Adaptive recursive terminal sliding mode based omnidirectional mobile robot control method and system

Abstract

The application discloses a kind of omnidirectional mobile robot control method and system based on adaptive recursive terminal sliding mode, belongs to robot motion control technical field, by establishing the robot dynamics model containing parameter uncertainty and external disturbance, trajectory tracking error of the dynamics model is defined, and the non-singular fast recursive terminal sliding surface of omnidirectional mobile robot is constructed;Based on the sliding surface, the adaptive recursive terminal sliding mode controller of system is constructed;The controller is used to carry out trajectory tracking control to robot, and controller parameter is adjusted to make system state converge in finite time.The controller designed according to the control method can quickly, high-precision control omnidirectional mobile robot to track the given desired trajectory, and can converge in finite time, adaptive adjustment gain, effectively handle the influence of system uncertainty and external disturbance.

Description

Technical Field

[0001] This invention belongs to the field of robot motion control technology, specifically relating to an omnidirectional mobile robot control method and system based on adaptive recursive terminal sliding mode. Background Technology

[0002] With the rapid development of automation technology, mobile robots are widely used in industry, agriculture, and special environments. Traditional mobile robots mostly adopt a four-wheel or six-wheel rubber wheel structure, and their movement is limited by non-omnidirectional movement characteristics. They need to rely on turning radius to adjust direction, resulting in insufficient mobility in narrow spaces such as warehouses and greenhouses. Compared with traditional mobile robots, Mecanum wheel mobile robots have become a research hotspot due to their superior mobility, zero turning radius, and omnidirectional movement capability. Mecanum wheels are composed of multiple 45° oblique rollers, which achieve arbitrary translation and rotation of the vehicle body through inter-wheel cooperative drive. This characteristic makes them widely used in narrow environments such as factories, warehouses, and greenhouses. However, the control of Mecanum mobile robots is a complex and challenging task because it needs to consider multi-degree-of-freedom motion and the interaction of the inter-wheel cooperative drive system. Its trajectory tracking control faces the following challenges: 1. The nonlinearity of the dynamic model and the multi-round coupling effect significantly increase the difficulty of control; 2. The robot has multiple degrees of freedom of movement, requiring simultaneous control of translational and rotational motions; 3. Uncertainties such as sensor errors, sudden changes in ground friction, and load variations may affect the control accuracy of the system.

[0003] Some positive results have been achieved both domestically and internationally in the field of trajectory tracking control for Mecanum wheel mobile robots. However, current control algorithms still have significant limitations. For example, traditional PID algorithms perform poorly when dealing with nonlinear systems or large external disturbances, and cannot achieve fast and accurate control. Ordinary sliding mode control cannot converge within a finite time and the control input exhibits high-frequency oscillations, affecting the actuator's lifespan. Summary of the Invention

[0004] The purpose of this invention is to provide an omnidirectional mobile robot control method and system based on adaptive recursive terminal sliding mode, so as to solve the technical problems of poor anti-interference ability and inability to converge within a finite time in traditional control algorithms mentioned in the background art, and to realize fast and high-precision trajectory tracking of omnidirectional mobile robots.

[0005] This invention provides a control method for an omnidirectional mobile robot based on adaptive recursive terminal sliding mode, applicable to omnidirectional mobile robot systems, comprising: A robot dynamics model containing parameter uncertainties and external disturbances is established, wherein the dynamics model concentrates the uncertainties of the system; Define the trajectory tracking error of the dynamic model and construct the non-singular fast recursive terminal sliding surface of the omnidirectional mobile robot; Based on the sliding surface, an adaptive recursive terminal sliding mode controller for the system is constructed to counteract the nominal dynamic characteristics of the system and overcome system uncertainties. The robot is tracked and controlled using the controller, and the controller parameters are adjusted to make the system state converge within a finite time.

[0006] Furthermore, the dynamic model is constructed based on the kinematic model and motion characteristics of the omnidirectional mobile robot, and the formula is as follows: , , in, This is used to describe the robot's actual pose vector. For the desired acceleration, , This represents the robot's lateral and longitudinal displacements, and angles, in the world coordinate system. This represents the yaw angle of the robot body about its geometric center. Indicates the wheel diameter of the robot. This represents the matrix of rated rotational inertia of the robot's wheels. It is the angle after aligning with the Mecanum wheel. , This represents the transformation matrix used to transform the robot from its body coordinate system to the world coordinate system. Indicates control input, This represents centralized system uncertainty. These represent the distances from the robot's edge to its geometric center and the distances from the axle to its geometric center, respectively.

[0007] Furthermore, the system uncertainties in the aforementioned dynamic model set include parameter uncertainties, external disturbances, and unmodeled dynamics, as expressed in the formula: ,in, This represents the lumped uncertainty vector acting on the four wheels. and express and The uncertainty of the parameters, among which The coefficient of viscous friction of the system. This represents unmodeled dynamics.

[0008] Furthermore, the trajectory tracking error The formula is: , in, , represents the desired trajectory vector of the system. For the desired horizontal coordinate, For the desired vertical coordinate, The desired heading angle; For longitudinal position error, This is the lateral position error. This is for angular error; This is the robot's actual pose vector. , This represents the robot's lateral and longitudinal displacements in the world coordinate system. This represents the yaw angle of the robot body about its geometric center.

[0009] Furthermore, the construction of the robot's non-singular fast recursive terminal sliding surface based on the trajectory tracking error includes: Based on trajectory tracking error Calculate intermediate sliding mode variables The intermediate sliding mode variable Further combining the integral term Generate the final nonsingular fast recursive terminal sliding surface The formula is: , , , Integral term The initial value is set to: , in, For intermediate synovial membrane variables, Non-singular fast recursive terminal sliding surface , It is a function Simplified expression, For the rate of change of error, linear gain Nonlinear gain Integral gain matrix , , It is a nonlinear exponent used to adjust the dynamic performance of the controller.

[0010] Furthermore, the control input of the adaptive recursive terminal sliding mode controller From equivalent control rate and approach control rate Composition; among which, equivalent control rate Used to offset nominal dynamic characteristics based on a dynamic model, driving the system state to move along the sliding surface; approaching the control law. To achieve the sliding mode convergence rate, the system's uncertainty is overcome by utilizing adaptive gain, ensuring that the system state converges to the sliding surface within a finite time; the adaptive gain is generated based on a leakage adaptive mechanism.

[0011] Furthermore, the control input of the adaptive recursive terminal sliding mode controller for: , , , , , in, , , In the formula, This represents the transformation matrix used to transform the robot from its body coordinate system to the world coordinate system. Assign a control matrix to the robot's dynamics system. satisfy , It is the identity matrix; For the symbolic function vector, , , , These are the sliding surface variable vectors. The three components; , It is a gain diagonal matrix, and all its elements are positive numbers. These are adjustable parameters for the boundary layer. For adaptive parameter vectors, Its adaptive rate, and An adjustable parameter for the leakage adaptive rate; For adaptive gain, This represents the angular velocity of each wheel; and Design parameters for the sliding surface. This is the state weight vector; It is a norm of 1, defined as follows: , It is a 2-norm, defined as follows: .

[0012] Furthermore, the step of using the controller to perform trajectory tracking control on the robot and adjusting the controller parameters to make the system state converge within a finite time includes: The total convergence time of the system is determined based on the preset control response speed requirements. The total convergence time is the time to reach the sliding surface. Sum of error convergence time composition; Adjust the dynamic parameters of the sliding surface to optimize the error convergence trajectory and balance the dynamic response speed of the system with the control chattering while ensuring system stability; Adjust adaptive parameters to accelerate the estimation of system uncertainties while suppressing high-frequency disturbances and maintaining system robustness; Adjust the controller parameters to control the growth rate of the adaptive rate, effectively compensate for disturbances, and prevent overestimation of gain; Substitute the adjusted parameters into the controller and monitor the trajectory tracking error during actual system operation. If the error fails to converge to zero or within the allowable error range within the preset finite time, or if the control input exhibits saturation / severe chattering, return to the parameter adjustment step until the system meets the convergence time requirement while the control input is smooth and without saturation.

[0013] Furthermore, the total convergence time of the system Time to reach the sliding surface With error convergence time The sum of the terms is given by the following formula: , in: , , Among them, the dynamic parameters of the sliding surface For linear gain, For nonlinear gain, and They represent linear gains respectively. and nonlinear gain Corresponding to the The component of one degree of freedom, Nonlinear exponent; adaptive rate parameter Here is the integral gain matrix. Represents the integral gain matrix The 1 eigenvalue, It is a non-linear exponent; Indicates the first in the sliding surface Linear error weighting coefficients for each degree of freedom; and Represent the sliding surface variables and tracking error respectively in the th... Initial values ​​for each degree of freedom; The adjustment of the dynamic parameters of the sliding surface is specifically as follows: Increase linear gain The numerical value improves the dynamic performance of the sliding surface and accelerates the error correction. Convergence speed far from the equilibrium point; increasing nonlinear gain The numerical value accelerates the error Improve the convergence speed near the equilibrium point and enhance steady-state accuracy; adjust the nonlinear exponent. Change the degree of nonlinearity of the convergence trajectory, in conjunction with , Achieve convergent combinations of "fast-slow" or "slow-fast"; The adjustment of the adaptive parameter specifically involves: Choose a larger integral gain matrix A higher value accelerates the estimation of system uncertainties by the adaptive rate, thus improving control accuracy; a larger nonlinear exponent is selected. The value increases the growth rate of the adaptive rate, enhancing the system's robustness against sudden disturbances; a smaller nonlinear exponent is selected. The value makes the adaptive process smoother and suppresses high-frequency disturbances; The adjustment of the controller parameters is specifically as follows: First pass , ,and Establish basic robust control performance, and then utilize and Fine-tune the leakage adaptive rate to ensure that the system can respond quickly and maintain stable operation when faced with uncertainty.

[0014] This invention also provides a control system for an omnidirectional mobile robot based on an adaptive recursive terminal sliding mode, corresponding to the above method. The system is used to implement the method described in any of the above claims, including a model building module, a sliding surface building module, a controller building module, and a control execution module. The model building module is used to establish a robot dynamics model containing parameter uncertainties and external disturbances, the dynamics model concentrating the system's uncertainties; the sliding surface building module is used to define the trajectory tracking error of the dynamics model and construct a non-singular fast recursive terminal sliding surface for the omnidirectional mobile robot; the controller building module is used to construct an adaptive recursive terminal sliding controller for the system based on the sliding surface to offset the nominal dynamic characteristics of the system and overcome system uncertainties; the control execution module is used to use the controller to perform trajectory tracking control on the robot and adjust the controller parameters to make the system state converge within a finite time.

[0015] The beneficial effects of this invention are as follows: Compared with existing technologies, the omnidirectional mobile robot control method and system based on adaptive recursive terminal sliding mode provided by this invention establishes a dynamic model of the omnidirectional mobile robot and decomposes and concentrates the unmodeled uncertainties. Based on this, an adaptive recursive terminal sliding surface is proposed. The controller designed based on this sliding surface can ensure that the system state is located on the sliding surface from the beginning, thereby realizing "full-process sliding mode" control. This design fundamentally eliminates the time-consuming and easily disturbed "approaching phase" in traditional sliding mode control, allowing the system state to immediately enter the ideal sliding mode without undergoing a dynamic approaching process from the initial point to the sliding surface. This not only significantly improves the dynamic response speed of the system and ensures faster convergence performance, but also effectively suppresses the influence of external disturbances and internal uncertainties that may be introduced during the approaching phase because the system state is always constrained to move on the sliding surface, thereby significantly improving control accuracy and system robustness. Furthermore, the introduction of the adaptive recursive terminal sliding surface further optimizes the convergence characteristics of the system in the sliding mode, enabling it to achieve more precise and stable control within a finite time, thus meeting the stringent requirements of omnidirectional mobile robots for rapid response and high-precision operation. Attached Figure Description

[0016] Figure 1 Flowchart of a control method for an omnidirectional mobile robot based on adaptive recursive terminal sliding mode according to an embodiment of the present invention; Figure 2 A schematic diagram showing the position of the robot in the world coordinate system according to an embodiment of the invention; Figure 3 This is a structural diagram of the non-singular fast recursive terminal sliding mode control method according to an embodiment of the invention; Figure 4 This is a schematic diagram of the trajectory tracking experiment results in an embodiment of the present invention; Figure 5 A structural diagram of a control system for an omnidirectional mobile robot based on adaptive recursive terminal sliding mode according to an embodiment of the present invention. Detailed Implementation

[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0018] like Figure 1As shown, this embodiment provides a finite-time sliding mode control method for mobile robots based on adaptive recursive terminal sliding mode, applicable to omnidirectional mobile robots, such as Mecanum wheel omnidirectional mobile robots. This embodiment will take a Mecanum wheel omnidirectional mobile robot as an example, combined with... Figure 1 This document describes the specific implementation process of this embodiment.

[0019] S1. Establish a dynamic model of the motion of an omnidirectional mobile robot containing parameter uncertainties and external disturbances, and concentrate the uncertainties in the system.

[0020] In this embodiment, the parameter uncertainty refers to the deviation between the estimated value and the actual value of the parameters in the system, such as sensor error; external disturbance refers to uncontrollable forces from outside the system, such as system disturbances caused by load changes or road conditions; uncertainty in the system refers to all factors that cause the inconsistency between the "acceleration calculated by the theoretical model" and the "actual acceleration of the robot", which may include parameter uncertainty, external disturbance and unmodeled dynamics.

[0021] In one embodiment of this invention, the wheels of the Mecanum wheel omnidirectional mobile robot are dynamically modeled, and the formula is as follows: (1), in, The input voltage for each of the four DC motors is supplied to the four wheels. This is the proportional factor for converting motor input voltage into output torque. Indicates the rotation angle of the wheel. Let be the angular velocity vector of the wheel. Let be the acceleration vector of the wheel. and These represent its rated moment of inertia and coefficient of viscous friction, respectively. and This indicates the uncertainty of its parameters. This represents the unmodeled dynamics, facilitating subsequent controller design. The lumped uncertainties of the system are defined as follows: The wheel dynamics model can be rewritten as: (2), in, This represents the concentrated uncertainty vector acting on the four wheels.

[0022] Furthermore, based on the motion characteristics of the omnidirectional mobile robot and combined with the dynamic model, a kinematic model is performed on it, as shown in the following formula: (3), (4), like Figure 3 As shown, where This is used to describe the robot's actual pose vector. , Represents the robot's lateral and longitudinal displacements in the world coordinate system, such as Figure 2 In - , - ;angle This represents the yaw angle of the robot body about its geometric center. Indicates the wheel diameter of the robot. It refers to the angle after aligning the Mecanum wheel (i.e., adding the 45° mounting angle unique to the Mecanum wheel). , This represents the transformation matrix used to transform the robot from its body coordinate system to the world coordinate system. Let represent the distances from the robot's edge to its geometric center and the distances from the wheel axle to its geometric center, respectively. For the formula... Differentiation yields: (5), Utilizing angles With the robot's yaw angle The fixed relationship between them, for the formula In The items are decomposed and reorganized, and rewritten as follows: (6), (7), in, It is a geometry and inertia coupling matrix used to calculate the effect of the Coriolis effect generated when the robot rotates on the wheel acceleration.

[0023] Next, combining the formula and formula The complete dynamic model of the robot system is obtained, as shown in the following formula: (8), To facilitate the design of subsequent controllers, the control input will be... The preliminary design is as follows: (9), in, This is the control input, specifically a secondary control input, representing the virtual control quantity of the robot's ideal acceleration command after feedback linearization. The formula... Substitute into the formula A simpler system dynamics model is obtained, with the following formula: (10) in, For the robot's acceleration vector, For the robot's angular velocity, Let be the angular velocity vector of the wheel. Let be the acceleration vector of the wheel.

[0024] Thus, step S1 successfully established a dynamic model of the Mecanum wheeled omnidirectional mobile robot motion, which contains parameter uncertainties and external disturbances.

[0025] Specifically, the values ​​of the inherent physical parameters of the robot system in this example are shown in Table 1: Table 1. Inherent physical parameters of the system

[0026] S2. Define the trajectory tracking error of the dynamic model and construct the non-singular fast recursive terminal sliding surface of the omnidirectional mobile robot.

[0027] like Figure 3 As shown, this embodiment constructs a non-singular fast recursive terminal sliding surface. The non-singular fast recursive terminal sliding surface is an artificially designed error function. This sliding surface recursively expands the non-singular fast terminal sliding surface by introducing an integral term, thereby further improving the robustness of the system while maintaining non-singularity and fast convergence.

[0028] In this embodiment, the trajectory tracking error of the dynamic model is first defined. for: (11), like Figure 3 As shown, , where represents the desired trajectory vector of the system. It is the expected horizontal coordinate. For the desired vertical coordinate, The desired heading angle; For longitudinal position error, This is the lateral position error. This refers to the angle error. The design trajectory tracking error... The goal is to make Tend to In this way, the actual trajectory tends to the reference trajectory.

[0029] Furthermore, according to Define a non-singular fast terminal sliding surface The formula is as follows: (12) in, The rate of change of the error, linear gain Nonlinear gain , It is a non-linear exponent.

[0030] Furthermore, combining non-singular fast recursive terminal sliding surfaces Continue designing non-singular fast recursive terminal sliding surfaces The formula is as follows: (13) (14) in, Here is the integral gain matrix. , , As an adjustable parameter, it is used to adjust the dynamic performance of the controller. To reduce convergence time, the integral term... The initial value is set to: (15) It should be noted that the non-singular fast recursive terminal sliding surface constructed in this embodiment is divided into two layers, which serve as the final sliding surface. and the final synovial surface intermediate synovial variables The purpose of designing two sliding surfaces is to achieve phased convergence. By setting the initial values ​​of the integral terms, the system state is made to reach the state of the second sliding surface from the beginning. =0, and then in a finite time from =0 reached =0, by setting the initial value of the recursive structure and integral term, the system is located on the sliding surface from the beginning, thereby eliminating the arrival stage of sliding mode control, shortening the convergence time of the system state variables, ensuring that the robot can still reach the designated position smoothly, quickly and accurately within a limited time under the condition of disturbance, and improving the robustness of the system.

[0031] S3. Based on the non-singular fast recursive terminal sliding surface, construct an adaptive recursive terminal sliding controller for the system to counteract the nominal dynamic characteristics of the system, overcome system uncertainties, and ensure that the system state converges to the sliding surface within a finite time.

[0032] In one feasible manner, continue to refer to Figure 3 The control input of the controller From equivalent control rate and approach control rate Composition, including the equivalent control rate Used to offset nominal dynamic characteristics based on a dynamic model, driving the system state to move along the sliding surface; approaching the control law. To achieve sliding mode convergence, by utilizing adaptive gain To overcome unknown disturbances and parameter uncertainties in the system, and to ensure that the system state converges to the sliding surface within a finite time.

[0033] Furthermore, adaptive gain Designed based on a leakage-type adaptive mechanism, it consists of an error-driven learning term and a leakage term to prevent overestimation, thus preventing overestimation of the control gain and effectively suppressing control chattering while ensuring robustness.

[0034] In existing technologies, traditional adaptive sliding mode control, while capable of handling uncertainty, often exhibits monotonically increasing gain. In vibration-sensitive systems like Mecanum wheel robots, this can lead to excessive accumulation of control gain (overestimation), resulting in severe control chattering and impacting tracking accuracy. This embodiment creatively introduces a leakage-type adaptive mechanism. By designing specific leakage terms, it automatically reduces unnecessary gain when the system state approaches the sliding surface. This not only preserves the adaptive control's ability to resist interference but, more importantly, effectively suppresses chattering caused by gain overestimation, achieving smoother and more precise omnidirectional motion control than existing technologies.

[0035] In this embodiment, the specific formula for constructing the system's adaptive recursive terminal sliding mode controller is as follows: (16) (17) (18) (19) (20) in, (twenty one), (twenty two), In the formula, The control allocation matrix for the robot dynamics system is constructed based on the geometry and kinematic constraints of the omnidirectional mobile robot. Its function is to map and allocate the virtual control commands (such as total longitudinal force, total lateral force and total yaw moment) calculated by the high-level controller to the specific execution commands (such as the driving force or steering force of each wheel) of the four wheels. satisfy ,in As an identity matrix, this property ensures the decoupling characteristic of control allocation: that is, the actual wheel force allocated by this matrix can be accurately synthesized into the total control quantity desired by the controller, eliminating allocation error; Let be a vector of sign functions, and its expression is: ,in, , , These are the sliding surface variable vectors. The vector has three components; it switches the direction of control action in real time according to the direction of the tracking error (positive or negative), thereby improving the anti-interference capability of the control. , It is a gain diagonal matrix with all positive elements, used to adjust the convergence speed and robustness of the controller; These are adjustable parameters for the boundary layer, used to adjust the robustness of the controller; For adaptive parameter vectors, Its adaptive rate; and These are adjustable parameters of the adaptive rate, used to adjust the growth and decay rates of the adaptive rate, respectively. The gain is estimated online in real time by the adaptive rate of Formula 21, which can effectively compensate for disturbances while preventing the gain from being overestimated. This represents the rotational speed (or angular velocity) of each wheel. and The design parameters for the sliding surface determine its nonlinear characteristics; As a state weight vector, when the robot is in a state of rapid acceleration or deceleration or on the edge of slippage (large angular acceleration / angular velocity), the controller will assign higher weights to it to prioritize improving robustness. In the formula It is a norm of 1, defined as follows: , It is a 2-norm, defined as follows: ; Therefore, Equation 21 describes a leakage-type adaptive mechanism with dynamic awareness. Its final output is... The derivative of This means it's a continuous variable obtained through integration, which helps ensure the smoothness of the control signal. It can determine not only the magnitude of the error... Adjusting the control intensity allows for a keen perception of the robot's dynamic intensity. ), and through leaks when strong control is not required ( It automatically "depressurizes," thereby suppressing chattering to the maximum extent while ensuring robustness.

[0036] Meanwhile, the leakage-type adaptive mechanism with dynamic awareness designed in this embodiment can compensate for system disturbances caused by load changes or road conditions in real time; that is, it only needs to estimate this... The maximum value (upper bound) of the disturbance is obtained, and then the estimated value is output to the approach control law module to generate a sufficiently large force to counteract it. There is no need to know the precise upper bound of the disturbance in advance, which greatly simplifies the design of the controller.

[0037] In this example, the specific values ​​of the parameters for the sliding surface and the controller can be: , , , , , , , .

[0038] S4. Use the adaptive recursive terminal sliding mode controller to perform trajectory tracking control on the robot, and adjust the controller parameters to make the system state converge within a finite time.

[0039] The adaptive recursive terminal sliding mode controller designed in this embodiment has the characteristic of finite-time convergence. The convergence process of the control system is divided into two stages: first, the process of the system state trajectory moving from the initial position to the sliding surface (approaching stage); second, the process of the state converging along the sliding surface to the equilibrium point (sliding stage). To ensure the overall speed and stability of the system, the controller parameters are tuned through the following logic: S41. Determine convergence time constraints The total convergence time of the system is determined based on the preset control response speed requirements. The total convergence time is the time to reach the sliding surface. Sum of error convergence time The composition satisfies the following relationship: (twenty three), in, and Subject to controller parameters , and and adaptive rate parameters and To address the constraints, these parameters are adjusted to make the calculated theoretical convergence time shorter than the preset time. .

[0040] Specifically, the two stages of control system convergence: In a limited time Converging inwards to 0 (i.e., the approaching phase); exist In a limited time It converges to 0 (sliding phase), therefore the total convergence time is... The specific formula is as follows: (twenty four), (25), Among them, the dynamic parameters of the sliding surface For linear gain, For nonlinear gain, and They represent linear gains respectively. and nonlinear gain Corresponding to the The component of one degree of freedom, Nonlinear exponent; adaptive rate parameter Here is the integral gain matrix. Represents the integral gain matrix The diagonal elements (eigenvalues) It is a non-linear exponent; In the non-singular fast recursive terminal sliding surface, the first... Linear error weighting coefficients for each degree of freedom; and Represent the non-singular fast terminal sliding surface variables and the tracking error at the th... Initial values ​​for each degree of freedom.

[0041] From formulas (14) and (15), it can be seen that, and Dynamic parameters of the sliding surface , and and adaptive parameters and By adjusting the above parameters, the calculated theoretical convergence time can be made shorter than the preset time. .

[0042] S42. Adjust the dynamic parameters of the sliding surface ( , and ) Dynamic parameters of sliding surface , and The dynamic performance of the sliding mode can be adjusted; the higher the value, the better. The faster the convergence to 0, the better the dynamic performance; however, excessively large values ​​can exacerbate chattering and may cause control input saturation. The specific adjustment method is as follows: Linear gain Increase The numerical value improves the dynamic performance of the sliding surface and accelerates the error correction. The convergence speed when far from the equilibrium point; however, an excessively large value may cause high-frequency chattering in the system.

[0043] Nonlinear gain Increase The numerical value accelerates the error Improving the convergence speed near the equilibrium point enhances steady-state accuracy; however, the risk of chattering must also be weighed.

[0044] Nonlinear exponent :adjust (Usually the value ranges from 0 to 1) to change the degree of nonlinearity of the convergence trajectory, in conjunction with , Achieve convergent combinations of "fast-slow" or "slow-fast".

[0045] S43. Adjust the adaptive rate parameter ( and ) Larger adaptive parameters and smaller adaptive parameters It can speed up This improves convergence speed, control accuracy, and reduces steady-state error, but at the cost of increased measurement noise and control chattering. The specific adjustment method is as follows: Integral gain matrix Select the larger one A higher value accelerates the estimation of system uncertainties by the adaptive rate, thereby improving control accuracy; however, an excessively high value... This will increase the sensitivity to measurement noise and exacerbate chattering.

[0046] Nonlinear exponent Select the larger one The value increases the growth rate of the adaptive rate, enhancing the system's robustness against sudden disturbances; a smaller value is selected. The value makes the adaptive process smoother and suppresses high-frequency disturbances.

[0047] S44, Adjust the controller adjustment parameters ( , and ) Larger , and smaller It will improve robustness, but it is prone to causing chattering in the control signal. and For the adjustable parameter of the leakage adaptive rate, a larger one It will increase the growth rate of the adaptive rate, and the larger the rate. This will reduce the rate of increase in the adaptive rate. Adjusting these two parameters can effectively compensate for disturbances and prevent overestimation of gain. The specific adjustment method is as follows: First pass , and Establish basic robust control performance, and then utilize and Fine-tune the leakage adaptive rate to ensure that the system can respond quickly and maintain stable operation when faced with uncertainty.

[0048] S45, Verification and Iteration The adjusted parameters are then fed into the controller to monitor the trajectory tracking error during actual system operation. If the error is not within the preset finite time... If the system converges to zero or within the allowable error range, or if the control input exhibits saturation / severe chattering, return to steps S42 and S44 to fine-tune the parameters until the system meets the convergence time requirements while the control input is smooth and free of saturation.

[0049] Figure 4 This is a schematic diagram of the trajectory tracking experiment results in this embodiment. From... Figure 4 As can be seen, by using the adaptive recursive terminal sliding mode control method of this embodiment, the Mecanum wheeled omnidirectional mobile robot can quickly and accurately track a given reference trajectory when tracking a relatively complex figure-eight trajectory.

[0050] In summary, this embodiment proposes a finite-time control method based on adaptive recursive terminal sliding mode to address the trajectory tracking control problem of a Mecanum wheeled omnidirectional mobile robot. A dynamic model of the Mecanum wheeled omnidirectional mobile robot is established, and unmodeled uncertainties are decomposed and concentrated. Based on this, a novel adaptive recursive terminal sliding surface is proposed. The controller designed based on this sliding surface ensures that the system state is initially located on the sliding surface, improving convergence speed and control accuracy. Furthermore, a novel leaky adaptive rate is proposed. Compared to the ordinary incremental adaptive rate, this leaky adaptive rate avoids the problem of overestimation of adaptive parameters. The controller designed according to this method can quickly and accurately control the Mecanum wheeled omnidirectional mobile robot to track the given desired trajectory, converge within a finite time, adaptively adjust the gain, and effectively handle the influence of system uncertainties and external disturbances.

[0051] Based on the finite-time control method for an omnidirectional mobile robot based on adaptive recursive terminal sliding mode disclosed in the above embodiments, this embodiment correspondingly discloses a finite-time control system for an omnidirectional mobile robot based on adaptive recursive terminal sliding mode. This system serves as the hardware and software implementation carrier for the above embodiments, with each functional module working collaboratively to ensure efficient operation throughout the entire process. For example... Figure 5 As shown, the finite-time control system for the omnidirectional mobile robot based on adaptive recursive terminal sliding mode includes: a model building module, a sliding surface building module, a controller building module, and a control execution module; The model building module is used to establish a robot dynamics model containing parameter uncertainties and external disturbances, the dynamics model concentrating the system's uncertainties; the sliding surface building module is used to define the trajectory tracking error of the dynamics model and construct a non-singular fast recursive terminal sliding surface for the omnidirectional mobile robot; the controller building module is used to construct an adaptive recursive terminal sliding controller for the system based on the sliding surface to offset the nominal dynamic characteristics of the system and overcome system uncertainties; the control execution module is used to use the controller to perform trajectory tracking control on the robot and adjust the controller parameters to make the system state converge within a finite time.

[0052] The embodiments in this specification are described in a progressive manner. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant details can be found in the method section.

[0053] Components not described in detail in this application are all existing conventional technologies and will not be described further here.

[0054] It is understood that the above specific description of the present invention is only for illustrating the present invention and is not limited to the technical solutions described in the embodiments of the present invention. Those skilled in the art should understand that modifications or equivalent substitutions can still be made to the present invention to achieve the same technical effect; as long as the use needs are met, they are all within the protection scope of the present invention.

Claims

1. A control method for an omnidirectional mobile robot based on adaptive recursive terminal sliding mode, applicable to omnidirectional mobile robot systems, characterized in that, include: A robot dynamics model containing parameter uncertainties and external disturbances is established, wherein the dynamics model concentrates the uncertainties of the system; Define the trajectory tracking error of the dynamic model and construct the non-singular fast recursive terminal sliding surface of the omnidirectional mobile robot; Based on the sliding surface, an adaptive recursive terminal sliding mode controller for the system is constructed to counteract the nominal dynamic characteristics of the system and overcome system uncertainties. The robot is tracked and controlled using the controller, and the controller parameters are adjusted to make the system state converge within a finite time.

2. The control method according to claim 1, characterized in that, The dynamic model is constructed based on the kinematic model and motion characteristics of the omnidirectional mobile robot, and the formula is as follows: ， ， in, This is used to describe the robot's actual pose vector. For the desired acceleration, , This represents the robot's lateral and longitudinal displacements, and angles, in the world coordinate system. This represents the yaw angle of the robot body about its geometric center. Indicates the wheel diameter of the robot. This represents the matrix of rated rotational inertia of the robot's wheels. It is the angle after aligning with the Mecanum wheel. , This represents the transformation matrix used to transform the robot from its body coordinate system to the world coordinate system. Indicates control input, The system uncertainty is represented by a set of values, where a and b represent the distances from the robot's edge to the geometric center and the wheel axle to the geometric center, respectively.

3. The control method according to claim 2, characterized in that, The system uncertainties in the dynamic model set include parameter uncertainties, external disturbances, and unmodeled dynamics, as expressed in the formula: ,in, This represents the lumped uncertainty vector acting on the four wheels. and express and The uncertainty of the parameters, among which The coefficient of viscous friction of the system. This represents unmodeled dynamics.

4. The control method according to claim 1, characterized in that, The trajectory tracking error The formula is: ， in, , represents the desired trajectory vector of the system. For the desired horizontal coordinate, For the desired vertical coordinate, The desired heading angle; For longitudinal position error, This is the lateral position error. This is for angular error; This is the robot's actual pose vector. , This represents the robot's lateral and longitudinal displacements in the world coordinate system. This represents the yaw angle of the robot body about its geometric center.

5. The control method according to claim 4, characterized in that, The construction of the robot's non-singular fast recursive terminal sliding surface based on trajectory tracking error includes: Based on trajectory tracking error Calculate intermediate sliding mode variables The intermediate sliding mode variable Further combining the integral term Generate the final nonsingular fast recursive terminal sliding surface The formula is: ， ， ， Integral term The initial value is set to: ， in, For intermediate synovial membrane variables, Non-singular fast recursive terminal sliding surface , It is a function Simplified expression, For the rate of change of error, the linear gain Nonlinear gain Integral gain matrix , , It is a nonlinear exponent used to adjust the dynamic performance of the controller.

6. The control method according to claim 5, characterized in that, The control input of the adaptive recursive terminal sliding mode controller From equivalent control rate and approach control rate Composition; among which, equivalent control rate Used to offset nominal dynamic characteristics based on a dynamic model, driving the system state to move along the sliding surface; approaching the control law. To achieve the sliding mode convergence rate, the system's uncertainty is overcome by utilizing adaptive gain, ensuring that the system state converges to the sliding surface within a finite time; the adaptive gain is generated based on a leakage adaptive mechanism.

7. The control method according to claim 6, characterized in that, The control input of the adaptive recursive terminal sliding mode controller for: ， ， ， ， ， in, ， ， In the formula, This represents the transformation matrix used to transform the robot from its body coordinate system to the world coordinate system. Assign a control matrix to the robot's dynamics system. satisfy , It is the identity matrix; For the symbolic function vector, , , , These are the sliding surface variable vectors. The three components; , It is a gain diagonal matrix, and all its elements are positive numbers. These are adjustable parameters for the boundary layer. For adaptive parameter vectors, Its adaptive rate, and An adjustable parameter for the leakage adaptive rate; For adaptive gain, This represents the angular velocity of each wheel; and Design parameters for the sliding surface. This is the state weight vector; It is a norm of 1, defined as follows: , It is a 2-norm, defined as follows: .

8. The control method according to claim 7, characterized in that, The step of using the controller to perform trajectory tracking control on the robot and adjusting the controller parameters to make the system state converge within a finite time includes: The total convergence time of the system is determined based on the preset control response speed requirements. The total convergence time is the time to reach the sliding surface. Sum of error convergence time composition; Adjust the dynamic parameters of the sliding surface to optimize the error convergence trajectory and balance the dynamic response speed of the system with the control chattering while ensuring system stability; Adjust adaptive parameters to accelerate the estimation of system uncertainties while suppressing high-frequency disturbances and maintaining system robustness; Adjust the controller parameters to control the growth rate of the adaptive rate, effectively compensate for disturbances, and prevent overestimation of gain; Substitute the adjusted parameters into the controller and monitor the trajectory tracking error during actual system operation. If the error fails to converge to zero or within the allowable error range within the preset finite time, or if the control input exhibits saturation / severe chattering, return to the parameter adjustment step until the system meets the convergence time requirement while the control input is smooth and without saturation.

9. The control method according to claim 8, characterized in that, The total convergence time of the system Time to reach the sliding surface With error convergence time The sum of the terms is given by the following formula: ， in: ， ， Among them, the dynamic parameters of the sliding surface For linear gain, For nonlinear gain, and They represent linear gains respectively. and nonlinear gain Corresponding to the The component of each degree of freedom, Nonlinear exponent; adaptive rate parameter Here is the integral gain matrix. Represents the integral gain matrix The 1 eigenvalue, It is a non-linear exponent; Indicates the first in the sliding surface Linear error weighting coefficients for each degree of freedom; and Represent the sliding surface variables and tracking error respectively in the th... Initial values ​​for each degree of freedom; The adjustment of the dynamic parameters of the sliding surface specifically includes: Increase linear gain The numerical value improves the dynamic performance of the sliding surface and accelerates the error correction. Convergence rate far from the equilibrium point; increasing nonlinear gain The numerical value accelerates the error Improve the convergence speed near the equilibrium point and enhance steady-state accuracy; adjust the nonlinear exponent. Change the degree of nonlinearity of the convergence trajectory, in conjunction with , Achieve convergent combinations of "fast-slow" or "slow-fast"; The adjustment of the adaptive parameter specifically involves: Choose a larger integral gain matrix A higher value accelerates the estimation of system uncertainties by the adaptive rate, thus improving control accuracy; a larger nonlinear exponent is selected. The value increases the growth rate of the adaptive rate, enhancing the system's robustness against sudden disturbances; a smaller nonlinear exponent is selected. The value makes the adaptive process smoother and suppresses high-frequency disturbances; The adjustment of the controller parameters is specifically as follows: First pass , ,and Establish basic robust control performance, and then utilize and Fine-tune the leakage adaptive rate to ensure that the system can respond quickly and maintain stable operation when faced with uncertainty.

10. A control system for an omnidirectional mobile robot based on adaptive recursive terminal sliding mode, characterized in that, The system is used to implement the method according to any one of claims 1 to 9, and includes a model building module, a sliding surface building module, a controller building module, and a control execution module; The model building module is used to establish a robot dynamics model containing parameter uncertainties and external disturbances, and the dynamics model concentrates the uncertainties of the system; the sliding surface building module is used to define the trajectory tracking error of the dynamics model and construct the non-singular fast recursive terminal sliding surface of the omnidirectional mobile robot. The controller construction module is used to construct an adaptive recursive terminal sliding mode controller for the system based on the sliding surface, so as to counteract the nominal dynamic characteristics of the system and overcome the uncertainty of the system. The control execution module is used to perform trajectory tracking control on the robot using the controller, and to adjust the controller parameters so that the system state converges within a finite time.

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