Method for trajectory tracking control of mobile robot under unknown slip

Abstract

The application relates to a mobile robot trajectory tracking control method under unknown slip. The method comprises the following steps: constructing a double-closed-loop control strategy of an outer ring kinematic controller and an inner ring sliding mode controller, designing a fixed-time kinematic controller, obtaining virtual linear velocity and angular velocity, and realizing fixed-time convergence of pose tracking error; according to the speed tracking error of the virtual linear velocity and angular velocity of the mobile robot and the actual linear velocity and angular velocity and the dynamics model of the mobile robot, a fixed-time terminal sliding mode controller is designed, the control voltage of the left and right drive wheels of the mobile robot is determined, the actual linear velocity and angular velocity of the mobile robot are controlled to asymptotically converge to the virtual linear velocity and angular velocity; a fixed-time extended state observer is designed to estimate the velocity state and the lumped disturbance of the mobile robot, and the lumped disturbance is fed forwardly compensated, so that the mobile robot realizes fixed-time trajectory tracking control, and the control performance of the mobile robot under wheel slip is improved.

Description

Technical Field

[0001] This invention relates to the field of trajectory tracking and control technology, and in particular to a trajectory tracking and control method for a mobile robot under unknown slippage conditions. Background Technology

[0002] In recent years, mobile robots have played an increasingly important role in both military and civilian engineering fields, such as unmanned reconnaissance, hospital epidemic prevention, logistics handling, unmanned delivery, and intelligent cleaning. Their trajectory tracking and control issues have attracted widespread attention. In actual operation, mobile robots are subject to unknown slippage conditions. Factors such as tire deformation, wet or icy road surfaces, and rapid turns can easily cause wheel slippage, which can disrupt the non-integrity constraints of the mobile robot's control system and reduce its control accuracy.

[0003] Current research either neglects the influence of the drive motor or fails to consider the impact of longitudinal and lateral slip disturbances and model parameter uncertainties on the motion control of mobile robots. Furthermore, the designed controllers are typically based on asymptotically stable or exponentially stable controllers, which theoretically lead to infinite-time convergence of the system's closed-loop state, failing to achieve time-optimal control. To enable rapid convergence of the system state in a finite time, scholars have proposed finite-time stability theory. One key issue is estimating the convergence time, which is generally a function of the system's initial conditions; different initial state values ​​result in different convergence times. Since the initial conditions of real-world systems may be difficult to obtain precisely in advance, the convergence time cannot be accurately estimated in certain situations, limiting its application. Summary of the Invention

[0004] To address the issue of poor trajectory tracking control performance in mobile robots, a trajectory tracking control method for mobile robots under unknown slippage conditions is provided. This method includes:

[0005] A kinematic model of a mobile robot under unknown slippage and a dynamic model considering the dynamics of the drive motor are established. The unknown longitudinal slip and sideslip disturbances, model parameter uncertainties and unknown input disturbances in the dynamic model are referred to as lumped disturbances.

[0006] A fixed-time kinematic controller is designed based on the pose tracking error of the mobile robot to output the virtual linear velocity and angular velocity of the mobile robot.

[0007] Based on the speed tracking error between the virtual linear velocity and angular velocity of the mobile robot and the actual linear velocity and angular velocity, and the dynamic model, a fixed-time terminal sliding mode controller is designed to determine the control voltage of the drive motors of the left and right drive wheels of the mobile robot, and to control the actual linear velocity and angular velocity of the mobile robot to asymptotically converge to the virtual linear velocity and angular velocity.

[0008] Based on the fixed-time terminal sliding mode controller and the actual linear and angular velocities of the mobile robot, a fixed-time extended state observer is designed to estimate the velocity state and lumped disturbances of the mobile robot, and to perform feedforward compensation on the lumped disturbances to eliminate the impact of disturbances on the system control performance.

[0009] In one embodiment, the kinematic model of the mobile robot under unknown slippage conditions is represented as follows:

[0010]

[0011] Where q = [xy θ] T Let z be the pose of the mobile robot; z = [v ω] T Let v be the actual velocity of the mobile robot, and v and ω be its linear velocity and angular velocity, respectively; η = [η v η ω ] T η v =r(ξ r +ξ l ) / 2 is the longitudinal slip velocity, η ω =r(ξ r -ξ l ) / (2b) represents the yaw rate disturbance caused by longitudinal slippage, r is the radius of the mobile robot's drive wheel, 2b is the distance between the two drive wheels, and ξ l ξ r These are the disturbance angular velocity vectors caused by the longitudinal slippage of the left and right drive wheels of the mobile robot, respectively. Let μ be the mismatched disturbance vector caused by the sideslip of the mobile robot, and μ be the sideslip velocity of the mobile robot. This is the transformation matrix.

[0012] In one embodiment, the dynamic model considering the dynamics of the drive motor under the condition of the mobile robot slipping is expressed as follows:

[0013]

[0014] in, K1=Nk t / R a K2 = N 2 k t k b / R a r is the radius of the mobile robot's drive wheel, 2b is the distance between the two drive wheels, m and J are the mass and moment of inertia of the mobile robot, respectively, and R a k t k b These represent the armature resistance, torque constant, and back electromotive force constant of the drive motor, respectively, where N is the mechanical gear reduction ratio, and u... a =[uar u al ] T d represents the control voltage of the drive motors for the right and left drive wheels; d represents the lumped disturbance that includes unknown longitudinal and sideslip disturbances of the system, uncertain model parameters, and unknown input disturbances.

[0015] In one embodiment, the method further includes:

[0016] Define the reference pose of the mobile robot as q r =[x r y r θ r ] T ∈R 3×1 It satisfies the following kinematic equations:

[0017]

[0018] Among them, (x r ,y r θ represents the reference position of the mobile robot's geometric center in the global coordinate system. r z is the reference heading angle for the mobile robot. r =[v r ω r ] T For reference speed, v r Let ω be the reference linear velocity for the mobile robot's forward movement. r The reference angular velocity of the mobile robot body around its geometric center;

[0019] The pose tracking error of a mobile robot is defined as:

[0020]

[0021] Among them, e x e y e θ These represent the tracking errors of the mobile robot in the x, y, and θ directions, respectively.

[0022] The differential equation for pose tracking error is obtained by taking the derivative:

[0023]

[0024] Design sliding surfaces s1 and s2:

[0025]

[0026] Among them, the coupling coefficients c1 and c2 are positive constants.

[0027] In one embodiment, the fixed-time kinematic controller is implemented using the following formula:

[0028]

[0029] Among them, z c =[v c ω c ] T For the virtual speed of the mobile robot, v c Let ω be the virtual linear velocity. c e represents the virtual angular velocity. x e y e θ These represent the tracking errors of the mobile robot in the x, y, and θ directions, respectively; v r Let ω be the reference linear velocity for the mobile robot's forward movement. r The reference angular velocity of the mobile robot body around its geometric center; controller gains c1, c2, k 11 k 12 k 21 k 22 All are positive constants, 0 < a1, a2 < 1, b1, b2 > 1, s1 and s2 are the designed sliding surfaces; the function sgn a (·) is defined as sgn a (x)=|x| a sign(x), It is a symbolic function;

[0030] Design the following candidate Lyapunov functions:

[0031]

[0032] Differentiation yields:

[0033]

[0034]

[0035] Sliding surfaces s1 and s2 can converge to zero within fixed times t1 and t2, respectively, let The convergence times t1 and t2 are then expressed as:

[0036]

[0037]

[0038] In one embodiment, the fixed-time terminal sliding mode controller is implemented by the following formula:

[0039]

[0040] Among them, u a =[uar u al ] T This refers to the control voltage for the drive motors of the right and left drive wheels; K1=Nk t / R a K2 = N 2 k t k b / R a r is the radius of the mobile robot's drive wheel, 2b is the distance between the two drive wheels, m and J are the mass and moment of inertia of the mobile robot, respectively, and R a k t k b These are the armature resistance, torque constant, and back electromotive force constant of the drive motor, respectively, and N is the mechanical gear reduction ratio; The estimated value of the state vector x2; control gain k 51 k 52 k 61 k 62 For positive constants, control gains a5, b5, a6, and b6 are positive constants and satisfy 0 < a5 < 1 < b5, 0 < a6 < 1 < b6; e z s is the velocity tracking error vector; s3 is the global integration terminal sliding surface vector; the function sgn a (·) is defined as sgn a (x)=|x| a sign(x), It is a symbolic function;

[0041] Design the following candidate Lyapunov functions:

[0042]

[0043] Differentiation yields:

[0044]

[0045] The sliding surface s3 converges to zero within a fixed time t3; let The convergence time t3 is then expressed as

[0046]

[0047] The pose tracking error and velocity tracking error of the mobile robot can converge within a fixed time, and the total convergence time satisfies:

[0048] t≤t1+t2+t3.

[0049] In one embodiment, the fixed-time extended state observer is:

[0050]

[0051] Here, the state vectors x1 = z and x2 = d are defined, where z is the actual speed of the mobile robot and d is the lumped disturbance that includes unknown longitudinal and lateral slip disturbances of the system, uncertain model parameters, and unknown input disturbances. These are the estimated values ​​of state vectors x1 and x2, respectively; For observation error; k 31 ,k 32 ,k 41 ,k 42 >0 represents the observer gain, a3∈(0.5,1), b3∈(1,1.5), a4=2a3-1, b4=2b3-1.

[0052] function sgn a (·) is defined as sgn a (x)=[|x1| a sign(x)|x2| a sign(x)] T x = [x1 x2] T .

[0053] In one embodiment, the specific method for designing a fixed-time kinematics controller based on the pose tracking error of the mobile robot and outputting the virtual linear velocity and angular velocity of the mobile robot includes:

[0054] The actual linear velocity and angular velocity of the mobile robot are used as inputs to the kinematic model of the mobile robot to obtain the actual pose of the mobile robot.

[0055] The reference pose and the pose tracking error of the actual pose of the mobile robot are obtained. Based on the pose tracking error, the steps of obtaining the virtual linear velocity and angular velocity of the mobile robot according to the fixed-time kinematics controller are performed.

[0056] In one embodiment, the lumped disturbance is determined by the mobile robot's mass, moment of inertia, torque, longitudinal slip velocity, sideslip velocity, the disturbance angular velocity vector caused by the longitudinal slip of the mobile robot's drive wheel, the mismatch disturbance vector caused by the sideslip of the mobile robot, and the mobile robot's orientation angle.

[0057] In one embodiment, the specific method for controlling the actual speed of the mobile robot to converge to the virtual speed includes: inputting the control voltage of the drive motors of the left and right drive wheels of the mobile robot into the dynamic model of the mobile robot, thereby determining the actual speed of the mobile robot.

[0058] The aforementioned trajectory tracking control method for a mobile robot under unknown slippage conditions constructs a dual-closed-loop control strategy consisting of an outer-loop kinematic controller and an inner-loop sliding mode controller. By acquiring the pose tracking error between the mobile robot's reference pose and actual pose, a fixed-time kinematic controller is designed to obtain virtual linear velocity and angular velocity, achieving fixed-time convergence of the pose tracking error and improving the system's state response speed. Based on the velocity tracking error between the virtual linear velocity and angular velocity and the mobile robot's actual linear velocity and angular velocity, and the dynamic model, a fixed-time terminal sliding mode controller is designed to determine the control voltages of the drive motors for the left and right drive wheels of the mobile robot, controlling the actual linear velocity and angular velocity of the mobile robot to asymptotically converge to the virtual linear velocity and angular velocity. A fixed-time extended state observer is designed to estimate the mobile robot's velocity state and lumped disturbance, and feedforward compensation is applied to the lumped disturbance to eliminate the impact of disturbance on the system's control performance. By executing the above dual-closed-loop control strategy, fixed-time trajectory tracking control of the mobile robot is achieved, improving the control performance of the mobile robot under wheel slippage conditions. Attached Figure Description

[0059] Figure 1 This is a block diagram of a dual closed-loop control system for a mobile robot in one embodiment;

[0060] Figure 2 This is a flowchart of a trajectory tracking and control method for a mobile robot under unknown slippage conditions in one embodiment.

[0061] Figure 3 This is a schematic diagram illustrating the trajectory tracking and control effect of a sweeping robot under a circular reference trajectory in one embodiment.

[0062] Figure 4 This is a schematic diagram of the pose tracking of a sweeping robot under a circular reference trajectory in one embodiment;

[0063] Figure 5 This is a schematic diagram illustrating the pose tracking error of a sweeping robot under a circular reference trajectory in one embodiment.

[0064] Figure 6 This is a schematic diagram illustrating the actual speed of a sweeping robot under a circular reference trajectory in one embodiment;

[0065] Figure 7 This is a schematic diagram illustrating the estimation effect of a fixed-time extended state observer of a sweeping robot on lumped disturbances under a circular reference trajectory in one embodiment.

[0066] Figure 8 This is a schematic diagram of the control voltage of the drive motor of the sweeping robot's drive wheel under a circular reference trajectory in one embodiment.

[0067] Figure 9 This is a schematic diagram illustrating the tracking and control effect of a sweeping robot under a rectangular reference trajectory in one embodiment.

[0068] Figure 10 This is a schematic diagram of the pose tracking of a sweeping robot under a rectangular reference trajectory in one embodiment;

[0069] Figure 11 This is a schematic diagram illustrating the pose tracking error of a sweeping robot under a rectangular reference trajectory in one embodiment.

[0070] Figure 12 This is a schematic diagram of the actual speed of a sweeping robot under a rectangular reference trajectory in one embodiment;

[0071] Figure 13 This is a schematic diagram illustrating the estimation effect of a fixed-time extended state observer of a sweeping robot on lumped disturbances under a rectangular reference trajectory in one embodiment.

[0072] Figure 14 This is a schematic diagram of the control voltage of the drive motor of the sweeping robot's drive wheel under a rectangular reference trajectory in one embodiment. Detailed Implementation

[0073] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0074] Numerous specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways than those described herein, and therefore the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0075] The following describes, with reference to the accompanying drawings, a method for trajectory tracking and control of a mobile robot under unknown slippage conditions, according to some embodiments of the present invention. The method of the present invention can be applied to the cloud or a server, or to a terminal capable of trajectory tracking and control, such as a sweeping robot, a sweeping and mopping robot, and a two-wheeled differential drive service robot. The following description uses the application of this method to a mobile robot as an example.

[0076] The trajectory tracking control method for a mobile robot under unknown slippage conditions of the present invention can be implemented through a pre-designed dual-closed-loop control system for the mobile robot. This dual-closed-loop control system controls the convergence time of velocity and pose errors based on a fixed-time control strategy. This dual-closed-loop control system is independent of the initial state of the mobile robot and convergence can be achieved through the parameters of the controller. The dual-closed-loop control system for the mobile robot is as follows: Figure 1 As shown.

[0077] Specifically, in the outer-loop control, a fixed-time kinematic controller is designed based on the kinematic model of the mobile robot to generate the virtual velocity of the robot. In the inner-loop control, the unknown longitudinal and lateral slip disturbances, model parameter uncertainties, and unknown input disturbances experienced by the mobile robot are treated as lumped disturbances. A fixed-time extended state observer is designed to estimate the lumped disturbances of the system in real time. By designing a fixed-time terminal sliding mode controller, the mobile robot is controlled to track the virtual velocity generated by the outer loop within a fixed time period, and the observed lumped disturbances are compensated in real time to improve the robustness of the dual-closed-loop control system.

[0078] To construct a dual closed-loop control system for a mobile robot, controllers for the inner and outer loops can be built:

[0079] Step S110: Establish a kinematic model of the mobile robot under unknown longitudinal and lateral slip conditions.

[0080] Define the pose of the mobile robot as q = [xy θ] T ∈R 3×1 Let (x, y) be the position of the geometric center of the mobile robot in the global coordinate system, and θ represent the orientation angle of the mobile robot. In the presence of longitudinal and lateral slip disturbances, the kinematic model of the mobile robot can be expressed as:

[0081]

[0082] Where z = [v ω] T v and ω are the linear velocity and angular velocity of the mobile robot, respectively; η = [η v η ω ] T η v =r(ξ r +ξ l ) / 2 is the longitudinal slip velocity, η ω =r(ξ r -ξ l ) / (2b) represents the yaw rate disturbance caused by longitudinal slippage, r is the radius of the mobile robot's drive wheel, 2b is the distance between the two drive wheels, and ξ l ξ r These are the disturbance angular velocity vectors caused by the longitudinal slippage of the left and right drive wheels of the mobile robot, respectively. Let be the mismatched disturbance vector caused by the robot's sideslip, μ be the robot's sideslip velocity, and S(q) be the transformation matrix, which has the following form:

[0083]

[0084] Step S120: Establish a dynamic model of the mobile robot that considers the dynamic characteristics of the mobile robot's drive motor, and use the drive motor control voltage as the system control input.

[0085] In the ideal case of pure rolling without slippage, the dynamic model of the mobile robot can be described as follows:

[0086]

[0087] in, Let m be the positive definite symmetric inertia matrix of the system, and let m and J be the mass and moment of inertia of the mobile robot, respectively. G(q)∈R represents the system's centrifugal and Coriolis force matrices. Since the mobile robot's center of mass coincides with its geometric center, this term is a matrix of all zeros. 3×1 This is the gravity vector of the system; for a mobile robot moving in a plane, this term is a zero vector. The system control torque transformation matrix; τ = [τ r τ l ] T ∈R 2×1 Input torque to the right and left drive wheels; A(q)=[-sinθ cosθ 0]∈R 1×3 Let S be the system's nonholonomic constraint vector, and S T (q)A T (q)=0∈R 2×1 ; This refers to the system constraint terms.

[0088] Combining equations (1) and (3), we get:

[0089]

[0090] in, F2 = S T V = 0 ∈ R 2×3 ;

[0091] Considering the uncertainty of the dynamic model parameters and the disturbance of unknown dynamic input, equation (4) can be rewritten as:

[0092]

[0093] Where, ΔM s ∈R 2×2 For M s The change in τ d ∈R 2×1 The input perturbation is an unknown, bounded, and differentiable perturbation.

[0094] definition Equation (5) can be further expressed as:

[0095]

[0096] Since unmodeled high-frequency disturbances also exist in motor dynamics, the influence of motor dynamics needs to be considered in the control design to improve the system control accuracy. Assuming the mobile robot is driven by two identical brushed DC motors, the dynamic equations of the right and left drive wheel motors are:

[0097]

[0098] Among them, L a R a k t k b These represent the armature inductance, armature resistance, torque constant, and back electromotive force constant of the drive motor, respectively; N is the mechanical gear reduction ratio; τ = [τ r τ l ] T u represents the input torque of the right and left drive wheels of the mobile robot. a =[u ar u al ] T ,I a =[I ar I al ] T These are the control voltage and armature current of the right and left drive wheel motors, respectively, ω w The angular velocity of the drive motor is given, and it has...

[0099]

[0100] in, This is the transformation matrix.

[0101] Considering that the drive motor is the actuator of the system, and its response speed is relatively fast compared to the system as a whole, the drive motor model can be appropriately simplified, ignoring inductance. The result is:

[0102] τ=K1u a -K2Xz (9)

[0103] Where K1=Nk t / R a K2 = N 2 k t k b / R a .

[0104] Combining equations (6) and (9), the dynamic model of the mobile robot with DC motor control voltage as the control input can be expressed as:

[0105]

[0106] in, It is a lumped disturbance that includes unknown longitudinal and sideslip disturbances of the system, uncertain model parameters, and unknown input disturbances.

[0107] Thus, the control task of the dual closed-loop control system is to design the control voltage u for the right and left drive wheel motors of a mobile robot system with uncertain model parameters and unknown external disturbances. a This enables mobile robots to accurately complete trajectory tracking tasks even under unknown slippage conditions, and allows trajectory tracking errors to converge within a fixed time.

[0108] Step S130: The outer loop is designed with a fixed-time kinematic controller based on the non-singular terminal sliding mode control method. The fixed-time kinematic controller is used to generate virtual velocities, which include virtual linear velocity and virtual angular velocity.

[0109] Furthermore, the reference pose of the mobile robot is defined as q. r =[x r y r θ r ] T ∈R 3×1 It satisfies the following kinematic equations:

[0110]

[0111] Among them, (x r ,y r θ represents the reference position of the mobile robot's geometric center in the global coordinate system. r z is the reference heading angle for the mobile robot. r =[v r ω r ] T For reference speed, v r Let ω be the reference linear velocity for the mobile robot's forward movement. r This is the reference angular velocity of the mobile robot body around its geometric center.

[0112] The pose tracking error of a mobile robot is defined as:

[0113]

[0114] Among them, e x e y e θ These represent the tracking errors of the mobile robot in the x, y, and θ directions, respectively.

[0115] Taking the derivative, we obtain the differential equation for the pose tracking error as follows:

[0116]

[0117] Design the sliding surface:

[0118]

[0119] Among them, the coupling coefficients c1 and c2 are positive constants.

[0120] To suppress high-frequency chattering in the sliding mode controller and to make the sliding surface converge to zero at a relatively fast speed, the following fixed-time terminal sliding mode reaching law can be used:

[0121]

[0122] Where, k 11 k 12 k 21 k 22 For positive constants, 0 < a1, a2 < 1, b1, b2 > 1, the function sgn a (·) is defined as sgn a (x)=|x| a sign(x) and sign(x) are sign functions, defined as follows:

[0123]

[0124] Based on the above equation, the following fixed-time virtual kinematic control input is designed:

[0125]

[0126] In the formula, z c =[v c ω c ] T For the virtual speed of the mobile robot, v c Let ω be the virtual linear velocity. c e represents the virtual angular velocity. x e y e θ These represent the tracking errors of the mobile robot in the x, y, and θ directions, respectively; z r =[v r ω r ] T v is the reference speed for the mobile robot. r Let ω be the reference linear velocity for the mobile robot's forward movement. r The reference angular velocity of the mobile robot body around its geometric center; controller gain k 11 k 12 k 21 k 22 All are positive constants; coupling coefficients c1 and c2 are positive constants; 0 < a1, a2 < 1, b1, b2 > 1; s1 and s2 are the designed sliding surfaces; the function sgn a (·) is defined as sgn a(x)=|x| a sign(x), It is a symbolic function.

[0127] To prove the convergence of this control law, consider the following candidate Lyapunov function:

[0128]

[0129] Taking the derivative and substituting equation (15) into the equation, we get:

[0130]

[0131] This indicates that the sliding surfaces s1 and s2 converge to zero within fixed times t1 and t2, respectively. Let The convergence times t1 and t2 can then be expressed as:

[0132]

[0133] Step S140: Design a fixed-time extended state observer (FxESO) within the inner loop to observe the lumped disturbances in the dynamic model. The design process of the fixed-time extended state observer (FxESO) is as follows.

[0134] Define state vectors x1 = z and x2 = d, then equation (10) can be described in state-space form:

[0135]

[0136] The fixed-time extended state observer for equation (21) is designed as follows:

[0137]

[0138] Here, the state vectors x1 = z and x2 = d are defined, where z is the actual speed of the mobile robot and d is the lumped disturbance that includes unknown longitudinal and lateral slip disturbances of the system, uncertain model parameters, and unknown input disturbances. These are the estimated values ​​of state vectors x1 and x2, respectively; For observation error; k 31 ,k 32 ,k 41 ,k 42 >0 represents the observer gain, a3∈(0.5,1), b3∈(1,1.5), a4=2a3-1, b4=2b3-1, and the function sgn a (·) is defined as sgn a (x)=[|x1| a sign(x) |x2| a sign(x)] T x = [x1 x2]T .

[0139] Step S150: Based on the observation results of the extended state observer, a non-singular terminal sliding mode controller is designed to control the mobile robot for inner-loop velocity tracking, thereby achieving fixed-time trajectory tracking. The design steps of the fixed-time terminal sliding mode controller (TSMC) are as follows:

[0140] Define speed tracking error:

[0141] e z =zz c (twenty three)

[0142] Its derivative is:

[0143]

[0144] To ensure that the system state variables converge quickly to the equilibrium point, the following global integral terminal sliding surface is designed:

[0145]

[0146] Where, k 51 k 52 For positive constants, 0 < a5 < 1 < b5.

[0147] Differentiating the above equation, we get:

[0148]

[0149] Combining equations (10) and (24), equation (26) can be written as follows:

[0150]

[0151] Selecting the power-sum approach law:

[0152]

[0153] Where, k 61 k 62 For positive constants, 0 < a6 < 1 < b6.

[0154] The fixed-time dynamic control law of equation (10) is designed as follows:

[0155]

[0156] Among them, u a =[u ar u al ] T The control voltage for the drive motors of the right and left drive wheels.

[0157] Consider the following candidate Lyapunov functions:

[0158]

[0159] Differentiation yields:

[0160]

[0161] This indicates that the sliding surface s3 can converge to zero within a fixed time t3. Let The convergence time t3 is then expressed as:

[0162]

[0163] In summary, the error system equations (13) and (24) converge to zero in a fixed time, and the upper bound of the total convergence time is...

[0164] t≤t1+t2+t3 (33)

[0165] The convergence time is independent of the initial state of the mobile robot and depends only on the controller parameters. The system convergence time can be adjusted by adjusting the controller parameters, thereby adjusting the trajectory tracking effect of the mobile robot.

[0166] It should be noted that the design steps of each controller in the above dual closed-loop control system are not specifically limited, because according to the present invention, some steps can be performed in other orders or simultaneously.

[0167] In one embodiment, such as Figure 2 As shown, a trajectory tracking control method for a mobile robot under unknown slippage conditions is provided. This trajectory tracking control method can be partially or fully implemented through the aforementioned dual closed-loop control system. Taking the application of this method to a mobile robot as an example, the method includes the following steps:

[0168] Step S210: Establish the kinematic model of the mobile robot under slippage and the dynamic model considering the dynamics of the drive motor. The unknown longitudinal slip and sideslip disturbances, model parameter uncertainties and unknown input disturbances in the dynamic model are called lumped disturbances.

[0169] The kinematic and dynamic models can be implemented through the above steps S110 and S120.

[0170] Among them, the lumped disturbance d includes disturbance factors such as unknown longitudinal and sideslip disturbances of the system, uncertain model parameters and unknown input disturbances. It can be determined by parameters such as the mass, moment of inertia, torque, longitudinal speed, sideslip speed, disturbance angular velocity vector caused by longitudinal slip of the mobile robot's drive wheel, non-matching disturbance vector caused by sideslip of the mobile robot, and the direction angle of the mobile robot.

[0171] Step S220: Design a fixed-time kinematic controller based on the pose tracking error of the mobile robot, and output the virtual linear velocity and angular velocity of the mobile robot.

[0172] The virtual velocity, comprising virtual linear velocity and virtual angular velocity, is obtained from the designed fixed-time kinematics controller. Under this controller, the pose error convergence time of the mobile robot is independent of the initial pose of the mobile robot and depends only on the parameters of the virtual kinematics controller.

[0173] Among them, the virtual speed can be obtained through an outer loop kinematic controller. This kinematic controller can be a fixed-time kinematic controller, as shown in equation (17) above, which can realize the convergence of the pose error within a fixed time. It can also be obtained through other common kinematic controllers, such as classic backstepping control, sliding mode control, etc.

[0174] Step S230: Based on the speed tracking error between the virtual linear velocity and angular velocity of the mobile robot and the actual linear velocity and angular velocity, and the dynamic model, design a fixed-time terminal sliding mode controller, determine the control voltage of the drive motors of the left and right drive wheels of the mobile robot, and control the actual speed of the mobile robot to converge to the virtual speed.

[0175] Among them, the control voltage of the mobile robot's drive motor can be used as the control input of the mobile robot. This control voltage can change with time, enabling the mobile robot to accurately complete the trajectory tracking task even when slipping.

[0176] In specific implementation, the mobile robot can design the terminal sliding surface based on the speed tracking error between the virtual linear velocity and angular velocity and the actual linear velocity and angular velocity of the mobile robot. Combined with the lumped disturbance estimation value, the control voltage of the left and right drive wheel motors of the mobile robot is obtained. The dynamic model of the above formula (10) is input to determine the actual speed of the mobile robot, so that the actual speed of the mobile robot converges to the virtual speed within a fixed time.

[0177] Step S240: Based on the terminal sliding mode controller and the actual speed of the mobile robot, design a fixed-time extended state observer to estimate the speed state and lumped disturbance of the mobile robot, and perform feedforward compensation on the lumped disturbance to eliminate the impact of the disturbance on the system control performance.

[0178] The fixed-time extended state observer can be implemented through the above step S140.

[0179] In practice, a fixed-time extended state observer can be designed for the mobile robot to estimate the robot's speed state and lumped disturbances, and to perform feedforward compensation on the lumped disturbances to eliminate the impact of disturbances on the system's control performance.

[0180] Disturbances are always present in trajectory tracking control and can affect the speed and pose of mobile robots. Disturbances can be estimated in real time by extending the state observer and fed forward compensation can be performed in the controller, so that the mobile robot can complete the trajectory tracking task under the influence of longitudinal slip, sideslip or other disturbances.

[0181] The method described in the above embodiments constructs a dual-closed-loop control strategy consisting of an outer-loop kinematic controller and an inner-loop sliding mode controller. By acquiring the pose tracking error between the reference pose and the actual pose of the mobile robot, a fixed-time kinematic controller is designed to obtain virtual linear velocity and angular velocity, achieving fixed-time convergence of the pose tracking error and improving the system's response speed. Based on the velocity tracking error between the virtual linear velocity and angular velocity and the actual linear velocity and angular velocity of the mobile robot, and the mobile robot's dynamic model, a fixed-time terminal sliding mode controller is designed to determine the control voltages of the drive motors for the left and right drive wheels of the mobile robot, controlling the actual linear velocity and angular velocity of the mobile robot to asymptotically converge to the virtual linear velocity and angular velocity. A fixed-time extended state observer is designed to estimate the mobile robot's velocity state and lumped disturbances, and feedforward compensation is applied to the lumped disturbances to eliminate the impact of disturbances on the system's control performance. By executing the above dual-closed-loop control strategy, fixed-time trajectory tracking control of the mobile robot is achieved, improving the control performance of the mobile robot under wheel slippage.

[0182] In one embodiment, a method for trajectory tracking and control of a mobile robot under unknown slippage conditions is provided, comprising:

[0183] The system tracks the virtual linear velocity and angular velocity of a mobile robot over a fixed time period; estimates the lumped disturbance of the mobile robot in real time; obtains the control voltage of the drive motor of the mobile robot based on the actual linear velocity and angular velocity and the estimated value of the lumped disturbance, and drives the mobile robot so that its actual velocity gradually converges to the virtual velocity; obtains the current pose parameters of the mobile robot based on its actual velocity; and performs trajectory tracking on the mobile robot based on the current pose parameters.

[0184] The current pose parameters refer to the position of the robot's geometric center in the global coordinate system and the robot's orientation angle at the current moment. Based on the pose tracking error between these current pose parameters and the reference pose parameters, the pose tracking error is converged through an outer-loop kinematic controller. If a fixed-time kinematic controller is used in the outer loop, the pose error can converge within a fixed time.

[0185] In one embodiment, the above method further includes: obtaining the pose tracking error and reference velocity of the mobile robot, inputting them into a pre-set fixed-time kinematics controller, and obtaining the virtual linear velocity and angular velocity based on the output of the fixed-time kinematics controller;

[0186] In this embodiment, a fixed-time kinematics controller for the mobile robot can be pre-configured. This fixed-time kinematics controller can be derived according to the steps of equations (11) to (20) above. The sliding surfaces s1 and s2 of the fixed-time kinematics controller can be obtained by designing the pose tracking error of the mobile robot. The sliding surfaces s1 and s2 converge within fixed times t1 and t2, respectively. Among them, the sliding surface s1 represents the tracking error of the mobile robot in the x-direction in the global coordinate system, and the sliding surface s2 represents the tracking error of the mobile robot in the y-direction and the azimuth tracking error in the global coordinate system. The convergence of the sliding surfaces s1 and s2 within a fixed time can be understood as the pose tracking error of the mobile robot converging to zero within this fixed time.

[0187] By introducing the fixed-time terminal sliding mode approach law of formula (15), the high-frequency chattering of the sliding mode controller can be suppressed, and the sliding surface can be made to converge to zero at a faster speed, thereby improving the convergence efficiency.

[0188] In some embodiments, when the mobile robot is initially started, the initial pose and reference pose of the mobile robot can be obtained, the pose tracking error can be calculated according to equation (12), and the pose tracking error and reference velocity can be input into the fixed-time kinematics controller of equation (17) to obtain the virtual linear velocity and angular velocity of the mobile robot. As can be seen from the design process of equation (17), the convergence time of the mobile robot pose tracking error is independent of the initial pose of the mobile robot and depends only on the controller gain.

[0189] In some embodiments, during the process of the mobile robot converging toward the reference pose, the current pose and reference pose of the mobile robot can also be obtained, and the new virtual linear velocity and angular velocity can be calculated according to Equation (17) to drive the mobile robot so that its pose tracking error converges within a fixed time. The convergence time is independent of the initial state of the mobile robot.

[0190] The method described above obtains the virtual linear velocity and angular velocity of the mobile robot in the outer loop of the dual closed-loop control system by using the pose tracking error and the reference velocity. The convergence time of the mobile robot pose tracking error is independent of the initial pose.

[0191] In one embodiment, tracking the virtual linear velocity and angular velocity of a mobile robot over a fixed time interval includes:

[0192] The virtual linear velocity and angular velocity are tracked by a pre-designed terminal sliding mode controller.

[0193] In this embodiment, the tracking of virtual linear velocity and angular velocity can be achieved through the inner loop terminal sliding mode controller of the dual closed-loop control system, which can be implemented using the above equation (25). Further, the actual speed of the mobile robot can be obtained based on the virtual linear velocity and angular velocity, the estimated lumped disturbance of the mobile robot, and the control voltage of the mobile robot's drive motor. In the inner loop processing, the mobile robot's state and lumped disturbance can be estimated based on a fixed-time extended state observer, and the lumped disturbance can be feedforward compensated in the terminal sliding mode controller.

[0194] Among them, the speed tracking error parameter e z It can be based on the actual speed z of the mobile robot and the virtual linear velocity and angular velocity z. c The difference is calculated as shown in equation (23) above.

[0195] In this process, the mobile robot can input its actual speed into a pre-designed fixed-time extended state observer (as shown in equation (22)) to obtain an estimate of its actual speed. As input to the inner-loop dynamics controller, the actual speed of the mobile robot gradually converges to the virtual linear velocity and angular velocity during the tracking process. This speed tracking error can be converged within a fixed time t3 using the terminal sliding mode controller of equation (25). Additionally, the output of the fixed-time extended state observer also includes a lumped disturbance estimate. It enables real-time and accurate estimation of disturbances of mobile robots under unknown longitudinal and lateral slip factors.

[0196] Among them, the terminal sliding surface s3 can be designed according to the speed tracking error parameters. Referring to the process of formulas (23) to (33), the terminal sliding surface s3 converges within a fixed time t3.

[0197] In some embodiments, the upper bound of the total convergence time for the pose tracking error and velocity tracking error of the mobile robot to converge is t, where t≤t1+t2+t3. At this time, the pose error and velocity error of the dual closed-loop control system can converge to zero in a fixed time t, thereby achieving convergence in a fixed time and improving the efficiency of trajectory tracking of the mobile robot.

[0198] The above embodiments, by configuring a fixed-time sliding mode controller, enable the mobile robot to converge its pose and velocity errors within a fixed time, thereby improving the efficiency of trajectory tracking.

[0199] In one embodiment, based on the velocity tracking error between the virtual linear velocity and angular velocity of the mobile robot and its actual linear velocity and angular velocity, and the dynamic model of the mobile robot, a fixed-time terminal sliding mode controller is designed to determine the control voltage of the drive motors for the left and right drive wheels of the mobile robot, thereby obtaining the actual speed of the mobile robot. The method further includes:

[0200] The control voltages of the left and right drive wheel motors of the mobile robot are corrected using the estimated lumped disturbance values. These corrected control voltages are then input into a pre-set dynamic model, and the actual speed of the mobile robot is obtained from the model's output. By fully considering the influence of lumped disturbances during inner-loop speed tracking, the system exhibits stronger anti-disturbance performance and smaller pose error fluctuations.

[0201] In this embodiment, the dynamic model of the mobile robot considering the dynamics of the drive motor can be obtained according to the machine parameters of the mobile robot, as shown in equation (10).

[0202] In the dual closed-loop control system of mobile robots, the control voltage of the drive motor can be used as the control input variable. According to the control requirements of the mobile robot, the change curve of the control voltage over time is designed to make the change of the control voltage smoother and avoid damage to the drive motor caused by sudden increase in control voltage.

[0203] In one embodiment, obtaining the current pose parameters of the mobile robot based on its actual operating speed includes:

[0204] The actual speed of the mobile robot is input into the kinematic model of the mobile robot, and the current pose parameters are obtained based on the output results.

[0205] In one embodiment, after tracking the trajectory of the mobile robot based on the current pose parameters, the method further includes:

[0206] The pose tracking error of the mobile robot is determined based on the current pose parameters and the reference pose parameters; based on the pose tracking error, the virtual linear velocity and angular velocity are obtained through the outer loop kinematic controller for trajectory tracking.

[0207] The methods described in the above embodiments are applied to a trajectory tracking simulation example of a sweeping robot to further illustrate the steps and effects of the trajectory tracking method for the mobile robot.

[0208] Specifically, simulation experiments were conducted on the fixed-time terminal sliding mode control and fixed-time extended state observer (FxTSMC+FxESO, hereinafter referred to as the method of this invention) and the traditional double-closed-loop PID (DCLPID) controller for trajectory tracking of the sweeping robot. To demonstrate the effectiveness of the comparative experiments, the trajectory path and initial conditions of the sweeping robot were the same during the simulation. The following sections will conduct simulation tests on the circular and rectangular trajectories of the sweeping robot.

[0209] The physical parameters and drive motor parameters of the laser radar-guided robotic vacuum cleaner are as follows:

[0210] m = 2.7 kg, J = 0.033 kg·m 2 r = 0.034m, b = 0.11m

[0211] R a =13.5Ω,k b =0.0239V / rad·s -1 ,k t =0.0239 (N·m) / A, N = 54.5

[0212] Assume the unknown input disturbance of the robot vacuum cleaner's dynamics follows a normal distribution function:

[0213]

[0214] To test the control effect of the designed controller on disturbances containing different frequencies and amplitudes, the simulation presents longitudinal slip and sideslip disturbances in the form of decaying sine waves, as well as longitudinal slip angular velocity disturbances of the left and right drive wheels:

[0215]

[0216]

[0217] The linear velocity disturbance of the robot vacuum cleaner's side-sliding motion:

[0218]

[0219] Among them, t s This is the start time of the disturbance.

[0220] Assume that the load on the robotic vacuum cleaner changes slowly between t = 5 and 8 seconds, with the change amount ΔM. s =0.1M s Longitudinal slip occurs between 10 and 13 seconds, sideslip occurs between 15 and 18 seconds, and lumped disturbances are introduced between 20 and 23 seconds.

[0221] The control law for the DCLPID controller is given as follows:

[0222] v c (k)=v c (k-1)+k px (e x (k)-e x (k-1))+k ix e x (k)+k dx (e x (k)-2ex (k-1)+e x (k-2))

[0223] ω c (k)=ω c (k-1)+k py (e y (k)-e y (k-1))+k iy e y (k)+k dy (e y (k)-2e y (k-1)+e y (k-2))+k pθ (e θ (k)-e θ (k-1))+k iθ e θ (k)+k dθ (e θ (k)-2e θ (k-1)+e θ (k-2))

[0224] u a (k)=u a (k-1)+k p (e z (k)-e z (k-1))+k i e z (k)+k d (e z (k)-2e z (k-1)+e z (k-2))

[0225] in, These are the proportional, integral, and derivative coefficients for velocity control in the outer-loop kinematic controller. The proportional, integral, and derivative coefficients for angular velocity control in the outer-loop kinematic controller. This is the diagonal matrix of proportional, integral, and derivative coefficients of the inner loop dynamics controller.

[0226] k px =60,k ix =1,k dx =4,

[0227] k py =50,k iy =1,k dy =5,

[0228] k pθ =60,kiθ =1,k dθ =4

[0229] The parameters of the inner loop controller are:

[0230] k p =diag([40,10]),k i =diag([1,1]),k d =diag([8,8])

[0231] The outer loop parameters of the FxTSMC+FxESO controller designed in this invention are:

[0232] c1 = 2.3, c2 = 0.5, k 11 =0.6,k 12 =2.4,k 21 =0.6,k 22 =2,

[0233] a1=0.6, b1=1.4, a2=0.7, b2=1.3,

[0234] The parameters of the fixed-time extended state observer are:

[0235] k 31 =100,k 32 =100,k 41 =2500,k 42 =2500,

[0236] a3=0.9, b3=1.4, a4=0.8, b4=1.8,

[0237] The dynamic controller parameters are:

[0238] k 51 =3,k 52 =1,k 61 =20,k 62 =10,

[0239] a5=0.6, b5=1.4, a6=0.8, b6=1.2,

[0240] Simulation Example 1 (Circular Trajectory Tracking):

[0241] like Figures 3 to 8 As shown, in circular trajectory tracking, the parameters are set as follows: simulation time 40s, sampling frequency 100Hz, and initial value of the reference trajectory q. r (0) = [0 0 0] T Reference speed v r =0.25m / s,ω r=0.5rad / s, the initial pose of the robot vacuum cleaner q(0) = [0.1 0.2 0] T The initial velocity is v = 0 m / s, ω = 0 rad / s.

[0242] The simulation results are as follows: Figure 3 , 4 As shown in Figure 5, when the actual initial pose of the robotic vacuum cleaner differs from the expected initial pose, the DCLPID will exhibit a large steady-state error and a long convergence time. The fixed-time trajectory tracking controller of this invention can effectively shorten the convergence time and reduce the steady-state error. Under lumped disturbances, the method of this invention has stronger anti-disturbance performance and smaller pose error fluctuations.

[0243] Figure 6 The actual speed and angular velocity changes of the sweeping robot under two control algorithms are shown. The control law designed based on the fixed-time method will have a smoother speed change at the beginning, while the DCLPID algorithm will have a more drastic initial speed change, which may damage the motor performance in practice.

[0244] Figure 7 The FxESO method designed for this invention is used to estimate lumped disturbances, demonstrating that it can provide real-time and accurate estimation of lumped disturbances. Figure 8 The curve of control voltage changing over time is given, and the control voltage designed by the method of the present invention changes more smoothly in the initial start-up stage.

[0245] Simulation Example 2 (Rectangular Trajectory Tracking):

[0246] Considering that robotic vacuum cleaners often perform edge cleaning operations in actual operation, a rectangle was selected as the reference trajectory in the simulation. Combined with slippage disturbances added to the simulation, this further verifies the robustness of the control algorithm to disturbances. The parameter settings are as follows: simulation time 40s, reference trajectory is a 2.5m × 2.5m rectangle, initial value q... r (0) = [0 0 0] T Reference speed v r =0.25m / s,ω r =0 rad / s, the initial pose of the robot vacuum cleaner is q(0) = [0.1 0.2 0] T The initial velocity is v = 0 m / s, ω = 0 rad / s. All other parameters are the same as above.

[0247] Depend on Figure 9 , 10As shown in section 11, when the actual initial pose of the robotic vacuum cleaner differs from the desired initial pose, when traversing the first rectangular edge, the DCLPID exhibits a significant steady-state error and fails to converge to the desired trajectory. The algorithm designed in this patent has a smaller steady-state error and a shorter convergence time. When traversing right-angle turns, the DCLPID exhibits less overshoot. However, comparing the angular velocity and input voltage at the turn, the DCLPID achieves a smaller overshoot with a larger angular velocity at the turn, and a sudden increase in input voltage may damage the motor. Under the influence of lumped disturbances, the method of this invention demonstrates stronger anti-disturbance performance and smaller pose error fluctuations.

[0248] Figure 12 The actual speed and angular velocity changes of the sweeping robot under two control algorithms are shown. At the initial position and turning position, the speed change of the control law designed based on the fixed time method is more gradual, while the speed change of the DCLPID algorithm is more drastic, which may damage the motor performance in practice.

[0249] Figure 13 The FxESO designed in this invention is used for estimating lumped disturbances. It can be seen that FxESO can perform real-time and accurate estimation of lumped disturbances. Figure 14 The curve of control voltage changing with time is given. The control voltage designed by the method of the present invention changes more smoothly during initial start-up and rotation.

[0250] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to fall within the scope of this specification.

[0251] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this patent should be determined by the appended claims.

Claims

1. A method for trajectory tracking and control of a mobile robot under unknown slippage conditions, characterized in that, The method includes: A kinematic model of a mobile robot under unknown slippage and a dynamic model considering the dynamics of the drive motor are established. The unknown longitudinal slip and sideslip disturbances, model parameter uncertainties and unknown input disturbances in the dynamic model are referred to as lumped disturbances. A fixed-time kinematic controller is designed based on the pose tracking error of the mobile robot to output the virtual linear velocity and angular velocity of the mobile robot. Based on the speed tracking error between the virtual linear velocity and angular velocity of the mobile robot and the actual linear velocity and angular velocity, and the dynamic model, a fixed-time terminal sliding mode controller is designed to determine the control voltage of the drive motors of the left and right drive wheels of the mobile robot, and to control the actual linear velocity and angular velocity of the mobile robot to asymptotically converge to the virtual linear velocity and angular velocity. Based on the fixed-time terminal sliding mode controller and the actual linear and angular velocities of the mobile robot, a fixed-time extended state observer is designed to estimate the velocity state and lumped disturbances of the mobile robot, and the lumped disturbances are fed forward to compensate for the disturbances and eliminate the impact of the disturbances on the system control performance. The specific steps for designing a fixed-time kinematic controller based on the pose tracking error of the mobile robot include: Define the reference pose of the mobile robot as It satisfies the following kinematic equations: in, This indicates the reference position of the mobile robot's geometric center in the global coordinate system. The reference heading angle for the mobile robot. For reference speed, The reference linear velocity for the mobile robot's forward movement. The reference angular velocity of the mobile robot body around its geometric center; The pose tracking error of a mobile robot is defined as: in, Mobile robots Direction tracking error; The differential equation for pose tracking error is obtained by taking the derivative: Design sliding surface : Wherein, coupling coefficient It is a positive number; The fixed-time kinematic controller is implemented using the following formula: in, For the virtual speed of the mobile robot, For virtual linear velocity, For virtual angular velocity, controller gain All are positive numbers. , ;function Defined as , It is a symbolic function; Design the following candidate Lyapunov functions: Differentiation yields: Sliding surface Can be done at fixed times Converging inward to zero, let , , , The convergence time is... Represented as: 。 2. The method according to claim 1, characterized in that, The kinematic model of the mobile robot under unknown slippage conditions is represented as follows: in, The pose of the mobile robot; The actual speed of the mobile robot. and These are the linear velocity and angular velocity of the mobile robot, respectively. , For longitudinal sliding speed, The yaw rate disturbance caused by longitudinal slippage. The radius of the drive wheels of the mobile robot. The distance between the two drive wheels. These are the disturbance angular velocity vectors caused by the longitudinal slippage of the left and right drive wheels of the mobile robot, respectively. This is the mismatched perturbation vector caused when the mobile robot sideslips. The lateral sliding speed of the mobile robot; This is the transformation matrix.

3. The method according to claim 1, characterized in that, The dynamic model of the mobile robot considering the dynamics of the drive motor under unknown slippage conditions is expressed as follows: in, , , , , The radius of the drive wheels of the mobile robot. The distance between the two drive wheels. , These are the mass and moment of inertia of the mobile robot, respectively. These are the armature resistance, torque constant, and back electromotive force constant of the drive motor, respectively. For mechanical gear reduction ratio, This refers to the control voltage for the drive motors of the right and left drive wheels; It is a lumped disturbance that includes unknown longitudinal and sideslip disturbances of the system, uncertain model parameters, and unknown input disturbances.

4. The method according to claim 1, characterized in that, The fixed-time terminal sliding mode controller is implemented using the following formula: in, This refers to the control voltage for the drive motors of the right and left drive wheels; , ; , , The radius of the drive wheels of the mobile robot. The distance between the two drive wheels. , These are the mass and moment of inertia of the mobile robot, respectively. These are the armature resistance, torque constant, and back electromotive force constant of the drive motor, respectively. This refers to the reduction ratio of mechanical gears; State vector The estimated value; control gain For positive numbers, control gain It is a positive integer and satisfies , ; This is the speed tracking error vector; The global integral terminal sliding surface vector; function Defined as , It is a symbolic function; Design the following candidate Lyapunov functions: Differentiation yields: Sliding surface Available at a fixed time Converges to zero; let , The convergence time is... Represented as: The pose tracking error and velocity tracking error of the mobile robot can converge within a fixed time, and the total convergence time satisfies: 。 5. The method according to claim 1, characterized in that, The fixed-time extended state observer is: Here, the state vector is defined. , , The actual speed of the mobile robot. It is a lumped disturbance that includes unknown longitudinal and sideslip disturbances of the system, uncertain model parameters, and unknown input disturbances; They are state vectors The estimated value; This is the observation error; For observer gain, , function Defined as .

6. The method according to claim 1, characterized in that, The specific method for designing a fixed-time kinematic controller based on the pose tracking error of the mobile robot and outputting the virtual linear velocity and angular velocity of the mobile robot includes: The actual linear velocity and angular velocity of the mobile robot are used as inputs to the kinematic model of the mobile robot to obtain the actual pose of the mobile robot. The reference pose and the pose tracking error of the actual pose of the mobile robot are obtained. Based on the pose tracking error, the steps of obtaining the virtual linear velocity and angular velocity of the mobile robot according to the fixed-time kinematics controller are performed.

7. The method according to claim 1, characterized in that, The lumped disturbance is determined by the mobile robot's mass, moment of inertia, torque, longitudinal slip velocity, lateral slip velocity, the disturbance angular velocity vector caused by the longitudinal slip of the mobile robot's drive wheel, the mismatch disturbance vector caused by the lateral slip of the mobile robot, and the mobile robot's orientation angle.

8. The method according to claim 1, characterized in that, The specific method for controlling the actual speed of the mobile robot to converge to the virtual speed includes: inputting the control voltage of the drive motors of the left and right drive wheels of the mobile robot into the dynamic model of the mobile robot, thereby determining the actual speed of the mobile robot.

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