Robot path tracking method based on time delay compensation and input saturation control

Abstract

This invention discloses a robot path tracking method, medium, and device based on time-delay compensation and input saturation control, relating to the field of robot control. The robot path tracking method based on time-delay compensation and input saturation control mainly includes: constructing a time-varying distributed observer using time-varying gain; obtaining a full-drive model using virtual controller parameters; and obtaining the leader's three-dimensional state information using the time-varying distributed observer; constructing a local tracking error and a virtual controller; obtaining the adaptive rate and control torque using an auxiliary compensation system; obtaining a dynamic compensator and controller based on the adaptive rate and control torque; and controlling the follower and monitoring and tracking the leader in real time using the controller based on the leader's three-dimensional state information. Implementing the robot path tracking method, medium, and device based on time-delay compensation and input saturation control provided by this invention can improve the robot's control performance when input time delay and input saturation coexist.

Description

Technical Field

[0001] This invention relates to the field of robot control, and more specifically, to a robot path tracking method, medium, and device based on time delay compensation and input saturation control. Background Technology

[0002] With the rapid development of robotics technology, mobile robot path tracking control has been widely applied in industries such as manufacturing, logistics, healthcare, and services. Accurate path tracking is crucial for these applications, improving both the efficiency and safety of robot operations. Input delay and input saturation are two common and significant issues that cannot be ignored in the implementation of path tracking control.

[0003] Input lag refers to the time delay between the generation of a control command and its actual application to the system. In practical applications, due to delays in sensors, processors, and actuators, input lag is unavoidable. This lag leads to decreased control performance and, in severe cases, even system instability. Ensuring system stability and trajectory tracking accuracy in the presence of input lag is an important research topic.

[0004] Input saturation refers to the situation where the input signal to a control system exceeds the physical limitations of the actuator. In practical applications, actuators exhibit saturation characteristics; exceeding their maximum or minimum input limits can lead to system response distortion, overshoot, or oscillation, and even system instability. Input saturation limits the effective range of control inputs, resulting in decreased control performance and affecting the system's precise control. Designing effective control strategies to ensure system stability and path-tracking accuracy in the presence of input saturation is an important research topic. In practical applications, the impact of input saturation cannot be ignored because actuators are subject to physical limitations during operation, such as maximum voltage, current, or torque constraints. When the control input exceeds these limits, the actuator cannot operate as expected, causing the actual output to deviate from the target value. This deviation not only reduces the system's response speed and control accuracy but may also trigger severe oscillations or instability, jeopardizing system safety. Therefore, control strategies addressing input saturation must consider how to ensure system stability and high-precision path-tracking capability under limited control input conditions.

[0005] In robot path tracking control, when input delay and input saturation coexist, existing technologies struggle to effectively address the following technical shortcomings: Existing control methods cannot effectively compensate for input delay, leading to slower system response, decreased tracking accuracy, and even system instability. They also cannot effectively handle input saturation, easily causing system response distortion, overshoot, or oscillation, potentially resulting in system instability and impacting overall system performance. Furthermore, when both problems exist simultaneously, traditional control strategies cannot simultaneously compensate for input delay and limit input saturation, further degrading system performance. Therefore, ensuring system stability and path tracking accuracy while simultaneously addressing input delay and input saturation is a crucial technical problem that urgently needs to be solved.

[0006] The existing control schemes have many shortcomings, and the existing control schemes and their defects are as follows:

[0007] (1) Traditional PID Control Method: The traditional proportional-integral-derivative (PID) controller is widely used in various control systems. PID controllers have advantages such as simple design and convenient implementation. However, the PID control method performs poorly when dealing with input time delay and input saturation problems. For input time delay, the PID controller cannot effectively compensate, resulting in a slower system response speed and reduced tracking accuracy. For input saturation, the PID controller is prone to overshoot or oscillation, which cannot guarantee the stability of the system.

[0008] (2) Predictive Control-Based Methods: Model Predictive Control (MPC) designs control inputs by predicting the future behavior of the system, effectively addressing input time delay issues. However, MPC methods suffer from high computational complexity and poor real-time performance, making them particularly difficult to apply in mobile robot systems with limited computing resources. Furthermore, MPC methods require complex constraints when dealing with input saturation, increasing algorithm complexity and limiting their effectiveness in practical applications.

[0009] (3) Adaptive Control Method: Adaptive control methods can automatically adjust the control law according to changes in system parameters, and are effective in handling uncertainties. However, adaptive control methods have certain limitations when dealing with input time delay and input saturation. For input time delay, adaptive control methods cannot provide effective compensation strategies and still rely on delayed feedback information. For input saturation, adaptive control methods struggle to maintain system performance when control input is restricted.

[0010] (4) Robust Control Methods: Robust control methods can ensure the stability and performance of a system under uncertainties and disturbances. However, robust control methods are usually complex to design and highly conservative. For input time delays, robust control methods need to introduce conservative compensation strategies, which leads to a slower system response. For input saturation, robust control methods are prone to introducing large control inputs when handling it, making it difficult to guarantee the stability of the system. Summary of the Invention

[0011] The purpose of this invention is to provide a robot path tracking method, medium, and device based on time delay compensation and input saturation control, which can improve the control performance of the robot when input time delay and input saturation coexist.

[0012] This invention provides a robot path tracking method based on time delay compensation and input saturation control, comprising:

[0013] S1: Construct a mathematical model system for a mobile robot, which includes leaders and followers;

[0014] S2: Utilize time-varying gain to construct a time-varying distributed observer. The time-varying distributed observer is used to obtain the leader's three-dimensional state information, which includes position and orientation information.

[0015] S3: Based on the mathematical model system of the mobile robot, the full drive model is obtained using the virtual controller parameters;

[0016] S4: Based on the full-drive model, the three-dimensional state information of the leader is obtained using a time-varying distributed observer; based on the three-dimensional state information, a local tracking error and a virtual controller are constructed using a time-varying distributed observer.

[0017] S5: Based on the virtual controller, the adaptive rate and control torque are obtained using the auxiliary compensation system;

[0018] S6: Based on the adaptive rate and control torque, the dynamic compensator is obtained;

[0019] S7: Utilize a dynamic compensator to obtain a controller; based on the leader's three-dimensional state information, use the controller to control the followers and monitor and track the leader in real time.

[0020] Furthermore, step S1 of the robot path tracking method based on time delay compensation and input saturation control specifically includes: constructing a mobile robot mathematical model system, which includes a leader and followers, as shown in the formula:

[0021]

[0022]

[0023]

[0024]

[0025] Ω i =[Ω i,1 Ω i,2 ] T

[0026]

[0027] V = {1, 2, …, N}, (i,j) ∈ ε

[0028]

[0029] L=DA

[0030] D = diag(υ1,υ2,...,υ) N )

[0031]

[0032] N i ={j|j∈V|(j,i)∈ε}

[0033]

[0034] in, υ is the rate of change of the robot's position and orientation. i and ω i Representing linear velocity and angular velocity respectively; η i This represents the position and orientation matrix of the robot in the global coordinate system. Indicates location; Indicates direction; Ω i Ω is the state matrix for the rotational speeds of the robot's left and right wheels. i,1 and Ω i,2 These represent the rotational speeds of the left and right wheels, respectively; τ i d(t) is the control torque, and d(t) is a bounded time-varying time delay. It is a positive constant; M is the mass matrix, C is the Coriolis force matrix, D is the damping matrix, m1, m2, c, d1 and d2 are predefined constants, M is a positive definite matrix, b i It is half the width of the i-th robot individual, r i Let be the radius of the wheel of the i-th robot. Communication in a multi-agent formation can be represented using a directed graph G. Define a directed graph. It consists of a directed graph G, node 0, and directed edges from leader 0 to G. Assume... It is contained in a spanning tree with a leader; N is the number of followers, ε is the edge set, representing the communication between each pair of agents, if (i,j)∈ε, it means that the j-th follower can receive data from the i-th follower; L is the Laplace matrix, representing the communication relationship between the leader and followers, N i Let i represent the neighbors of the i-th agent.

[0035] Furthermore, step S2 of the robot path tracking method based on time delay compensation and input saturation control specifically includes: constructing a time-varying distributed observer using time-varying gain, as shown in the formula:

[0036]

[0037]

[0038]

[0039]

[0040]

[0041] in, and Let be the rate of change of the state of the time-varying distributed observer. and Let r and β1 be the state of the time-varying distributed observer, where r and β1 are both design parameters. The β1 power is the time-varying gain, and N is the number of robots. Let j be the observation position of the j-th robot. Let μ(t) be the observed velocity of the j-th robot, μ(t) be the time-varying gain, and T be a specified finite time. Let q be the expected speed of the i-th robot. i,2,* Let be the expected speed of the i-th robot. For input, u i,* (t) is the input, q i,1,* Let * be the expected trajectory of the i-th robot, which can be represented by x, y, and ψ; and The state of the observer is used to estimate the leader's information within a specified finite time. The time-varying distributed observer is used to obtain the leader's three-dimensional state information, which includes position and orientation information.

[0042] Furthermore, step S3 of the robot path tracking method based on time delay compensation and input saturation control specifically includes: obtaining the full-drive model using virtual controller parameters based on the mobile robot's mathematical model system, as shown in the formula:

[0043]

[0044]

[0045]

[0046]

[0047] Where, x i (t) and y i (t) represents the position of the i-th robot. and Let R(ψ) be the desired position of the i-th robot. i (t) is the rotation matrix, representing the rotation transformation of the robot at time t, ψ i (t) represents the direction of the i-th robot, f 1i (ξ i Let f be the deviation function of the i-th robot in the x-direction. 2i (ξ i Let ξ be the deviation function of the i-th robot in the y-direction. i For virtual controller parameters, Let f be the desired direction of the i-th robot. 3i (ξ i Let f be the deviation function of the i-th robot in the orientation angle. 1i Let f be the deviation of the i-th robot in the x-direction. 2i Let f be the deviation of the i-th robot in the y-direction. 3i Let ε be the deviation of the i-th robot in the orientation angle. 1i and ε 2i It is a positive number.

[0048] Furthermore, step S4 of the robot path tracking method based on time delay compensation and input saturation control specifically includes: estimating the leader's information within a specified finite time T using a time-varying distributed observer based on the full-drive model; observing and updating the leader's observed state in real time to obtain the leader's three-dimensional state information; and constructing a local tracking error and a virtual controller using the time-varying distributed observer, as shown in the formula:

[0049]

[0050]

[0051]

[0052]

[0053]

[0054]

[0055]

[0056] Among them, e ix Let x be the tracking error of the i-th robot in the x-direction. i Let i be the desired trajectory of the i-th robot in the x-direction. Let e ​​be the trajectory observed by the i-th robot in the x-direction. iy Let y be the tracking error of the i-th robot in the y-direction. i Let i be the desired trajectory of the i-th robot in the y-direction. Let e ​​be the trajectory observed by the i-th robot in the y-direction. iψ Let ψ be the tracking error of the i-th robot in terms of orientation angle. i Let i be the desired trajectory of the i-th robot in terms of orientation angle. Let i be the observed trajectory of the i-th robot in terms of orientation angle. Let υ be the linear velocity error of the i-th robot. i Let υ be the expected linear velocity of the i-th robot. ic Let be the linear velocity of the i-th robot in the virtual controller. Let ω be the angular velocity error of the i-th robot. i Let ω be the expected angular velocity of the i-th robot. ic Let be the angular velocity of the i-th robot in the virtual controller. Let x be the rate of change of the tracking error of the i-th robot in the x-direction. Let Q be the rate of change of the tracking error of the i-th robot in the y-direction. i Let be the robot's position vector in the global coordinate system. R(ψ) is the update rate. i f is a rotation matrix, representing the rotational transformation of the robot at time t. 1i Let f be the deviation of the i-th robot in the x-direction. 2i Let be the deviation of the i-th robot in the y-direction. Let be the rate of change of direction of the i-th robot. Let x be the observed velocity of the i-th robot in the x-direction. Let be the observed velocity value of the i-th robot in the y-direction. Let f be the rate of change of the tracking error of the i-th robot in the orientation angle. 3i Let ξ be the deviation of the i-th robot in the orientation angle. i To control variables, For update rate, Let be the velocity observation value of the i-th robot in the direction angle. Let k be the direction of the i-th robot. i,1 and k i,2 For positive integers, f is the velocity input of the i-th robot in the direction angle. 3i Let be the deviation of the i-th robot in the direction angle.

[0057] Furthermore, step S5 of the robot path tracking method based on time delay compensation and input saturation control specifically includes: obtaining the adaptive rate and control torque using the auxiliary compensation system based on the virtual controller, as shown in the formula:

[0058]

[0059] Θ i =[c d1 d2 m1 m2]

[0060]

[0061]

[0062]

[0063]

[0064] in, Ω is the transpose of the simplified variable matrix. i2 Let ω be the rotational speed of the right wheel of the i-th robot. i Let Ω be the angular velocity of the i-th robot. i1 Let be the rotational speed of the i-th robot's left wheel. Let be the rate of change of the expected angular velocity of the i-th robot's left wheel. Let Θ be the rate of change of the expected angular velocity of the i-th robot's right wheel. i Here is the simplified variable matrix, where c is the Coriolis force, d1 and d2 are the damping coefficients, and m1 and m2 are the robot's masses. Let M be the rate of change of the compensation function of the auxiliary compensation system, M be the mass matrix, and τ be the variable. i (t) represents the control torque, τ i (td) represents the control torque at time td, d is the time delay, and Ω i1c Let Ω be the expected angular velocity of the i-th robot's left wheel. i2c Let be the expected angular velocity of the right wheel of the i-th robot. υ is the reciprocal of a known matrix as defined. ic Let ω be the linear velocity of the i-th robot in the virtual controller. ic Let e ​​be the angular velocity of the i-th robot in the virtual controller.iΩ Let M be the tracking error of the rotational speed of the i-th robot wheel, η1 be the compensation function, and M be the error of the rotational speed of the i-th robot wheel. i Let be the mass matrix of the i-th robot. Let be the rate of change of the tracking error of the i-th robot wheel rotation speed. For the j-th row of the transposed variable matrix after simplification, Θ ij τ is the j-th element of the simplified variable matrix. i1 (t) represents the control torque of the left wheel of the i-th robot, τ i2 (t) represents the right wheel control torque of the i-th robot, k i,3 It is a positive integer. For adaptive rate, For the transpose of a known matrix, π i1 For a positive constant, Ξ ij For the j-th row of the simplified variable matrix, γ ij κ ij and Θ ij0 It is a positive number.

[0065] Furthermore, step S6 of the robot path tracking method based on time delay compensation and input saturation control specifically includes: obtaining a dynamic compensator based on the adaptive rate and control torque, as shown in the formula:

[0066] Δv sat =sat(v(td(t))-v(td(t))

[0067] Δv delay =v(td(t))-v(t)

[0068] Where, τ i (t) represents the control torque of the i-th robot, sat(·) is the saturation function of the input constraint B, sat(v(t)) is the final control torque applied to the robot, v(t) is the control input, sign(v(t)) is the maximum value that the saturation function can take, u(t) is the maximum input, B is a positive constant generated by the controller design program, and u M It is the boundary value of u(t), Δv sat and v delay For dynamic compensators, d(t) is the time delay.

[0069] Furthermore, step S7 of the robot path tracking method based on time delay compensation and input saturation control specifically includes: obtaining a controller using a dynamic compensator; controlling the follower and monitoring and tracking the leader in real time using the controller based on the leader's three-dimensional state information, as shown in the formula:

[0070]

[0071]

[0072] Where, τ i (t) represents the control torque, τ i1 (t) represents the control torque of the left wheel of the i-th robot, τ i2 (t) represents the right wheel control torque of the i-th robot, k i,3 It is a positive integer. This is the transpose of the simplified variable matrix. For adaptive rate, For the transpose of a known matrix, π i1 Let be a positive constant, sat(v(t)) be the final control torque applied to the robot, v(t) be the control input, sign(v(t)) be the maximum value that the saturation function can take, u(t) be the maximum input, and B be a positive constant generated by the controller design program. M It is the boundary value of u(t).

[0073] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the robot path tracking method based on time delay compensation and input saturation control described above.

[0074] The present invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the robot path tracking method based on time delay compensation and input saturation control described above.

[0075] The robot path tracking method, medium, and device based on time delay compensation and input saturation control provided by this invention have the following beneficial effects:

[0076] First, this invention addresses the input time delay problem by introducing an auxiliary compensator, ensuring that the system maintains stability and high-precision trajectory tracking even with input time delay, and ensuring the boundedness of the closed-loop signal, thereby improving system stability and trajectory tracking accuracy. This compensation strategy effectively eliminates the negative impact of input time delay on the system, ensuring a rapid response from the control system.

[0077] Secondly, this invention considers input saturation constraints, designs appropriate saturation functions to limit the amplitude of the control input, and prevents potential risks caused by excessive control input. By designing a Lyapunov function, the control input is ensured to be within the allowable range, thereby improving the stability of the system, avoiding the degradation of system performance due to input saturation, and ensuring the stability and performance of the system under input saturation conditions.

[0078] Finally, considering the two factors of input time delay and input saturation, a dynamic compensator is proposed, and the virtual controller, virtual control law and adaptive law are recursively designed using the adaptive backstepping method. This method ensures that the controller tracking error approaches an acceptable range in a small region near zero within a specified finite time by specifying a time performance function, thereby eliminating the influence of uncertainty and further improving the stability and tracking accuracy of the system. Attached Figure Description

[0079] The present invention will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings:

[0080] Figure 1 This is a flowchart of the robot path tracking method based on time delay compensation and input saturation control provided by the present invention;

[0081] Figure 2 This is a schematic diagram of the robot path tracking method based on time delay compensation and input saturation control provided by the present invention;

[0082] Figure 3 This is a schematic diagram of the time delay function provided by the present invention;

[0083] Figure 4 This is a schematic diagram of the saturation function provided by the present invention;

[0084] Figure 5 This is a structural block diagram of the computer device provided by the present invention. Detailed Implementation

[0085] To provide a clearer understanding of the technical features, objectives, and effects of the present invention, specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0086] Figure 1 A schematic diagram of the robot path tracking method based on time delay compensation and input saturation control according to this embodiment is shown. In this embodiment, the robot path tracking method based on time delay compensation and input saturation control includes:

[0087] S1: Construct a mathematical model system for a mobile robot, which includes leaders and followers;

[0088] Specifically, step S1 of the robot path tracking method based on time delay compensation and input saturation control includes: constructing a mobile robot mathematical model system, which includes a leader and followers, as shown in the formula:

[0089]

[0090]

[0091]

[0092]

[0093] Ω i =[Ω i,1 Ω i,2 ] T

[0094]

[0095] V = {1, 2, …, N}, (i,j) ∈ ε

[0096]

[0097] L=DA

[0098] D = diag(υ1,υ2,...,υ) N )

[0099]

[0100] N i ={j|j∈V|(j,i)∈ε}

[0101]

[0102] in, υ is the rate of change of the robot's position and orientation. i and ω i Representing linear velocity and angular velocity respectively; η i This represents the position and orientation matrix of the robot in the global coordinate system. Indicates location; Indicates direction; Ω i Ω is the state matrix for the rotational speeds of the robot's left and right wheels. i,1 and Ω i,2 These represent the rotational speeds of the left and right wheels, respectively; τ i d(t) is the control torque, and d(t) is a bounded time-varying time delay. It is a positive constant; M is the mass matrix, C is the Coriolis force matrix, D is the damping matrix, m1, m2, c, d1 and d2 are predefined constants, M is a positive definite matrix, b i It is half the width of the i-th robot individual, r i Let be the radius of the wheel of the i-th robot. Communication in a multi-agent formation can be represented using a directed graph G. Define a directed graph. It consists of a directed graph G, node 0, and directed edges from leader 0 to G. Assume... It is contained in a spanning tree with a leader; N is the number of followers, ε is the edge set, representing the communication between each pair of agents, if (i,j)∈ε, it means that the j-th follower can receive data from the i-th follower; L is the Laplace matrix, representing the communication relationship between the leader and followers, N i Indicates the neighbors of the i-th agent;

[0103] S2: Utilize time-varying gain to construct a time-varying distributed observer. The time-varying distributed observer is used to obtain the leader's three-dimensional state information, which includes position and orientation information.

[0104] Specifically, step S2 of the robot path tracking method based on time delay compensation and input saturation control includes: constructing a time-varying distributed observer using time-varying gain, as shown in the formula:

[0105]

[0106]

[0107]

[0108]

[0109]

[0110] in, and Let be the rate of change of the state of the time-varying distributed observer. and Let r and β1 be the state of the time-varying distributed observer, where r and β1 are both design parameters. The β1 power is the time-varying gain, and N is the number of robots. Let j be the observation position of the j-th robot. Let μ(t) be the observed velocity of the j-th robot, μ(t) be the time-varying gain, and T be a specified finite time. Let q be the expected speed of the i-th robot. i,2,* Let be the expected speed of the i-th robot. For input, u i,* (t) is the input, q i,1,* Let * be the expected trajectory of the i-th robot, which can be represented by x, y, and ψ; and The state of the observer is used to estimate the leader's information within a specified finite time. The time-varying distributed observer is used to obtain the leader's three-dimensional state information, which includes position and orientation information.

[0111] S3: Based on the mathematical model system of the mobile robot, the full drive model is obtained using the virtual controller parameters;

[0112] Specifically, step S3 of the robot path tracking method based on time delay compensation and input saturation control includes: obtaining the full-drive model using virtual controller parameters based on the mobile robot's mathematical model system, as shown in the formula:

[0113]

[0114]

[0115]

[0116]

[0117] Where, x i (t) and y i (t) represents the position of the i-th robot. and Let R(ψ) be the desired position of the i-th robot. i (t) is the rotation matrix, representing the rotation transformation of the robot at time t, ψ i (t) represents the direction of the i-th robot, f 1i (ξ i Let f be the deviation function of the i-th robot in the x-direction. 2i (ξ i Let ξ be the deviation function of the i-th robot in the y-direction. i For virtual controller parameters, Let f be the desired direction of the i-th robot. 3i (ξ i Let f be the deviation function of the i-th robot in the orientation angle. 1i Let f be the deviation of the i-th robot in the x-direction. 2i Let f be the deviation of the i-th robot in the y-direction. 3i Let ε be the deviation of the i-th robot in the orientation angle. 1i and ε 2i It is a positive number;

[0118] S4: Based on the full-drive model, the three-dimensional state information of the leader is obtained using a time-varying distributed observer; based on the three-dimensional state information, a local tracking error and a virtual controller are constructed using a time-varying distributed observer.

[0119] Specifically, step S4 of the robot path tracking method based on time delay compensation and input saturation control includes: estimating the leader's information within a specified finite time T using a time-varying distributed observer based on the full-drive model; observing and updating the leader's observed state in real time to obtain the leader's three-dimensional state information; and constructing a local tracking error and a virtual controller using the time-varying distributed observer, as shown in the formula:

[0120]

[0121]

[0122]

[0123]

[0124]

[0125]

[0126]

[0127] Among them, e ix Let x be the tracking error of the i-th robot in the x-direction. i Let i be the desired trajectory of the i-th robot in the x-direction. Let e ​​be the trajectory observed by the i-th robot in the x-direction. iy Let y be the tracking error of the i-th robot in the y-direction. i Let i be the desired trajectory of the i-th robot in the y-direction. Let e ​​be the trajectory observed by the i-th robot in the y-direction. iψ Let ψ be the tracking error of the i-th robot in terms of orientation angle. i Let i be the desired trajectory of the i-th robot in terms of orientation angle. Let i be the observed trajectory of the i-th robot in terms of orientation angle. Let υ be the linear velocity error of the i-th robot. i Let υ be the expected linear velocity of the i-th robot. ic Let be the linear velocity of the i-th robot in the virtual controller. Let ω be the angular velocity error of the i-th robot. i Let ω be the expected angular velocity of the i-th robot. ic Let be the angular velocity of the i-th robot in the virtual controller. Let x be the rate of change of the tracking error of the i-th robot in the x-direction. Let Q be the rate of change of the tracking error of the i-th robot in the y-direction. i Let be the robot's position vector in the global coordinate system. R(ψ) is the update rate. i f is a rotation matrix, representing the rotational transformation of the robot at time t. 1i Let f be the deviation of the i-th robot in the x-direction. 2i Let be the deviation of the i-th robot in the y-direction. Let be the rate of change of direction of the i-th robot. Let x be the observed velocity of the i-th robot in the x-direction. Let be the observed velocity value of the i-th robot in the y-direction. Let f be the rate of change of the tracking error of the i-th robot in the orientation angle. 3i Let ξ be the deviation of the i-th robot in the orientation angle. i To control variables, For update rate, Let be the velocity observation value of the i-th robot in the direction angle. Let k be the direction of the i-th robot. i,1 and k i,2 For positive integers, f is the velocity input of the i-th robot in the direction angle. 3i Let be the deviation of the i-th robot in the orientation angle;

[0128] S5: Based on the virtual controller, the adaptive rate and control torque are obtained using the auxiliary compensation system;

[0129] Specifically, step S5 of the robot path tracking method based on time delay compensation and input saturation control includes: obtaining the adaptive rate and control torque using the auxiliary compensation system based on the virtual controller, as shown in the formula:

[0130]

[0131] Θ i =[c d1 d2 m1 m2]

[0132]

[0133]

[0134]

[0135]

[0136] in, Ω is the transpose of the simplified variable matrix. i2 Let ω be the rotational speed of the right wheel of the i-th robot. i Let Ω be the angular velocity of the i-th robot. i1Let be the rotational speed of the i-th robot's left wheel. Let be the rate of change of the expected angular velocity of the i-th robot's left wheel. Let Θ be the rate of change of the expected angular velocity of the i-th robot's right wheel. i Here is the simplified variable matrix, where c is the Coriolis force, d1 and d2 are the damping coefficients, and m1 and m2 are the robot's masses. Let M be the rate of change of the compensation function of the auxiliary compensation system, M be the mass matrix, and τ be the variable. i (t) represents the control torque, τ i (td) represents the control torque at time td, d is the time delay, and Ω i1c Let Ω be the expected angular velocity of the i-th robot's left wheel. i2c Let be the expected angular velocity of the right wheel of the i-th robot. υ is the reciprocal of a known matrix as defined. ic Let ω be the linear velocity of the i-th robot in the virtual controller. ic Let e ​​be the angular velocity of the i-th robot in the virtual controller. iΩ Let M be the tracking error of the rotational speed of the i-th robot wheel, η1 be the compensation function, and M be the error of the rotational speed of the i-th robot wheel. i Let be the mass matrix of the i-th robot. Let be the rate of change of the tracking error of the i-th robot wheel rotation speed. For the j-th row of the transposed variable matrix after simplification, Θ ij τ is the j-th element of the simplified variable matrix. i1 (t) represents the control torque of the left wheel of the i-th robot, τ i2 (t) represents the right wheel control torque of the i-th robot, k i,3 It is a positive integer. For adaptive rate, For the transpose of a known matrix, π i1 For a positive constant, Ξ ij For the j-th row of the simplified variable matrix, γ ij κ ij and Θ ij0 It is a positive number;

[0137] S6: Based on the adaptive rate and control torque, the dynamic compensator is obtained;

[0138] Specifically, step S6 of the robot path tracking method based on time delay compensation and input saturation control includes: obtaining a dynamic compensator based on the adaptive rate and control torque, as shown in the formula:

[0139]

[0140] Δv sat=sat(v(td(t))-v(td(t))

[0141] Δv delay =v(td(t))-v(t)

[0142] Where, τ i (t) represents the control torque of the i-th robot, sat(·) is the saturation function of the input constraint B, sat(v(t)) is the final control torque applied to the robot, v(t) is the control input, sign(v(t)) is the maximum value that the saturation function can take, u(t) is the maximum input, B is a positive constant generated by the controller design program, and u M It is the boundary value of u(t), Δv sat and Δv delay For dynamic compensators, d(t) is the time delay;

[0143] S7: Utilize a dynamic compensator to obtain a controller; based on the leader's three-dimensional state information, use the controller to control the followers and monitor and track the leader in real time.

[0144] Specifically, step S7 of the robot path tracking method based on time delay compensation and input saturation control includes: obtaining a controller using a dynamic compensator; controlling the follower and monitoring and tracking the leader in real time using the controller based on the leader's three-dimensional state information, as shown in the formula:

[0145]

[0146]

[0147] Where, τ i (t) represents the control torque, τ i1 (t) represents the control torque of the left wheel of the i-th robot, τ i2 (t) represents the right wheel control torque of the i-th robot, k i,3 It is a positive integer. This is the transpose of the simplified variable matrix. For adaptive rate, For the transpose of a known matrix, π i1 Let be a positive constant, sat(v(t)) be the final control torque applied to the robot, v(t) be the control input, sign(v(t)) be the maximum value that the saturation function can take, u(t) be the maximum input, and B be a positive constant generated by the controller design program. M It is the boundary value of u(t).

[0148] In some embodiments, the robot path tracking method based on time delay compensation and input saturation control described above can also be implemented in the following ways.

[0149] The overall flowchart of this embodiment is shown below. Figure 2 As shown, the robot path tracking method based on time delay compensation and input saturation control mainly includes the following steps:

[0150] S01: Establishing a mathematical model system for mobile robots: The robots in the mathematical model system for mobile robots include: leaders and followers;

[0151] S02: Introduce time-varying gain and design a time-varying distributed observer to obtain the leader's three-dimensional state information, which includes: position information and direction information;

[0152] S03: Based on the mathematical model, the underdriven mathematical model is converted into a fully driven mathematical model. By using a time-varying distributed observer, the information of the leader within a specified finite time T is estimated, and the observation state of the leader is determined.

[0153] S04: Using the information observed by the observer, define the local tracking error and design a virtual controller in combination with a finite-time function;

[0154] S05: Introduce an auxiliary compensation system to handle the input time delay in the controller and obtain the adaptive law and control torque;

[0155] S06: Combining adaptive law and control torque, and considering input constraints, design a dynamic compensator;

[0156] S07: The controller design is completed through a dynamic compensator. Combined with the leader's observed state, when input delay and input saturation exist simultaneously, the followers are controlled to monitor and track the leader's state in real time to achieve the formation control objective.

[0157] The design process of the mobile robot mathematical model is as follows: Consider the mobile robot mathematical model system, which is described as follows:

[0158]

[0159]

[0160] Let i = 1,...,N, where υ i and ω i These represent linear velocity and angular velocity, respectively. and Ω represents position and direction respectively; i =[Ω i,1 Ω i,2 ] T Ω i,1 and Ω i,2These represent the rotational speeds of the left and right wheels, respectively; τ i d(t) is the control torque, and d(t) is a bounded time-varying time delay that satisfies It is a positive constant; the definitions of M, C, and D are as follows:

[0161]

[0162] Where m1, m2, c, d1, and d2 are all predefined constants; and M is a positive definite matrix; furthermore, υ i ω i and Ω i satisfy

[0163]

[0164] Where b i It is half the width of the i-th robot individual, r i Let E be the radius of the wheel of the i-th robot. It can be proven that E... i It is reversible;

[0165] Communication in a multi-agent formation can be represented using a directed graph G. Let V = {1, 2, ..., N} represent N followers, and let the edge set ε represent the communication between each pair of agents. If (i,j)∈ε, it means that the j-th follower can receive data from the i-th follower. Define the matrix... If (i,j)∈ε, then a ij =1, if Then a ij =0; Define the Laplacian matrix L = DA, where D = diag(υ1,υ2,...,υ N ), N i N represents the neighbors of the i-th agent. i ={j|j∈V|(j,i)∈ε}; Define a i0 (i∈V), if the i-th agent is connected to the leader, then a i0 =1, otherwise a i0 =0, let a 0i =0; defines a directed graph. It consists of a directed graph G, node 0, and directed edges from leader 0 to G. Assume... It is contained in a leader-based spanning tree; based on this, the control problem is designed and solved.

[0166] The above describes an underactuated model. For easier control, the underactuated model needs to be converted into a fully acted model, as described below:

[0167]

[0168]

[0169] in,

[0170]

[0171]

[0172] ε 1i and ε 2i It is a positive integer, and

[0173] The design process of the observer is as follows: to process the desired trajectory x r (t), y r (t) and ψ r (t), design the following leader information:

[0174]

[0175]

[0176] Let q i,1,* Let * be the expected trajectory of the i-th robot, which can be represented by x, y, and ψ;

[0177] A distributed estimator was designed for each robot to estimate leader information over a specified finite time T. The observer is shown below:

[0178]

[0179] in, and The state of the observer; r > 0 and β1 ∈ (1, +∞) are all design parameters; It is a time-varying gain used to estimate information about the leader within a specified finite time period;

[0180] Based on this step, an adaptive tracking controller is designed for each robot;

[0181] The controller design process is as follows: First, the local tracking error is defined as:

[0182]

[0183]

[0184] Where υ ic and ω ic If it is a virtual controller, then the derivative of the local tracking error can be calculated as:

[0185]

[0186]

[0187] in Given Q i For full rank;

[0188] Then, design the virtual controller and virtual update rate:

[0189]

[0190]

[0191] Where, k i,1 and k i,2 All are positive numbers;

[0192] Proof: Consider the following Lyapunov function:

[0193]

[0194] Taking its derivative and substituting it into the above expression, we get:

[0195]

[0196] Where a1=min{2k 1,1 2k 1,2 ,...,2k N,1 2k N,2}and

[0197]

[0198]

[0199] You can get Me iΩ The derivative is:

[0200]

[0201] Define two variables:

[0202]

[0203] Θ i =[c d1 d2 m1 m2]

[0204] On the other hand, an auxiliary compensation system is introduced to handle the input time delay, which is defined as:

[0205]

[0206] Where d is the time delay, and the time delay function is illustrated in the diagram below. Figure 3 As shown:

[0207] At this point, the local error can be obtained:

[0208]

[0209]

[0210] Ξ ij Represents Ξ i The j-th row, Θ ij Represents Θ i The j-th element;

[0211] The control torque is designed as follows:

[0212]

[0213] Where k i,3 It is a positive number. It is Θ ij The estimate.

[0214] Adaptive rate Designed as follows:

[0215]

[0216] Where γ ij κ ij and Θ ij0 All are positive numbers;

[0217] To address the input constraint problem, the following dynamic compensator is proposed. First, let:

[0218]

[0219] If both input constraints and state constraints need to be satisfied simultaneously, that is, if ||u(t)|| ∞ < B, where B is a positive constant, and sat(·) is the saturation function of the input constraint B, v(t) is the control input, which is generated by the controller design program, and there exists |v(t)| < u. M u M It is an unknown boundary value of u(t), and the control torque τ i The relationship between (t) and the control input v(t) is as follows: Figure 3 As shown; sat(v(t)) is the final control torque applied to the robot, which means that the control torque cannot be very large and is subject to input constraints;

[0220] Ultimately, we can obtain:

[0221] Δv sat=sat(v(td(t))-v(td(t))

[0222] Δv delay =v(td(t))-v(t)

[0223] Proof: Consider the following Lyapunov function:

[0224]

[0225] in available for:

[0226]

[0227] According to Young's inequality, we can obtain:

[0228]

[0229] Therefore, we can obtain:

[0230]

[0231] in

[0232]

[0233]

[0234] Integrating both sides, we get:

[0235]

[0236] e ix e iy and e iψ Bounded;

[0237] The formation error is defined as: definition:

[0238]

[0239] Where p = 1, 2, it can be proven that:

[0240] s 1,* =(L+B)e 1,* ,s 2,* =(L+B)e 2,*

[0241] Define z i,* =γ1s i,1,* +s i,2,* , and z * =[z 1,*,...,z N,* ] T , for z * By taking the differential, we can obtain:

[0242]

[0243] Consider the following Lyapunov function:

[0244]

[0245] Based on u i,* And Young's inequality, can be calculated

[0246]

[0247] in d1=||P(L+B)|| 2 ;

[0248] Next, consider the following Lyapunov function:

[0249] V = V² + V 3,x +V 3,y +V 3,ψ

[0250] It can be calculated that:

[0251]

[0252] in,

[0253]

[0254]

[0255]

[0256] c1 = c x +c y +c ψ

[0257] Integrating both sides over t∈[t1,t2) yields:

[0258]

[0259] This embodiment provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the robot path tracking method based on time delay compensation and input saturation control described above. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), random access memory (RAM), flash memory, hard disk drive (HDD), or solid-state drive (SSD), etc.; the storage medium may also include combinations of the above types of memory.

[0260] This embodiment provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps of the robot path tracking method based on time delay compensation and input saturation control described above.

[0261] like Figure 5 As shown, the computer device may include: at least one processor 121, such as a CPU (Central Processing Unit), at least one communication interface 123, memory 124, and at least one communication bus 122. The communication bus 122 is used to enable communication between these components. The communication interface 123 may include a display screen and a keyboard; optionally, the communication interface 123 may also include a standard wired interface or a wireless interface. The memory 124 may be high-speed RAM (Random Access Memory) or non-volatile memory, such as at least one disk drive. Optionally, the memory 124 may also be at least one storage device located remotely from the processor 121. The memory 124 stores application programs, and the processor 121 calls the program code stored in the memory 124 to execute any of the aforementioned method steps. The communication bus 122 may be a peripheral component interconnect (PCI) bus or an extended industry standard architecture (EISA) bus, etc. The communication bus 122 can be divided into address bus, data bus, control bus, etc. For ease of representation, Figure 5The term 124 is represented by a single line, but this does not imply a single bus or a single type of bus. The memory 124 may include volatile memory, such as random-access memory (RAM); it may also include non-volatile memory, such as flash memory, hard disk drive (HDD), or solid-state drive (SSD); or a combination of the above types of memory. The processor 121 may be a central processing unit (CPU), a network processor (NP), or a combination of a CPU and an NP. The processor 121 may further include a hardware chip. This hardware chip may be an application-specific integrated circuit (ASIC), a programmable logic device (PLD), or a combination thereof. The aforementioned PLD can be a complex programmable logic device (CPLD), a field-programmable gate array (FPGA), a generic array logic (GAL), or any combination thereof. Optionally, the memory 124 is also used to store program instructions. The processor 121 can call the program instructions to implement the robot path tracking method based on time delay compensation and input saturation control as described in this embodiment.

[0262] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A robot path tracking method based on time delay compensation and input saturation control, characterized in that, Includes the following steps: S1: Construct a mathematical model system for a mobile robot, which includes a leader and followers; S2: Using time-varying gain, a time-varying distributed observer is constructed. The time-varying distributed observer is used to obtain the three-dimensional state information of the leader, which includes position information and orientation information. S3: Based on the aforementioned mobile robot mathematical model system, the full drive model is obtained using the virtual controller parameters; S4: Based on the full-drive model, the three-dimensional state information of the leader is obtained using the time-varying distributed observer; based on the three-dimensional state information, the local tracking error and virtual controller are constructed using the time-varying distributed observer. S5: Based on the virtual controller, the adaptive rate and control torque are obtained using the auxiliary compensation system; S6: Based on the adaptive rate and control torque, the dynamic compensator is obtained; S7: Using the dynamic compensator, a controller is obtained; based on the leader's three-dimensional state information, the controller is used to control the followers and monitor and track the leader in real time.

2. The robot path tracking method based on time delay compensation and input saturation control according to claim 1, characterized in that, Step S1 specifically includes: constructing a mathematical model system for the mobile robot, wherein the mathematical model system for the mobile robot includes a leader and followers, as shown in the formula: Oh i =[Ω i，1 Oh i，2 ] T V = {1, 2, ..., N}, (i, j) ∈ ε L=DA D=diag(υ1,υ2,...,υ N ) N i ={j|j∈V|(j,i)∈ε} in, υ is the rate of change of the robot's position and orientation. i and ω i Representing linear velocity and angular velocity respectively; η i This represents the position and orientation matrix of the robot in the global coordinate system. Indicates location; Indicates direction; Ω i Ω is the state matrix for the rotational speeds of the robot's left and right wheels. i，1 and Ω i，2 These represent the rotational speeds of the left and right wheels, respectively; τ i d(t) is the control torque, and d(t) is a bounded time-varying time delay. It is a positive constant; M is the mass matrix, C is the Coriolis force matrix, D is the damping matrix, m1, m2, c, d1 and d2 are predefined constants, M is a positive definite matrix, b i It is half the width of the i-th robot individual, r i Let be the radius of the wheel of the i-th robot. Communication in a multi-agent formation can be represented using a directed graph G. Define a directed graph. It consists of a directed graph G, node 0, and directed edges from leader 0 to G. Assume... It is contained in a spanning tree with a leader; N is the number of followers, ε is the edge set, representing the communication between each pair of agents, if (i,j)∈ε, it means that the j-th follower can receive data from the i-th follower; L is the Laplace matrix, representing the communication relationship between the leader and followers, N i Let i represent the neighbors of the i-th agent.

3. The robot path tracking method based on time delay compensation and input saturation control according to claim 1, characterized in that, Step S2 specifically includes: constructing a time-varying distributed observer using time-varying gain, as shown in the formula: in, and Let be the rate of change of the state of the time-varying distributed observer. and Let r and β1 be the state of the time-varying distributed observer, where r and β1 are both design parameters. The β1 power is the time-varying gain, and N is the number of robots. Let j be the observation position of the j-th robot. Let μ(t) be the observed velocity of the j-th robot, μ(t) be the time-varying gain, and T be a specified finite time. Let q be the expected speed of the i-th robot. i,2,* Let be the expected speed of the i-th robot. For input, u i,* (t) is the input, q i,1,* Let * be the expected trajectory of the i-th robot, which can be represented by x, y, and ψ; and The state of the observer is used to estimate the leader's information within a specified finite time. The time-varying distributed observer is used to obtain the leader's three-dimensional state information, which includes position and orientation information.

4. The robot path tracking method based on time delay compensation and input saturation control according to claim 1, characterized in that, Step S3 specifically includes: based on the mobile robot mathematical model system, using the virtual controller parameters, obtaining the full-drive model, as shown in the formula: Where, x i (t) and y i (t) represents the position of the i-th robot. and Let R(ψ) be the desired position of the i-th robot. i (t) is the rotation matrix, representing the rotation transformation of the robot at time t, ψ i (t) represents the direction of the i-th robot, f 1i (ξ i Let f be the deviation function of the i-th robot in the x-direction. 2i (ξ i Let ξ be the deviation function of the i-th robot in the y-direction. i For virtual controller parameters, Let f be the desired direction of the i-th robot. 3i (ξ i Let f be the deviation function of the i-th robot in the orientation angle. 1i Let f be the deviation of the i-th robot in the x-direction. 2i Let f be the deviation of the i-th robot in the y-direction. 3i Let ε be the deviation of the i-th robot in the orientation angle. 1i and ε 2i It is a positive number.

5. The robot path tracking method based on time delay compensation and input saturation control according to claim 1, characterized in that, Step S4 specifically includes: based on the full-drive model, using the time-varying distributed observer, estimating the leader's information within a specified finite time T, observing and updating the leader's observation state in real time, and obtaining the leader's three-dimensional state information; based on the three-dimensional state information, using the time-varying distributed observer, constructing a local tracking error and a virtual controller, as shown in the formula: Among them, e ix Let x be the tracking error of the i-th robot in the x-direction. i Let i be the desired trajectory of the i-th robot in the x-direction. Let e ​​be the trajectory observed by the i-th robot in the x-direction. iy Let y be the tracking error of the i-th robot in the y-direction. i Let i be the desired trajectory of the i-th robot in the y-direction. Let e ​​be the trajectory observed by the i-th robot in the y-direction. iψ Let ψ be the tracking error of the i-th robot in terms of orientation angle. i Let i be the desired trajectory of the i-th robot in terms of orientation angle. Let i be the observed trajectory of the i-th robot in terms of orientation angle. Let υ be the linear velocity error of the i-th robot. i Let υ be the expected linear velocity of the i-th robot. ic Let be the linear velocity of the i-th robot in the virtual controller. Let ω be the angular velocity error of the i-th robot. i Let ω be the expected angular velocity of the i-th robot. ic Let be the angular velocity of the i-th robot in the virtual controller. Let x be the rate of change of the tracking error of the i-th robot in the x-direction. Let Q be the rate of change of the tracking error of the i-th robot in the y-direction. i Let be the robot's position vector in the global coordinate system. R(ψ) is the update rate. i f is a rotation matrix, representing the rotational transformation of the robot at time t. 1i Let f be the deviation of the i-th robot in the x-direction. 2i Let be the deviation of the i-th robot in the y-direction. Let be the rate of change of direction of the i-th robot. Let x be the observed velocity of the i-th robot in the x-direction. Let be the observed velocity value of the i-th robot in the y-direction. Let f be the rate of change of the tracking error of the i-th robot in the orientation angle. 3i Let ξ be the deviation of the i-th robot in the orientation angle. i To control variables, For update rate, Let be the velocity observation value of the i-th robot in the direction angle. Let k be the direction of the i-th robot. i,1 and k i,2 For positive integers, f is the velocity input of the i-th robot in the direction angle. 3i Let be the deviation of the i-th robot in the direction angle.

6. The robot path tracking method based on time delay compensation and input saturation control according to claim 1, characterized in that, Step S5 specifically includes: based on the virtual controller, using the auxiliary compensation system, obtaining the adaptive rate and control torque, as shown in the formula: Θ i =[c d1 d2 m1 m2] in, Ω is the transpose of the simplified variable matrix. i2 Let ω be the rotational speed of the right wheel of the i-th robot. i Let Ω be the angular velocity of the i-th robot. i1 Let be the rotational speed of the i-th robot's left wheel. Let be the rate of change of the expected angular velocity of the i-th robot's left wheel. Let Θ be the rate of change of the expected angular velocity of the i-th robot's right wheel. i Here is the simplified variable matrix, where c is the Coriolis force, d1 and d2 are the damping coefficients, and m1 and m2 are the robot's masses. Let M be the rate of change of the compensation function of the auxiliary compensation system, M be the mass matrix, and τ be the variable. i (t) represents the control torque, τ i (td) represents the control torque at time td, d is the time delay, and Ω i1c Let Ω be the expected angular velocity of the i-th robot's left wheel. i2c Let be the expected angular velocity of the right wheel of the i-th robot. υ is the reciprocal of a known matrix as defined. ic Let ω be the linear velocity of the i-th robot in the virtual controller. ic Let e ​​be the angular velocity of the i-th robot in the virtual controller. iΩ Let M be the tracking error of the rotational speed of the i-th robot wheel, η1 be the compensation function, and M be the error of the rotational speed of the i-th robot wheel. i Let be the mass matrix of the i-th robot. Let be the rate of change of the tracking error of the i-th robot wheel rotation speed. For the j-th row of the transposed variable matrix after simplification, Θ ij τ is the j-th element of the simplified variable matrix. i1 (t) represents the control torque of the left wheel of the i-th robot, τ i2 (t) represents the right wheel control torque of the i-th robot, k i,3 It is a positive integer. For adaptive rate, For the transpose of a known matrix, π i1 For a positive constant, Ξ ij For the j-th row of the simplified variable matrix, γ ij κ ij and Θ ij0 It is a positive number.

7. The robot path tracking method based on time delay compensation and input saturation control according to claim 1, characterized in that, Step S6 specifically includes: obtaining the dynamic compensator based on the adaptive rate and control torque, as shown in the formula: Δv sat =sat(v(t-d(t))-v(t-d(t)) Δv delay =v(t-d(t))-v(t) Where, τ i (t) represents the control torque of the i-th robot, sat(·) is the saturation function of the input constraint B, sat(v(t)) is the final control torque applied to the robot, v(t) is the control input, sign(v(t)) is the maximum value that the saturation function can take, u(t) is the maximum input, B is a positive constant generated by the controller design program, and u M It is the boundary value of u(t), Δv sat and Δv delay For dynamic compensators, d(t) is the time delay.

8. The robot path tracking method based on time delay compensation and input saturation control according to claim 1, characterized in that, Step S7 specifically includes: obtaining a controller using the dynamic compensator; controlling the followers and monitoring and tracking the leader in real time using the controller based on the leader's three-dimensional state information, as shown in the formula: Where, τ i (t) represents the control torque, τ i1 (t) represents the control torque of the left wheel of the i-th robot, τ i2 (t) represents the right wheel control torque of the i-th robot, k i,3 It is a positive integer. This is the transpose of the simplified variable matrix. For adaptive rate, For the transpose of a known matrix, π i1 Let be a positive constant, sat(v(t)) be the final control torque applied to the robot, v(t) be the control input, sign(v(t)) be the maximum value that the saturation function can take, u(t) be the maximum input, and B be a positive constant generated by the controller design program. M It is the boundary value of u(t).

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the robot path tracking method based on time delay compensation and input saturation control as described in any of claims 1-8.

10. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the robot path tracking method based on time delay compensation and input saturation control as described in any one of claims 1-8.

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