Four-Mecanum-wheel mobile robot fixed time path tracking control method based on sliding mode

Abstract

The invention discloses a four-Mecanum-wheel mobile robot fixed time path tracking control method based on a sliding mode, and relates to the technical field of control. Aiming at the problems of parameter uncertainty, external disturbance and the like in a four-Mecanum wheel mobile robot system, the method combines neural network compensation and a sliding mode control technology to construct a fixed time sliding mode controller based on a neural network: establishing a system kinematics and dynamics fusion model containing the parameter uncertainty and the external disturbance; designing a novel fast nonsingular terminal sliding mode surface; a radial basis function neural network is adopted to approach system coupling uncertainty in real time, a controller is designed in combination with an adaptive updating law and a smooth sign function, high-precision path tracking is achieved, and buffeting is effectively restrained. According to the control method provided by the invention, rapid convergence of tracking errors of the four-Mecanum-wheel mobile robot can be realized, and the method has high robustness, high tracking precision and a good buffeting suppression effect.

Description

Technical Field

[0001] This invention relates to the field of robot control technology, specifically to a fixed-time path tracking control method for a four-Mecanum wheel mobile robot based on sliding mode. Background Technology

[0002] As a typical representative of mobile robots, the four-Mecanum wheel mobile robot is widely used in various fields such as medical assistance, warehousing and logistics sorting, military reconnaissance, and home services due to its ability to achieve three degrees of freedom in a plane without adjusting the wheel orientation. Through the coordinated action of its four independent drive wheels, the four-Mecanum wheel mobile robot can flexibly complete translation, rotation, and compound movements, making it particularly suitable for high-precision operations in confined spaces. However, the four-Mecanum wheel mobile robot faces many technical challenges in actual path tracking. On the one hand, the system suffers from uncertainties in parameters such as the viscous friction coefficient and inertia matrix, and is also affected by external disturbances such as ground friction and external impacts, making it difficult for traditional control methods to guarantee tracking accuracy.

[0003] Among existing path tracking control methods, sliding mode control is widely used due to its strong robustness. However, traditional sliding mode control suffers from chattering, affecting the smoothness of robot path tracking. While terminal sliding mode control can achieve finite-time convergence, it suffers from singularity issues, and the convergence time depends on the initial state. The emergence of fixed-time control theory solves the problem of convergence time being dependent on initial conditions, ensuring that the system converges within a fixed time. However, most existing fixed-time control methods assume that the uncertainty boundary of the system is known, but in practical engineering, this boundary is often difficult to obtain accurately, limiting its application effectiveness.

[0004] Neural networks, with their powerful nonlinear approximation capabilities, provide an effective way to handle unknown uncertainties. Among them, radial basis function neural networks (RBNs) have a simple structure and high approximation accuracy, and have been used to compensate for modeling errors in robot systems. However, combining neural networks with fixed-time sliding mode control to simultaneously address the coordinated control problem of parameter uncertainties and external disturbances remains a challenge in current research. Existing techniques suffer from slow convergence speed, poor robustness, and inadequate chatter suppression, making it difficult to meet the high-precision, fast-response path tracking requirements of robot systems.

[0005] In summary, a fixed-time path tracking control method based on sliding mode control and neural network control needs to be developed for a four-Mecanum wheel mobile robot. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention proposes a fixed-time path tracking control method for a four-Mecanum wheel mobile robot based on sliding mode. By designing a novel fast non-singular terminal sliding surface and combining it with the uncertainty compensation capability of radial basis function neural networks, a fixed-time high-precision path tracking method for the four-Mecanum wheel mobile robot is achieved, while effectively suppressing controller chattering.

[0007] To achieve the above objectives, the present invention provides a fixed-time path tracking control method for a four-Mecanum wheel mobile robot based on sliding mode, specifically comprising the following steps:

[0008] S1. Establish a system model of a four-Mecanum wheel mobile robot with parameter uncertainties and external disturbances. The system model integrates kinematic equations and dynamic equations.

[0009] S2. Define the path tracking error vector of the four Mecanum wheel mobile robot system, and construct a novel fast non-singular terminal sliding surface. The sliding surface has fixed-time convergence characteristics and no singularity problem.

[0010] S3. A radial basis function neural network is used to approximate the coupling uncertainty of the four-Mecanum wheel mobile robot system. Combined with adaptive control technology, a fixed-time sliding mode controller based on the neural network is constructed to achieve high-precision trajectory tracking and effectively suppress chattering.

[0011] The present invention is further configured such that the establishment method of the four-Mecanum wheel mobile robot system model containing parameter uncertainties and external disturbances includes:

[0012] S11. Establish the kinematic equations of the four-Mecanum wheel mobile robot;

[0013] S111, Define the global coordinate system O w X w Y w With the local coordinate system O of the vehicle body b X b Y b The pose vector of the four-Mecanum wheeled mobile robot is

[0014]

[0015] In the formula, x w y w These are the position coordinates in the global coordinate system. For heading angle;

[0016] Obtain coordinate system O w X w Y w With coordinate system O b X b Yb Transformation matrix between:

[0017]

[0018] S112. Construct the initial kinematic velocity equations for the four-Mecanum wheel mobile robot:

[0019]

[0020] In the formula, Let l1 and l2 be the velocity vectors in the local coordinate system, l1 and l2 be the longitudinal and lateral distances from the wheel center to the vehicle body center, respectively, r be the wheel radius, and θ be the velocity vector. i (i = 1, 2, 3, 4) represents the turning angle of the i-th wheel. Let be the angular velocity of the i-th wheel;

[0021] S113. Taking the second derivative of the pose vector and combining it with the derivative terms of the transformation matrix, we obtain the final kinematic equations of the four-Mecanum wheel mobile robot containing acceleration information:

[0022]

[0023] In the formula, The Mecanum round coupling matrix, for The derivative matrix, Let be the second derivative of the pose vector Θ, where and These represent linear accelerations along the X and Y axes, respectively. Angular acceleration representing the direction of the heading angle. Let be the robot's angular acceleration vector.

[0024] for The first derivative,

[0025] S12. The methods for establishing the dynamic equations of the four-Mecanum wheel mobile robot include:

[0026] S121. Establish the initial dynamic equations for the four-Mecanum wheel mobile robot:

[0027]

[0028] In the formula, J is the inertia matrix, B=B0+ΔB is the viscous friction matrix, B0 is the nominal part, ΔB is the uncertain part; χ is the external disturbance vector, and u is the control input signal;

[0029] S122. Rewrite the initial dynamic equations in a form that separates the nominal and uncertain parts:

[0030]

[0031] In the formula, This represents the system coupling uncertainty vector;

[0032] S13, The specific methods for fusing the kinematic and dynamic equations of the four-Mecanum wheel mobile robot include:

[0033] Substituting the dynamic equations of the four-Mecanum wheel mobile robot into the kinematic equations, we obtain the second-order state-space model of the system:

[0034]

[0035] In the formula, The equivalent control input signal is M, where M is the coupling matrix.

[0036]

[0037] The present invention is further configured such that: the novel method for constructing a fast non-singular terminal sliding surface includes:

[0038] S21. Define the path tracking error vector for a four-Mecanum wheel mobile robot system:

[0039]

[0040] In the formula, Let ε1 be the position error in the X-axis direction, ε2 be the position error in the Y-axis direction, and ε3 be the angle error in the heading direction.

[0041] The velocity error equation for a four-Mecanum wheel mobile robot is expressed as follows:

[0042]

[0043] In the formula, Represents the velocity error in the X and Y axis directions and the angular velocity error in the heading angle direction. Let be the second derivative of the desired pose vector, where and These represent the desired linear accelerations in the X and Y directions, respectively. The angular acceleration is the expected value in the direction of the heading angle.

[0044] S22. Constructing a novel fast non-singular terminal sliding surface:

[0045]

[0046] In the formula, α1=diag{α 11 ,α 12 ,α 13} and α2=diag{α 21 ,α 22 ,α 23} is the gain matrix, α i,j >0 represents a design constant, i = 1, 2, j = 1, 2, 3, Sig κ (ε)=[|ε1| κ sign(ε1),|ε2| κ sign(ε2),|ε3| κ sign(ε3)] T , sign() represents the sign function, κ>1 is the convergence rate parameter of the design, Q(ε)=[q(ε1),q(ε2),q(ε3)] T ,q(ε j (j=1,2,3) is a piecewise nonlinear function that satisfies the following equation:

[0047]

[0048] In the formula, For the design constant, To adjust the parameters.

[0049] The present invention is further configured such that the design method of the fixed-time sliding mode controller based on neural networks includes:

[0050] S31. A radial basis function neural network is used to approximate the coupling uncertainty γ of a four-Mecanum wheel mobile robot system. The network expression is:

[0051] γ=ω T φ(Z)+ξ(Z)

[0052] In the formula, For network input vectors, Let Z be the weight vector, and ξ(Z) be the bounded approximation error, satisfying... φ(Z) is the Gaussian function, and its expression is:

[0053]

[0054] In the formula, c k d k Let be the center and width parameters of the k-th hidden layer neuron, respectively, where k = 1, 2, ..., p, and p is the number of hidden layer neurons;

[0055] Design an adaptive update law for the weight vector:

[0056]

[0057] In the formula, Λ j >0 indicates a positive definite diagonal matrix. Γ is the estimated value of the weight vector ω. j >0 is the adjustment constant, j = 1, 2, 3;

[0058] S32. Construct a fixed-time sliding mode controller based on a neural network:

[0059]

[0060] In the formula, K1=diag{K 11 ,K 12 ,K 13} and K2=diag{K 21 ,K 22 ,K 23} is the gain matrix, K i,j >0 represents a design constant, i = 1, 2, j = 1, 2, 3, Y κ-1 (ε)=diag{|ε1| κ-1 ,|ε2| κ-1 ,|ε3| κ-1}, It is the inverse of the coupling matrix.

[0061] in The expression is:

[0062]

[0063] This invention provides a fixed-time path tracking control method for a four-Mecanum wheel mobile robot based on sliding mode, which has the following advantages:

[0064] (1) The present invention designs a novel fast non-singular terminal sliding surface, which combines piecewise nonlinear functions and power term structures. This avoids the singularity problem of traditional terminal sliding and ensures fixed-time convergence characteristics, ensuring that the convergence time is independent of the initial state.

[0065] (2) This invention uses a radial basis function neural network to approximate the coupling uncertainty of the system. It does not require information on the uncertainty boundary. The network weights are adjusted in real time through an adaptive update law, which effectively compensates for parameter uncertainty and external disturbances and improves the robustness of the system. At the same time, a smooth sign function is introduced in the controller to replace the traditional sign function, and the control gain configuration is optimized to effectively suppress the chattering phenomenon inherent in sliding mode control.

[0066] (3) The control method proposed in this invention has proven the actual fixed-time stability of the system through Lyapunov stability analysis. The tracking error can converge to a small neighborhood near zero within a fixed time. Compared with traditional control methods, it has a faster convergence speed and higher tracking accuracy. Attached Figure Description

[0067] Figure 1 This is a block diagram of the four-Mecanum wheel mobile robot architecture for verifying the algorithm of this invention;

[0068] Figure 2 This is a block diagram of the control system structure of the four-Mecanum wheel mobile robot of the present invention;

[0069] Figure 3 This invention relates to a path tracking contour curve based on a fixed-time sliding mode controller using a neural network.

[0070] Figure 4 The path tracking curves in three directions are shown in the fixed-time sliding mode controller based on neural networks of this invention.

[0071] Figure 5 The path tracking error curves in three directions are shown for the fixed-time sliding mode controller based on neural networks of this invention.

[0072] Figure 6 The curve showing the change of the sliding surface of the fixed-time sliding mode controller based on the neural network in this invention;

[0073] Figure 7 The path tracking curve of a conventional non-singular terminal sliding mode controller is compared with the fixed-time sliding mode controller based on neural networks of the present invention.

[0074] Figure 8 The path tracking error curves of a conventional non-singular terminal sliding mode controller are compared with the fixed-time sliding mode controller based on neural networks of this invention. Detailed Implementation

[0075] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0076] Please see Figure 1-8 The present invention provides the following technical solution: a fixed-time path tracking control method for a four-Mecanum wheel mobile robot based on sliding mode, specifically including the following steps:

[0077] S1. Establish a four-Mecanum wheel mobile robot system model, which includes parameter uncertainties and external disturbances. The specific construction method of the four-Mecanum wheel mobile robot system model includes:

[0078] S11. Establish the kinematic equations of the four-Mecanum wheel mobile robot;

[0079] S111. Provide a block diagram of the architecture of a four-Mecanum wheel mobile robot as follows: Figure 1 As shown, a global coordinate system O is defined. w X w Y w With the local coordinate system O of the vehicle body b X b Y b The pose vector of the four-Mecanum wheeled mobile robot is

[0080]

[0081] In the formula, x w y w These are the position coordinates in the global coordinate system. For heading angle;

[0082] Obtain coordinate system O w X w Y w With coordinate system O b X b Y b Transformation matrix between:

[0083]

[0084] S112. Construct the initial kinematic velocity equations for the four-Mecanum wheel mobile robot:

[0085]

[0086] In the formula,

[0087] Let l1 and l2 be the velocity vectors in the local coordinate system, l1 and l2 be the longitudinal and lateral distances from the wheel center to the vehicle body center, respectively, r be the wheel radius, and θ be the velocity vector. i (i = 1, 2, 3, 4) represents the turning angle of the i-th wheel, θ i Let be the angular velocity of the i-th wheel;

[0088] S113, Based on Transformation Matrix Starting with the initial kinematic equations, the velocity relationships in the global coordinate system are derived. The second derivative of the pose vector is then calculated to obtain the final kinematic equations of the four-Mecanum wheel mobile robot, which include acceleration information.

[0089]

[0090] In the formula, The Mecanum round coupling matrix, for The derivative matrix, Let be the second derivative of the pose vector Θ, where and These represent linear accelerations along the X and Y axes, respectively. Angular acceleration representing the direction of the heading angle. Let be the robot's angular acceleration vector.

[0091] for The first derivative,

[0092] S12. Establish the dynamic equations of the four-Mecanum wheel mobile robot;

[0093] S121. Construct the initial dynamic equations for the four-Mecanum wheel mobile robot:

[0094]

[0095] In the formula, J is the inertia matrix, B=B0+ΔB is the viscous friction matrix, B0 is the nominal part, ΔB is the uncertain part; χ is the external disturbance vector, and u is the control input signal;

[0096] S122. Rewrite the initial dynamic equations of the four-Mecanum wheel mobile robot in a form that separates the nominal and uncertain parts:

[0097]

[0098] In the formula, This represents the system coupling uncertainty vector.

[0099] S13. Integrating kinematic and dynamic equations, a model of a four-Mecanum wheel mobile robot system is established, including:

[0100] Substituting the dynamic equations into the kinematic equations, and rearranging, we obtain the second-order state-space model of the system:

[0101]

[0102] In the formula,

[0103] The equivalent control input signal is M, where M is the coupling matrix.

[0104]

[0105] S2. Define the tracking error vector of the four Mecanum wheel mobile robot system and construct a novel fast non-singular terminal sliding surface. The specific construction method includes:

[0106] S21. Define the tracking error vector for a four-Mecanum wheel mobile robot:

[0107]

[0108] In the formula, Let ε1 be the position error in the X-axis direction, ε2 be the position error in the Y-axis direction, and ε3 be the angle error in the heading direction.

[0109] The velocity error equation for a four-Mecanum wheel mobile robot is expressed as follows:

[0110]

[0111] In the formula, Represents the velocity error in the X and Y axis directions and the angular velocity error in the heading angle direction. Let be the second derivative of the desired pose vector, where and These represent the desired linear accelerations in the X and Y directions, respectively. The angular acceleration is the expected value in the direction of the heading angle.

[0112] S22. Constructing a piecewise nonlinear function:

[0113]

[0114] In the formula, j = 1, 2, 3, For the design constant, To adjust the parameters;

[0115] Based on the piecewise nonlinear function q(ε) j Constructing a novel fast non-singular terminal sliding surface:

[0116]

[0117] In the formula, α1=diag{α 11 ,α 12 ,α 13} and α2=diag{α 21 ,α 22 ,α 23} is the gain matrix, α i,j >0 represents a design constant, i = 1, 2, j = 1, 2, 3, Sig κ (ε)=[|ε1| κ sign(ε1),|ε2| κ sign(ε2),|ε3| κ sign(ε3)] T, sign() represents the sign function, κ>1 is the convergence rate parameter of the design, Q(ε)=[q(ε1),q(ε2),q(ε3)] T .

[0118] It should be noted that parameters α1, α2, and κ together determine the dynamic characteristics of the sliding surface. When the error is large, the power term Sig... κ The piecewise nonlinear function Q(ε) plays a dominant role, ensuring rapid convergence; when the error is small, the piecewise nonlinear function Q(ε) plays a dominant role, achieving high-precision approximation. Parameters Smaller It can improve tracking speed, but may lead to increased overshoot, so adjustments need to be made based on the actual scenario.

[0119] S3. Construct a fixed-time sliding mode controller based on a neural network to eliminate the effects of external disturbances and parameter uncertainties. Specific construction methods include:

[0120] S31. A radial basis function neural network is used to approximate the coupling uncertainty γ of a four-Mecanum wheel mobile robot system. The network expression is:

[0121] γ=ω T φ(Z)+ξ(Z)

[0122] In the formula, For network input vectors, Let Z be the weight vector, and ξ(Z) be the bounded approximation error, satisfying... φ(Z) is the Gaussian function, and its expression is:

[0123]

[0124] In the formula, c k d k Let be the center and width parameters of the k-th hidden layer neuron, respectively, where k = 1, 2, ..., p, and p is the number of hidden layer neurons;

[0125] Design an adaptive update law for the weight vector:

[0126]

[0127] In the formula, Λ j >0 indicates a positive definite diagonal matrix. Γ is the estimated value of the weight vector ω. j >0 is the adjustment constant, j = 1, 2, 3;

[0128] S32. Construct a fixed-time sliding mode controller based on a neural network:

[0129]

[0130] In the formula, K1=diag{K 11 ,K 12 ,K 13} and K2=diag{K 21 ,K 22 ,K 23} is the gain matrix, K i,j >0 represents a design constant, i = 1, 2, j = 1, 2, 3, Y κ-1 (ε)=diag{|ε1| κ-1 ,|ε2| κ-1 ,|ε3| κ-1}, It is the inverse of the coupling matrix.

[0131] in The expression is:

[0132]

[0133] To suppress chattering in the controller, this invention replaces the traditional sign function with the following smooth sign function:

[0134]

[0135] In the formula, j = 1, 2, 3, and k > 0 are smoothing coefficients, which can be adjusted according to the effect of chatter suppression.

[0136] To further illustrate, a block diagram of the control system for a four-Mecanum wheeled mobile robot is provided as follows: Figure 2 As shown, for a four-Mecanum wheel mobile robot system with unknown dynamic parameters and external disturbances, under the action of a fixed-time sliding mode controller based on a neural network, the sliding surface will converge to the residual set of zero within a fixed time. Both the fast non-singular terminal sliding surface and the weight error can converge to their corresponding compact sets within a fixed time. If the state of the four-Mecanum wheel mobile robot system moves to the residual set of the fast non-singular terminal sliding surface ζ = 0, then the tracking error of the system along this sliding surface will converge to the residual set within the fixed time T as described below. s The area within the origin can be any small region around it.

[0137]

[0138] In the formula, 0 < v < 1, Γ min {·} represents the smallest eigenvalue of the matrix.

[0139] The following is a supplement to the specific details of the key lemma used:

[0140] Lemma 1: If there exists a Lyapunov function Make in κ > 0, l > 1, 0 < d < 1, If is a constant, then the system is actually stable in a fixed time, and the upper bound of the convergence time is . Where 0 < v < 1.

[0141] Lemma 2: For any vector When 0 < ν1 < 1 When ν2>1

[0142] Lemma 3: For any real numbers a, b and positive numbers m > 0, q > 1, p > 1, where p and q satisfy (q-1)(p-1) = 1, we have

[0143] Proof: Choose the Lyapunov function

[0144] V3 = V1 + V2

[0145] in This represents the weight estimation error.

[0146] Take the first derivative with respect to V1:

[0147]

[0148] Differentiating the expression for the fast nonsingular terminal sliding surface, we get:

[0149]

[0150] In the formula, Y κ-1 (ε)=diag{|ε1| κ-1 ,|ε2| κ-1 ,|ε3| κ-1};

[0151] Substitute the designed controller into the above formula. It can be written as:

[0152]

[0153] Using Lemma 2, by performing inequality bounding, we obtain the following equation:

[0154]

[0155] In the formula, Γ min {K1} and Γ min {K2} are the smallest eigenvalues ​​of matrices K1 and K2, respectively;

[0156] Based on the above scaling, we can conclude that:

[0157]

[0158] Take the first derivative with respect to V2:

[0159]

[0160] Adaptive update law Substituting, we get:

[0161]

[0162] Using Lemma 3, by scaling the above equation, we get:

[0163]

[0164] In the formula, k 1j ,k 2j To satisfy a j Positive numbers greater than 0 It is a bounded constant;

[0165] Based on the above analysis, we can conclude that:

[0166]

[0167] In the formula, for The largest eigenvalue; It is a bounded constant.

[0168] According to Lemma 1, the four-Mecanum wheel mobile robot system is practically fixed-time stable, and the upper bound of its convergence time is:

[0169]

[0170] In the formula, 0 < v < 1 are adjustment parameters, and the system state eventually converges to the residual set:

[0171]

[0172] In summary, sliding surface Weight estimation error All can be achieved within a fixed time T≤T max The convergence time of the system tracking error remains bounded, converging to a small neighborhood near zero.

[0173] At this point, the residual set converges to zero on the sliding surface. when At that time, the following conditions are met:

[0174]

[0175] Convergence analysis is discussed in the following two cases:

[0176] Scenario 1: When At that time, we can obtain:

[0177]

[0178] Choose the following Lyapunov functions:

[0179]

[0180] Differentiate with respect to V4 and convert the piecewise nonlinear function q(ε) j ) = sig μ (ε j Substitute:

[0181]

[0182] Using Lemma 2 and Lemma 3, we can obtain:

[0183]

[0184] In the formula, μ1=2 (μ+1) / 2 Γ min {α1}, μ2=2 (κ+1) / 2 3 (1-κ) / 2 Γ min {α2}.

[0185] Case 2: When |ε|<ζ, the piecewise nonlinear function will be... Substituting into the sliding surface expression, we get:

[0186]

[0187] Differentiating V4, we obtain the following inequality:

[0188]

[0189] This inequality shows that the V4 exponential convergence eventually leads to the following equation:

[0190] Combining the two scenarios above, and using Lemma 1, the tracking error ε will be within a fixed time T. s Converging inward to the residual set:

[0191]

[0192] Simulation Experiment

[0193] To verify the feasibility and advantages of the proposed solution, a closed-loop system of a four-Mecanum wheel mobile robot was simulated in the Simulink simulation environment.

[0194] The parameters for the mobile robot body and controller are selected as follows: β=1.7, μ=0.7, κ=1.5, α1=diag{1.2,1.2,1.2}, α2=diag{4,4,4}, K1=diag{1.2,1.1,1.4}, K2=diag{3,3,3}, Λ j =Γ j =8.5; J=0.098, B0=0.085, ΔB=0.2B0.

[0195] The perturbation is set as: χ=[sin(20πt),1.2cos3t+0.8sin(40πt),1.6cos2t,2.6sin(50πt)] T ;

[0196] The desired path uses a hyoid curve, and its expression is: x d =5cos(0.1t), y d =2.5sin(0.2t),

[0197] The initial conditions are set to Θ(0) = [4.0, 0.4, 0.1]. T ,

[0198] Figure 3 The path tracking profile curve of a four-Mecanum wheel mobile robot under a fixed-time sliding mode controller based on a neural network designed for this invention is shown. Results demonstrate that the proposed control scheme possesses excellent path tracking capability, and the actual trajectory closely follows the desired lemniscate path.

[0199] Figure 4 The figure shows the path tracking curves of a four-Mecanum wheel mobile robot with a fixed-time sliding mode controller based on a neural network designed for this invention, in the X-axis, Y-axis, and heading angle directions. As can be observed from the figure, the tracking effect between the actual position and the desired position is stable throughout the simulation time, with no significant fluctuations. The heading angle remains consistently near the desired trajectory, verifying that the controller has high tracking accuracy in all motion dimensions.

[0200] Figure 5The figure shows the path tracking error curves of the four Mecanum wheel mobile robot with a fixed-time sliding mode controller based on a neural network designed for this invention in the X-axis, Y-axis, and heading angle directions. As can be seen from the figure, the tracking error converges rapidly to near zero within 3 seconds, indicating that the system can quickly eliminate the initial deviation and maintain a high-precision tracking state, effectively suppressing the influence of disturbances and uncertainties.

[0201] Figure 6 The variation curves of the sliding surface of the fixed-time sliding mode controller based on neural networks designed for this invention are shown. The results show that the sliding surface can quickly approach the neighborhood of zero and remain stable after convergence without obvious oscillations. This indicates that the designed controller can ensure that the system state quickly enters the sliding mode motion stage, while chattering is effectively suppressed.

[0202] Figure 7 This is the path tracking contour curve of a four-Mecanum wheel mobile robot under a traditional non-singular terminal sliding mode controller. Figure 3 and Figure 7 The comparison shows that the path tracking accuracy of the four-Mecanum wheel mobile robot under the fixed-time sliding mode controller based on neural networks is higher.

[0203] Figure 8 This represents the path tracking curves of a four-Mecanum wheel mobile robot under a traditional non-singular terminal sliding mode controller in the X, Y, and heading directions. Figure 8 It is known that the convergence times of a four-Mecanum wheel mobile robot under a traditional non-singular terminal sliding mode controller in the X-axis, Y-axis, and heading angle are approximately 6s, 8s, and 4s, respectively; Figure 4 It can be seen that the convergence times of the four-Mecanum wheel mobile robot under the fixed-time sliding mode controller based on neural networks are approximately 3s, 2.5s, and 2s in the X-axis, Y-axis, and heading angle directions, respectively. The comparative results show that the fixed-time sliding mode controller based on neural networks enables the four-Mecanum wheel mobile robot to achieve faster trajectory convergence. The neural network fixed-time sliding mode control scheme proposed in this invention has significant advantages in both dynamic response performance and steady-state control accuracy.

[0204] In summary, simulation results show that the fixed-time sliding mode controller based on neural networks proposed in this invention can achieve fixed-time convergence of the four-Mecanum wheel mobile robot while avoiding singularity problems, with high tracking accuracy, strong robustness to disturbances and system uncertainties, and effective suppression of chattering.

[0205] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A fixed-time path tracking control method for a four-Mecanum wheel mobile robot based on sliding mode, characterized in that, Specifically, the following steps are included: S1. Establish a system model of a four-Mecanum wheel mobile robot with parameter uncertainties and external disturbances. The system model integrates kinematic equations and dynamic equations. S2. Define the path tracking error vector of the four Mecanum wheel mobile robot system, and construct a novel fast non-singular terminal sliding surface. The sliding surface has fixed-time convergence characteristics and no singularity problem. S3. A radial basis function neural network is used to approximate the coupling uncertainty of the four-Mecanum wheel mobile robot system. Combined with adaptive control technology, a fixed-time sliding mode controller based on the neural network is constructed to achieve high-precision trajectory tracking and effectively suppress chattering.

2. The fixed-time path tracking control method for a four-Mecanum wheel mobile robot based on sliding mode, as described in claim 1, is characterized in that... The methods for establishing a model of a four-Mecanum wheel mobile robot system containing parameter uncertainties and external disturbances include: S11. Define the global coordinate system and the local coordinate system of the vehicle body, derive the coordinate transformation matrix and the equation relating velocity and attitude, and establish the kinematic equations of the four-Mecanum wheel mobile robot. S12. Considering the nominal and uncertain parts of the viscous friction matrix, an external disturbance vector is introduced to establish the dynamic equations of the four-Mecanum wheel mobile robot. S13. By integrating the kinematic and dynamic equations of the four-Mecanum wheel mobile robot, parameter uncertainties and external disturbances are combined into a system coupling uncertainty vector, resulting in a complete system state space model.

3. The fixed-time path tracking control method for a four-Mecanum wheel mobile robot based on sliding mode, as described in claim 2, is characterized in that... The methods for establishing a model of a four-Mecanum wheel mobile robot system include: The operation of S11 is as follows: S111, Define the global coordinate system O w X w Y w With the local coordinate system O of the vehicle body b X b Y b The pose vector of the four-Mecanum wheeled mobile robot is In the formula, x w y w These are the position coordinates in the global coordinate system. For heading angle; Obtain coordinate system O w X w Y w With coordinate system O b X b Y b Transformation matrix between: S112. Construct the initial kinematic velocity equations for the four-Mecanum wheel mobile robot: In the formula, Let l1 and l2 be the velocity vectors in the local coordinate system, l1 and l2 be the longitudinal and lateral distances from the wheel center to the vehicle body center, respectively, r be the wheel radius, and θ be the velocity vector. i (i = 1, 2, 3, 4) represents the turning angle of the i-th wheel. Let be the angular velocity of the i-th wheel; S113. Taking the second derivative of the pose vector and combining it with the derivative terms of the transformation matrix, we obtain the final kinematic equations of the four-Mecanum wheel mobile robot containing acceleration information: In the formula, The Mecanum round coupling matrix, for The derivative matrix, Let be the second derivative of the pose vector Θ, where and These represent linear accelerations along the X and Y axes, respectively. Angular acceleration representing the direction of the heading angle. Let be the robot's angular acceleration vector. for The first derivative, The specific operation of S12 is as follows: S121. Establish the initial dynamic equations for the four-Mecanum wheel mobile robot: In the formula, J is the inertia matrix, B=B0+ΔB is the viscous friction matrix, B0 is the nominal part, ΔB is the uncertain part; χ is the external disturbance vector, and u is the control input signal; S122. Rewrite the initial dynamic equations in a form that separates the nominal and uncertain parts: In the formula, This represents the system coupling uncertainty vector; The specific operation of S13 is as follows: Substituting the dynamic equations of the four-Mecanum wheel mobile robot into the kinematic equations, we obtain the second-order state-space model of the system: In the formula, The equivalent control input signal is M, where M is the coupling matrix.

4. The fixed-time path tracking control method for a four-Mecanum wheel mobile robot based on sliding mode, as described in claim 1, is characterized in that... The novel method for constructing a fast non-singular terminal sliding surface includes: S21. Define the path tracking error vector for a four-Mecanum wheel mobile robot system: In the formula, Let ε1 be the position error in the X-axis direction, ε2 be the position error in the Y-axis direction, and ε3 be the angle error in the heading direction. The velocity error equation for a four-Mecanum wheel mobile robot is expressed as follows: In the formula, Represents the velocity error in the X and Y axis directions and the angular velocity error in the heading angle direction. Let be the second derivative of the desired pose vector, where and These represent the desired linear accelerations in the X and Y directions, respectively. The angular acceleration is the expected value in the direction of the heading angle. S22. Constructing a novel fast non-singular terminal sliding surface: In the formula, α1=diag{α 11 ,α 12 ,α 13 } and α2=diag{α 21 ,α 22 ,α 23 } is the gain matrix, α i,j >0 represents a design constant, i = 1, 2, j = 1, 2, 3, Sig κ (ε)=[|ε1| κ sign(ε1),|ε2| κ sign(ε2),|ε3| κ sign(ε3)] T sign(·) represents the sign function, κ>1 is the convergence rate parameter of the design, and Q(ε)=[q(ε1),q(ε2),q(ε3)] T ,q(ε j (j=1,2,3) is a piecewise nonlinear function that satisfies the following equation: In the formula, For the design constant, To adjust the parameters.

5. A fixed-time path tracking control method for a four-Mecanum wheel mobile robot based on sliding mode, as described in claim 1, is characterized in that... The design method of the fixed-time sliding mode controller based on the neural network is as follows: S31. A radial basis function neural network is used to approximate the coupling uncertainty γ of a four-Mecanum wheel mobile robot system. The network expression is: c = ω T φ(Z)+ξ(Z) In the formula, For network input vectors, Let Z be the weight vector, and ξ(Z) be the bounded approximation error, satisfying... φ(Z) is the Gaussian function, and its expression is: In the formula, c k d k Let be the center and width parameters of the k-th hidden layer neuron, respectively, where k = 1, 2, ..., p, and p is the number of hidden layer neurons; Design an adaptive update law for the weight vector: In the formula, Λ j >0 indicates a positive definite diagonal matrix. Γ is the estimated value of the weight vector ω. j >0 is the adjustment constant, j = 1, 2, 3; S32. Construct a fixed-time sliding mode controller based on a neural network: In the formula, K1=diag{K 11 ,K 12 ,K 13 } and K2=diag{K 21 ,K 22 ,K 23 } is the gain matrix, K i,j >0 represents a design constant, i = 1, 2, j = 1, 2, 3, Y κ-1 (ε)=diag{|ε1| κ-1 ,|ε2| κ-1 ,|ε3| κ-1 }, It is the inverse of the coupling matrix. in The expression is: By utilizing a fixed-time sliding mode controller based on neural networks, the parameter uncertainties and external disturbances in the four-Mecanum wheel mobile robot system can be effectively addressed, enabling the four-Mecanum wheel mobile robot to achieve high-precision tracking of the desired path, while improving the system's response speed and robustness.

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