop structure provided in this embodiment.

[0188] In summary, the embodiments of the present invention provide a kinematic and dynamic model that simultaneously considers the wheeled robot, fully considers the under-driven motion characteristics of the robot and the forces and unknown interferences during the motion process, and improves the universality of the control method.

[0189] The method of the embodiment of the present invention can effectively attenuate the influence of unknown disturbance torque, friction, and parameter perturbation on the control response during trajectory tracking control, so that the wheeled mobile robot can have a faster response speed when performing trajectory tracking tasks. The dual-loop control structure makes the output of the robot motor smoother and prolongs the service life of the motor.

[0190] Those skilled in the art can understand that the accompanying drawings are only schematic diagrams of an embodiment, and the modules or processes in the accompanying drawings are not necessarily required to implement the present invention.

[0191] It can be known from the description of the above implementation methods that those skilled in the art can clearly understand that the present invention can be implemented by means of software plus a necessary general hardware platform. Based on such an understanding, the technical solution of the present invention is essentially or the part that contributes to the prior art can be embodied in the form of a software product, which can be stored in a storage medium such as ROM / RAM, a magnetic disk, an optical disk, etc., and includes a number of instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in the various embodiments of the present invention or certain parts of the embodiments.

[0192] Each embodiment in this specification is described in a progressive manner, and the same or similar parts between the embodiments can be referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the device or system embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment. The device and system embodiments described above are merely schematic, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of this embodiment. Ordinary technicians in this field can understand and implement it without paying creative labor.

[0193] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A double closed-loop finite-time control method for a disturbed wheeled mobile robot, characterized in that: include: A kinematic model is established for the under-actuated motion mode unique to wheeled mobile robots, the external disturbance forces on the wheeled mobile robots are analyzed, and a dynamic model is established; The desired position and posture information of the wheeled mobile robot is obtained by decoupling the kinematic model, a kinematic posture tracking error model of the wheeled mobile robot is derived, and the kinematic posture tracking error model is decomposed into a position subsystem and a posture subsystem using a cascade control method; Constructing a non-singular terminal sliding surface with the position subsystem error in the kinematic attitude tracking error model as the sliding mode, and constructing a fixed time integral sliding surface with the dynamic velocity deviation as the sliding mode; A finite-time angular velocity controller is designed for the position subsystem, and a non-singular terminal sliding mode linear velocity controller is designed for the attitude subsystem; For the dynamic model of a disturbed wheeled mobile robot, a finite-time convergent extended state observer and a fixed-time dynamic loop speed tracking controller are designed using the fixed-time integral sliding surface; The observer and the controller are used to control the disturbed wheeled mobile robot to track a desired trajectory within a limited time, thereby realizing trajectory tracking control of the disturbed wheeled mobile robot.

2. The method according to claim 1, characterized in that The kinematic model is established for the under-driven motion mode unique to the wheeled mobile robot, the external disturbance force on the wheeled mobile robot is analyzed, and the dynamic model is established, including: The non-holonomic constrained motion of the wheeled mobile robot in the local coordinate system is analyzed, and the kinematic equations at the posture and velocity levels are established: Where v and w represent the linear velocity and angular velocity of the robot, respectively, and the posture q = (x, y, θ) represents the position and angle of the robot in the global coordinate system; The Euler-Lagrange method is used to establish the dynamic equation with the overall speed of the wheeled mobile robot as the output and the torque of the two driving wheels as the output: Where M is the inertia matrix of the system, are the centrifugal force and Coriolis force related to the position and velocity of the system, G(q), are the gravity term and friction term of the system, τ d is the external disturbance term, B(q) is the input transformation matrix, A T (q) is the Pfafian constraint matrix, m is the mass of the mobile robot, I is the moment of inertia, and the distance between the center of mass and the centroid of the robot is d; The specific expressions of each parameter matrix are as follows: In order to obtain the relationship between the output torque and the real-time speed of the robot, the kinematic model is used to eliminate the incomplete constraint matrix in the dynamic model, and the simplified dynamic model of the wheeled mobile robot is obtained: Without loss of generality, it is assumed that the wheels of the wheeled mobile robot obey pure rolling without sliding on the running surface during movement and the wheels always maintain point contact with the moving surface.

3. The method according to claim 2, characterized in that The method of obtaining the desired position and posture information of the wheeled mobile robot by decoupling the kinematic model, deriving the kinematic posture tracking error model of the wheeled mobile robot, and decomposing the kinematic posture tracking error model into a position subsystem and a posture subsystem by using a cascade control method includes: The expected trajectory z of a wheeled mobile robot is obtained using the differential flatness technique. r =(x r ,y r ) is used for planning, and the desired posture information of the wheeled mobile robot is obtained after decoupling the kinematic model, and the desired posture information includes the desired posture angle θ r , expected linear velocity v r and the desired angular velocity w r ; Taking the robot reference system as the local coordinate system, the kinematic posture tracking error model of the wheeled mobile robot in the local coordinate system is derived. The kinematic posture tracking error model is expressed as: The trajectory tracking control problem of the wheeled mobile robot at the kinematic level is transformed into controlling the actual robot motion speed V, so that the wheeled mobile robot can track the reference speed V of the reference trajectory in real time. r =[v r ,w r ] T , pose q r =(x r ,y r ,θ r ) T The trajectory error differential equation of the mobile robot is obtained by derivation of the kinematic posture tracking error model: The kinematic attitude tracking error model is decomposed into a position subsystem and an attitude subsystem in the form of an integral chain using a cascade control method. The underactuated system of the disturbed wheeled mobile robot with underactuated motion is decoupled according to its structural characteristics. The system is used as an interference subsystem. θ As a cascade intermediate term, the trajectory error differential equation of the mobile robot is decomposed into a first-order posture subsystem and an integral chain second-order position subsystem.

4. The method according to claim 3, characterized in that The construction of a non-singular terminal sliding surface with the position subsystem error in the kinematic posture tracking error model as the sliding mode and the construction of a fixed time integral sliding surface with the dynamic velocity deviation as the sliding mode include: The coordinate transformation of the attitude subsystem state in the kinematic attitude tracking error model is performed. When the transformed state converges, it is easy to obtain that the original system's x and y direction errors also converge to zero: After the coordinate transformation, the original attitude subsystem is decoupled into an integral chain form, with two states z1 and z2 respectively; Construct a non-singular terminal sliding mode surface with the position subsystem error in the kinematic attitude tracking error model as the sliding mode: where β kinematic is a positive number, p, q are positive odd numbers and 1<p / q<2; The control objective of the dynamic model is that the model output speed can track the virtual control law output by the kinematic controller. The speed tracking error of the dynamic model is defined as: yes dynamic =V d -V (12) Where V d =[v d ,w d ] is the kinematic controller output, and a fixed time integral sliding mode surface with dynamic velocity deviation as the sliding mode is constructed: where β dynamic are the parameters to be designed of the fixed time integral sliding surface.

5. The method according to claim 4, characterized in that The design of a finite-time angular velocity controller for the position subsystem and the design of a non-singular terminal sliding mode linear velocity controller for the attitude subsystem include: A finite-time angular velocity controller is designed for the position subsystem in the kinematic attitude tracking error model: Among them, α0, β0, m0, n0, p0, q0 are the fixed time controller design parameters respectively; A non-singular terminal sliding mode linear velocity controller is designed for the attitude subsystem in the kinematic attitude tracking error model: Where 0<α<1, k1, k2 are suitable positive constants and k1≤k2; where w r ,v r are the reference linear velocity and angular velocity, β kinematic are the parameters of the sliding surface designed above, z1, z2 are the integral chain states, p, q are positive odd numbers and 1<p / q<2; Substitute the controller and sliding surface parameters into formulas (16) and (17) to obtain the closed-loop system of kinematic attitude error; α0, β0, m0, n0, p0, q0 are the fixed time controller design parameters in equation (14), w r ,v r are the reference linear velocity and angular velocity, β kinematic are the parameters of the sliding surface designed above, z1, z2 are the integral chain states, p, q are positive odd numbers and 1<p / q<2e x ,e y ,e θ is the error state in equation (8).

6. The method according to claim 5, characterized in that The dynamic model of the disturbed wheeled mobile robot uses the fixed-time integral sliding surface to design a finite-time convergent extended state observer and a fixed-time dynamic loop speed tracking controller, including: For the dynamic model of a disturbed wheeled mobile robot, the fixed-time integral sliding surface is used to design an extended state observer with finite-time convergence: in is an estimate of the output velocity of the dynamics model, is the estimate of the lumped disturbance of the dynamic model, θ is the bandwidth of the observer to be designed, k3, k4 are the observer parameters to be designed, It's a signal The output after the low-pass filter; Designing a fixed-time dynamic loop speed tracking controller using the fixed-time integral sliding surface; where β dynamic ,a,λ,μ,α2,γ2 are the parameters to be designed for the sliding film controller, satisfying α2>1,1>γ2>0; Substituting the controller, observer, and sliding surface parameters into formula (20), we can obtain the closed-loop system of dynamic speed tracking error: where e dynamic is the deviation between the virtual speed control law and the dynamic speed output, a,α2,λ,μ,γ2,β dynamic are the design parameters of the integral sliding surface, satisfying λ,μ>0, 7. The method according to claim 6, characterized in that The method further comprises: The finite time angular velocity controller and the non-singular terminal sliding mode linear velocity controller constitute a closed loop system of kinematic attitude error, and the extended state observer and the fixed time dynamic loop velocity tracking controller constitute a closed loop system of dynamic velocity tracking error; The Lyapunov function is constructed to prove the fixed-time stability of the closed-loop system of the kinematic degree posture error: Analyze and organize , the kinematic loop posture subsystem converges asymptotically to zero in a fixed time; The Lyapunov function is constructed to prove the finite-time stability of the closed-loop system of the dynamic velocity tracking error: Analyze and organize And the sliding mode on the sliding surface approaches the origin in a finite time, and the closed-loop system of the dynamic speed tracking error converges asymptotically in a finite time; E θ As cascade items, through the knowledge of cascade control technology, the attitude subsystem can be regarded as the driven subsystem, and the position subsystem can be regarded as the driving subsystem, so as to obtain the finite time stabilization of the attitude error of the entire kinematic loop; Construct Lyapunov function to prove the fixed-time stability of dynamic loop: Analyze and organize That is, any tracking error state reaches the sliding mode at a fixed time, and then the derivative of both sides of the sliding membrane surface is obtained: The state on the synovial surface S2 is fixed at a fixed time The designed torque controller can make the speed tracking error of the dynamic model converge to 0 in a fixed time.

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