Composite Robot Arm Coordinated Active Disturbance Rejection Control Method Based on Optimal Operating Region

Abstract

The present invention discloses an auto-disturbance rejection control method for vehicle-arm coordination of a composite robot based on an optimal operating region. By constructing a kinematic and dynamic model of the composite robot vehicle-arm redundant system, a constraint manifold for the optimal operating region of vehicle-arm coordination is designed. Based on the kinematic and dynamic model and the optimal operating region constraint manifold, an optimal task trajectory allocation algorithm is constructed. A nonlinear extended state observer of the robot and a non-singular fast terminal sliding mode manifold of the robot are constructed, and an auto-disturbance rejection motion controller is constructed using the two to achieve finite-time global convergence of the trajectory tracking error of the composite robot. Through the Lyapunov function, an auto-disturbance rejection motion controller is obtained that satisfies the global finite-time stability criterion of the observation-control closed-loop system to control the dynamic tracking of the task trajectory.

Description

Technical Field

[0001] The present invention belongs to the field of robot motion control, and in particular relates to a composite robot vehicle-arm coordinated anti-disturbance control method based on an optimal operating area. Background Art

[0002] Hybrid robots, consisting of a mobile platform and a manipulator, offer a wide range of motion and flexible operational configurations. Related technologies have become a research hotspot and development direction in the robotics industry in recent years. However, mature products and applications for vehicle-arm coordinated operations in unstructured environments, such as personalized home furnishings, flexible production, defense and military applications, public services, and emergency rescue, are currently rare. This is primarily due to the inadequacy of hybrid robots' planning and control capabilities to address the numerous challenges posed by complex environments. The redundancy of vehicle-arm motions and high-dimensional spatial coordinated control are key challenges for autonomous operation. Furthermore, trajectory tracking accuracy is adversely affected by external disturbances such as uncertain dynamics, unknown loads, and road undulations, making it difficult to effectively accomplish complex tasks such as obstacle avoidance, grasping, coordinated handling, and human-robot collaboration. Therefore, just as humans use their feet to achieve a more comfortable working posture when manipulating or carrying objects, designing advanced vehicle-arm coordinated motion control methods to address the redundant degrees of freedom, dynamic uncertainty, and environmental disturbances of hybrid robots, ensuring robust response and motion coordination, is key to achieving efficient autonomous operation.

[0003] A large number of advanced control technologies incorporating artificial intelligence models have been proposed and applied in the field of hybrid robot motion control, including adaptive neural network control, approximate Jacobian matrix feedback control, computational torque / variable structure inversion sliding mode control, and fractional-order fuzzy logic control. However, these methods rely on nominal system models, which can lead to low precision in complex environmental prior knowledge, low computational efficiency, and poor stability of black-box models such as neural networks. These methods, however, cannot meet the convergence accuracy and speed requirements of motion control in practical applications. Existing control technologies for vehicle-arm coordination in hybrid robots, such as event-based linearized decoupling controllers, vehicle-arm decentralized nonlinear PID controllers, and hierarchical distributed fuzzy controllers, are also mostly task-oriented, solving independent vehicle-arm motions and rarely considering indicators such as the flexibility of coordinated vehicle-arm motion within the task space. Furthermore, these control methods often simplify the system's nonlinear dynamic characteristics or undercompensate for vehicle-arm dynamic coupling, resulting in reduced trajectory tracking accuracy and robustness, making it difficult to ensure operational efficiency and execution accuracy in practical applications. Therefore, constructing the optimal operating area constraint manifold for the coordinated operation of the composite robot vehicle-arm, designing an anti-disturbance motion control method based on the extended state observer to address uncertain dynamics and external interference, and improving the coordination of the vehicle-arm motion while ensuring trajectory tracking accuracy and robustness are important foundations for realizing efficient and high-quality autonomous operation of composite robots in actual engineering. Summary of the Invention

[0004] To address the shortcomings of the existing technology, while ensuring the coordination of vehicle-arm motion, achieve rapid convergence of task trajectory tracking errors and system robustness, and effectively improve the operational flexibility and application technology level of the composite robot, the present invention adopts the following technical solutions:

[0005] The composite robot-carriage coordinated active disturbance rejection control method based on the optimal operating area includes the following steps:

[0006] Step S1: Constructing the kinematic and dynamic models of the composite robot vehicle-arm redundant system. Based on the generalized Jacobian matrix, the maneuverability of the robot end is measured to design the optimal operation area constraint manifold for vehicle-arm coordination. Based on the kinematic and dynamic models and the optimal operation area constraint manifold, an optimal task trajectory allocation algorithm is constructed to achieve optimal allocation of task trajectories.

[0007] Step 2: A nonlinear extended state observer of the robot is constructed through the robot state variables and their estimated values. A non-singular fast terminal sliding mode manifold of the robot is constructed through the position tracking error and velocity tracking error of the task trajectory. Based on the nonlinear extended state observer and the non-singular fast terminal sliding mode manifold, an auto-disturbance rejection motion controller is constructed to enable the composite robot trajectory tracking error to globally converge in a finite time.

[0008] Furthermore, in step S1, the kinematic and dynamic models of the composite robot vehicle-arm redundant system are constructed as follows:

[0009]

[0010]

[0011] In formula (1) and formula (2), Represents the motion speed of the composite robot end in the task space coordinate system [W}, where represents a set of real numbers, m represents the degrees of freedom of the task space; represents the generalized joint space position, n represents the joint space degree of freedom of the composite robot manipulator, represents the generalized joint space velocity, represents the generalized joint space acceleration, where Represent the actual x, y coordinate position and rotation angle of the mobile platform, θ1,…,θ n Indicates the joint rotation angle of each link of the operating arm; represents the generalized Jacobian matrix, where They represent the inertia matrix, the Coriolis force and centrifugal force coefficient matrix, and the gravitational moment vector respectively; Represents the unknown torque caused by uncertain dynamics and external interference, represents the control torque, where τ O1 , τ O2 , τ O3 , τ O4 represents the driving torque of the Mecanum wheel set of the mobile platform, τ1,…,τ n Indicates the driving torque of each joint of the manipulator; represents the input torque conversion matrix;

[0012] Defining operability metrics for composite robot terminals as follows:

[0013]

[0014] In formula (3), det(·) represents the matrix determinant operator, It is proportional to the vehicle-arm coordination operability.

[0015] Furthermore, in step S1, based on the above-mentioned optimal operation area constraint manifold, the optimal task trajectory allocation algorithm is designed as follows:

[0016]

[0017] The first term on the right side of formula (4) The optimal solution that minimizes the Euclidean norm when representing the task trajectory to the joint space, the second term represents the homogeneous solution of the null space of the Jacobian matrix J(θ), i.e., the robot self-motion that does not affect the end pose to maximize maneuverability, where represents the pseudo-inverse of the Jacobian matrix, Represents the desired task space motion speed at the end, represents the nominal trajectory velocity in the generalized joint space, is an identity matrix; is a weight coefficient used to control the self-motion of the composite robot under the terminal path constraint and optimize the vehicle-arm coordination. represents the generalized Jacobian matrix, where m represents the degree of freedom in the task space, n represents the degree of freedom in the joint space of the composite robot manipulator, θ1,…,θ n represents the joint rotation angle of each link of the operating arm, represents the set of real numbers, Represents the operability metric of the composite robot terminal.

[0018] This task trajectory allocation method allows the hybrid robot's end-point to enter the optimal operating area through coordinated vehicle-arm motion in the generalized joint space when performing a specific task, maximizing the robot's maneuverability without affecting the end-point's pose. Furthermore, by transforming the J(θ) null space homogeneous solution, it is also possible to achieve gradient optimization of other performance indicators within the hybrid robot's end-point task constraints.

[0019] Furthermore, in step S2, a nonlinear extended state observer of the robot is constructed as follows:

[0020] Define the state variables x1=q of the composite robot system. x3=f(t), where represents the generalized dynamical uncertainty and satisfies |f i (t)|≤f i , known supremum i=1,…,n+3, represents the generalized joint space position, n represents the joint space degree of freedom of the composite robot manipulator, represents the generalized joint space velocity, where W x O 、 W y O 、 W φ O Represent the actual x, y coordinate position and rotation angle of the mobile platform, θ1,…,θ n Indicates the joint rotation angle of each link of the operating arm; They represent the inertia matrix, the Coriolis force and centrifugal force coefficient matrix, and the gravitational moment vector respectively; Represents the unknown torque caused by uncertain dynamics and external interference, represents the control torque, where τ O1 , τ O2 , τ O3 , τ O4 represents the driving torque of the Mecanum wheel set of the mobile platform, τ1,…,τ n Indicates the driving torque of each joint of the manipulator; Represents the input torque conversion matrix, then the state space expression of the composite robot dynamics is:

[0021]

[0022] in, They represent the differentials of the state variables x1, x2, and x3 of the composite robot system respectively.

[0023] The extended state observer is designed for the generalized uncertainty of the above system as follows:

[0024]

[0025] In formula (6), z1, z2, and z3 are the estimated values of the system state variables x1, x2, and x3 respectively, and the nonlinear error function and its constant coefficients δ>0, 0<λ1<1, represents the positive definite diagonal gain matrix of the observer, ε 1i , i = 1,…, n + 3 represent the elements of the observer error vector ε1; it can be seen that the extended state z3 is the estimated value of the generalized dynamics uncertainty of the system.

[0026] Furthermore, in step S2, a non-singular fast terminal sliding mode manifold of the robot is constructed as follows:

[0027] In order to improve the error convergence speed and robustness of the composite robot trajectory tracking, a non-singular fast terminal sliding surface s(t) = 0 is designed as follows:

[0028]

[0029] e=qq in formula (7) d and Represent the position tracking error and velocity tracking error of the task trajectory, q d represents the nominal trajectory of the generalized joint space, k1=diag{k 11 , k 12 ,…,k 1(n+3)} and k2=diag{k 21, k 22 ,…,k 2(n+3)} represents the positive definite diagonal gain matrix; , The normal coefficients γ1 and γ2 satisfy 1<γ2<2, γ1>γ2.

[0030] Furthermore, in step S2, an ADRC motion controller is constructed as follows:

[0031]

[0032] In formula (8) is the nominal acceleration in joint space, The constant coefficients satisfy σ1>0, σ2>0, 0<σ3<1. This control algorithm can make the trajectory tracking error of the composite robot converge to zero in a finite time and has good robustness.

[0033] Furthermore, the method also includes step 3: constructing the dynamic equations of the nonlinear extended state observer, using the pole placement method to construct the observer gain matrix for obtaining the bounded region of observer error convergence, thereby effectively estimating the non-generalized determinism of the compensation compound robot system; based on the non-singular fast terminal sliding mode manifold and the auto-disturbance rejection motion controller, constructing the Lyapunov function, and obtaining the auto-disturbance rejection motion controller to meet the global finite-time stability criterion of the observation-control closed-loop system to control the dynamic tracking of the task trajectory and achieve the stability of the dynamic tracking of the task trajectory and the robustness of the system.

[0034] Furthermore, in step S3, the observer gain matrix is constructed as follows:

[0035] The dynamic equations for constructing the nonlinear extended state observer are:

[0036]

[0037] In formula (9), ε1=z1-q, ε3=f(t)-z3 is the estimation error of the extended state observer, and the state variables of the composite robot system are x1=q, x3=f(t), represents the generalized dynamical uncertainty and satisfies |f i (t)|≤f i , known supremum i=1,…,n+3, represents the generalized joint space position, n represents the joint space degree of freedom of the composite robot manipulator, represents the generalized joint space velocity, where W xO 、 W y O 、 W φ O Represent the actual x, y coordinate position and rotation angle of the mobile platform, θ1,…,θ n represents the joint rotation angle of each link of the manipulator; z1, z2, z3 are the estimated values of the system state variables x1, x2, x3 respectively;

[0038] Based on this, the pole placement method is used to design the observer gain matrix as follows:

[0039]

[0040] The constant coefficient β0 in formula (10) is greater than 0; the observer error satisfies The supremum is f j , β0, ε ij , i = 1, 2, 3, j = 1, ..., n + 3 represent the elements of the observer error vector ε1, ε2, ε3 respectively; the bounded region of convergence of the extended state observer error is obtained, which can effectively estimate and compensate the non-generalized determinism of the composite robot system.

[0041] Furthermore, in step S3, the Lyapunov function is constructed as follows:

[0042] The stability of the control system is analyzed by Lyapunov method, and the Lyapunov function is designed. And deduce:

[0043]

[0044] In formula (11) The ADRC motion controller satisfies the global finite-time stability of the observation-control closed-loop system, that is, the error e will converge to zero quickly in a finite time; where s represents the non-singular fast terminal sliding surface, e = qq d and Represent the position tracking error and velocity tracking error of the task trajectory respectively. The normal coefficients γ1 and γ2 satisfy 1<γ2<2, γ1>γ2. k1 and k2 represent the positive definite diagonal gain matrix. represents the inertia matrix, q represents the generalized joint space position, represents the generalized joint space velocity, represents a set of real numbers, n represents the degrees of freedom of the joint space of the composite robot manipulator, represents the input torque conversion matrix, τ represents the control torque, q d represents the nominal trajectory in the generalized joint space, represents the nominal trajectory velocity in the generalized joint space, The nominal trajectory acceleration in the generalized joint space, f(t), represents the generalized dynamic uncertainty, and the constant coefficients satisfy σ1>0, σ2>0, 0<σ3<1.

[0045] The advantages and beneficial effects of the present invention are:

[0046] The present invention proposes an auto-disturbance rejection control method for vehicle-arm coordination of a composite robot based on an optimal operating area. Task trajectories are allocated through the constraint manifold of the terminal optimal operating area during the vehicle-arm coordinated motion process. Then, an auto-disturbance rejection motion controller is designed based on a nonlinear extended state observer and an error feedback terminal sliding mode manifold. This method can enable the task trajectory tracking error to converge quickly to zero within a finite time, while ensuring the vehicle-arm motion coordination and system robustness, and ultimately effectively improving the operational flexibility and execution efficiency of the composite robot. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 4 is a flow chart of an active disturbance rejection motion control method according to an embodiment of the present invention.

[0048] Figure 2 Schematic diagram of the task trajectory tracking effect of the composite robot in an embodiment of the present invention.

[0049] Figure 3 Schematic diagram of the optimization effect of the operability index of the composite robot in an embodiment of the present invention. DETAILED DESCRIPTION

[0050] The following describes the specific embodiments of the present invention in detail with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are only used to illustrate and explain the present invention and are not intended to limit the present invention.

[0051] like Figure 1 As shown in the figure, the optimal operating area-based coordinated active disturbance rejection control method for the composite robot vehicle-arm is used to allocate task trajectories through the optimal operating area constraint manifold at the terminal during the vehicle-arm coordinated motion. Then, based on the nonlinear extended state observer and the error feedback terminal sliding mode manifold, an active disturbance rejection motion controller is designed. This method achieves rapid convergence of the task trajectory tracking error and system robustness while ensuring the coordination of the vehicle-arm motion. Ultimately, it effectively improves the operational flexibility and application technology level of the composite robot. The specific steps include the following:

[0052] Step S1: Constructing the kinematic and dynamic models of the composite robot vehicle-arm redundant system. Based on the generalized Jacobian matrix, the maneuverability of the robot end is measured to design the optimal operation area constraint manifold for vehicle-arm coordination. Based on the kinematic and dynamic models and the optimal operation area constraint manifold, an optimal task trajectory allocation algorithm is constructed to achieve optimal allocation of task trajectories.

[0053] Constructing the kinematic and dynamic models of the composite robot vehicle-arm redundant system:

[0054]

[0055]

[0056] In formula (1) and formula (2), Represents the motion speed of the composite robot end in the task space coordinate system [W}, where represents a set of real numbers, m represents the degrees of freedom of the task space; represents the generalized joint space position, n represents the joint space degree of freedom of the composite robot manipulator, represents the generalized joint space velocity, represents the generalized joint space acceleration, where W x O 、 W y O 、 W φ O Represent the actual x, y coordinate position and rotation angle of the mobile platform, θ1,…,θ n Indicates the joint rotation angle of each link of the operating arm; represents the generalized Jacobian matrix, where They represent the inertia matrix, the Coriolis force and centrifugal force coefficient matrix, and the gravitational moment vector respectively; Represents the unknown torque caused by uncertain dynamics and external interference, represents the control torque, where τ O1 , τ O2 , τ O3 , τ O4 represents the driving torque of the Mecanum wheel set of the mobile platform, τ1,…,τ n Indicates the driving torque of each joint of the manipulator; Represents the input torque conversion matrix.

[0057] Defining operability metrics for composite robot terminals as follows:

[0058]

[0059] In formula (3), det(·) represents the matrix determinant operator, It is proportional to the vehicle-arm coordination operability.

[0060] Based on the above optimal operation area constraint manifold, the optimal task trajectory allocation algorithm is designed as follows:

[0061]

[0062] The first term on the right side of formula (4) The optimal solution that minimizes the Euclidean norm when representing the task trajectory to the joint space, the second term represents the homogeneous solution of the null space of the Jacobian matrix J(θ), i.e., the robot self-motion that does not affect the end pose to maximize maneuverability, where represents the pseudo-inverse of the Jacobian matrix, Represents the desired task space motion speed at the end, represents the nominal trajectory velocity in the generalized joint space, is an identity matrix; is a weight coefficient used to control the self-motion of the composite robot under the terminal path constraint and optimize the vehicle-arm coordination.

[0063] This task trajectory allocation method allows the hybrid robot's end-point to enter the optimal operating area through coordinated vehicle-arm motion in the generalized joint space when performing a specific task, maximizing the robot's maneuverability without affecting the end-point's pose. Furthermore, by transforming the J(θ) null space homogeneous solution, it is also possible to achieve gradient optimization of other performance indicators within the hybrid robot's end-point task constraints.

[0064] Step 2: A nonlinear extended state observer for the robot is constructed using the robot state variables and their estimated values. A nonsingular fast terminal sliding mode manifold of the robot is constructed using the position tracking error and velocity tracking error of the task trajectory. Based on the nonlinear extended state observer and the nonsingular fast terminal sliding mode manifold, an active disturbance rejection motion controller is constructed to achieve finite-time global convergence of the trajectory tracking error of the composite robot.

[0065] Define the state variables x1=q of the composite robot system. x3=f(t), where represents the generalized dynamical uncertainty and satisfies |f i (t)|≤f i , known supremum i=1,…,n+3, then the state space expression of the composite robot dynamics is:

[0066]

[0067] in, They represent the differentials of the state variables x1, x2, and x3 of the composite robot system respectively.

[0068] The extended state observer is designed for the generalized uncertainty of the above system as follows:

[0069]

[0070] In formula (6), z1, z2, and z3 are the estimated values of the system state variables x1, x2, and x3 respectively, and the nonlinear error function and its constant coefficients δ>0, 0<λ1<1, 0<λ2<1; represents the positive definite diagonal gain matrix of the observer, ε 1i , i = 1,…, n + 3 represent the elements of the observer error vector ε1; it can be seen that the extended state z3 is the estimated value of the generalized dynamics uncertainty of the system.

[0071] In order to improve the error convergence speed and robustness of the composite robot trajectory tracking, a non-singular fast terminal sliding surface s(t) = 0 is designed as follows:

[0072]

[0073] e=qq in formula (7) d and Represent the position tracking error and velocity tracking error of the task trajectory, q d represents the nominal trajectory of the generalized joint space, k1=diag{k 11 , k 12 ,…,k 1(n+3)} and k2=diag{k 21 , k 22 ,…,k 2(n+3)} represents the positive definite diagonal gain matrix; , The normal coefficients γ1 and γ2 satisfy 1<γ2<2, γ1>γ2.

[0074] Based on this, the composite robot self-disturbance rejection motion controller is designed as follows

[0075]

[0076] In formula (8) is the nominal acceleration in joint space, sgn(s)=[sign(s1),…,sign(s) n+3 )] T , the constant coefficients satisfy σ1>0, σ2>0, 0<σ3<1. This control algorithm can make the trajectory tracking error of the composite robot converge to zero in a finite time and has good robustness.

[0077] Step S3: Construct the dynamic equations of the nonlinear extended state observer, and use the pole placement method to construct the observer gain matrix to obtain the bounded region of observer error convergence, so as to effectively estimate the non-generalized determinism of the compensation composite robot system; based on the non-singular fast terminal sliding mode manifold and the auto-disturbance rejection motion controller, construct the Lyapunov function, and obtain the auto-disturbance rejection motion controller that meets the global finite-time stability criterion of the observation-control closed-loop system to control the dynamic tracking of the task trajectory and achieve the stability of the dynamic tracking of the task trajectory and the robustness of the system.

[0078] From formula (5) and formula (6), the dynamic equation of the nonlinear extended state observer can be obtained as follows:

[0079]

[0080] In formula (9), ε1=z1-q, ε3 = f(t) - z3 is the estimated error of the extended state observer. Based on this, the pole placement method is used to design the observer gain matrix as follows:

[0081]

[0082] The constant coefficient β0 in formula (10) is greater than 0; the observer error satisfies The supremum is f j , β0, ε ij , i = 1, 2, 3, j = 1, ..., n + 3 represent the elements of the observer error vector ε1, ε2, ε3 respectively; the bounded region of convergence of the extended state observer error is obtained, which can effectively estimate and compensate the non-generalized determinism of the composite robot system.

[0083] Then the stability of the control system is analyzed by the Lyapunov method, that is, the Lyapunov function is designed for the composite robot self-disturbance rejection motion controller formula (7)-(8) And deduce

[0084]

[0085] In formula (11) It is found that the ADRC motion controller satisfies the global finite-time stability of the observation-control closed-loop system, that is, the error e will converge quickly to zero within a finite time.

[0086] In the embodiment of the present invention, the specific implementation object is a composite robot consisting of a Mecanum wheeled mobile platform and a six-degree-of-freedom robotic arm, the kinematic parameters of the robotic arm are d1 = 0.140m, a2 = 0.375m, a3 = 0.345m, d4 = 0.122m, d5 = 0.122m, d6 = 0.083m, the kinematic parameters of the mobile platform are a = 0.225m, b = 0.270m, d = 0.300m; the mass of the robotic arm connecting rod is m1 = 4.785kg, m2 = 5.485kg, m3 = 3.101kg, m4 = 2.568kg, m5 = 2.568kg, m6 = 0.414kg, the mass of the mobile platform and the wheel group is m b =73.656kg, m w1 =m w2 =m w3 =m w4 =0.715kg; the moment of inertia of the robot arm connecting rod is I1 = 5.438kg·m 2 I2=6.251kg·m 2 I3=4.488kg·m 2 I4=1.075kg·m 2 I5=0.130kg·m 2 I6=0.025kg·m 2 , the mobile platform and the moment of inertia is I b =9.619kg·m 2 , I w1 =I w2 =I w3 =I w4 =0.007kg·m 2 ; The viscous friction coefficient of each joint of the robotic arm is f v1 =f v2 =f v3 =0.8N·m / (rad / s), f v4 =f v5 =f v6 =0.3N·m / (rad / s), viscous friction coefficient of each wheel group of the mobile platform f vw1 =f vw2 =f vw3 =f vw4 =5N·m / (rad / s).

[0087] The desired motion trajectory of the composite robot end is designed as Where ω = 0.1π. The initial position of the end of the composite robot is set to x(0) = [0.5, 0, 0.65] T m, the initial velocity is set to

[0088] The control law of the active disturbance rejection controller for the composite robot vehicle-arm coordination based on the optimal operation area is shown in formulas (4), (6), (7), and (8), where the weight of the task trajectory optimal allocation algorithm is α = 0.5, the parameters of the extended state observer are: δ = 0.05, λ1 = 0.5, λ2 = 0.25, β0 = 0.1; the parameters of the active disturbance rejection motion controller are: k1 = diag{3, 3, ..., 3}, k2 = diag{1.5, 1.5, ..., 1.5}, γ2 = 1.5, γ1 = 2, μ i∞ =0.001, σ1=25, σ2=0.4, σ3=0.5. Based on this, the implementation effect of the composite robot motion control can be obtained. Figure 2 and Figure 3 This shows that the motion error of the terminal of the composite robot can achieve fast and high-precision convergence, while keeping the operability measurement indicators of the terminal of the robot at a good level, and ultimately achieving vehicle-arm motion coordination and system robustness.

[0089] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some or all of the technical features therein. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A composite robot-carriage coordinated auto-disturbance rejection control method based on the optimal operating area, characterized in that: The following steps are involved: Step S1: Construct a kinematic and dynamic model of the composite robot vehicle-arm redundant system. Based on the generalized Jacobian matrix, measure the maneuverability of the robot end to design the optimal operation area constraint manifold for vehicle-arm coordination. Based on the kinematic and dynamic model and the optimal operation area constraint manifold, construct an optimal task trajectory allocation algorithm. Based on the optimal operation area constraint manifold, design the optimal task trajectory allocation algorithm as follows: In formula (4) represents the optimal solution that minimizes the Euclidean norm when mapping the task trajectory to the joint space, Represents the Jacobian matrix Homogeneous solution of the null space, where represents the pseudo-inverse of the Jacobian matrix, Represents the desired task space motion speed at the end, represents the nominal trajectory velocity in the generalized joint space, is an identity matrix; is a weight coefficient used to control the self-motion of the composite robot under the terminal path constraint. represents the generalized Jacobian matrix, where m represents the degree of freedom in the task space, n represents the degree of freedom in the joint space of the composite robot manipulator, θ1,…,θ n represents the joint rotation angle of each link of the operating arm, represents the set of real numbers, Indicates the operability metric of the composite robot terminal; Step S2: A nonlinear extended state observer of the robot is constructed through the robot state variables and their estimated values. A non-singular fast terminal sliding mode manifold of the robot is constructed through the position tracking error and the velocity tracking error of the task trajectory. Based on the nonlinear extended state observer and the non-singular fast terminal sliding mode manifold, an anti-disturbance motion controller is constructed to enable the composite robot trajectory tracking error to globally converge in a finite time.

2. The method for coordinated active disturbance rejection control of a composite robot vehicle-arm based on an optimal operating area according to claim 1, characterized in that: The kinematic and dynamic models of the composite robot vehicle-arm redundant system are constructed in step S1 as follows: In formula (1) and formula (2), Represents the motion speed of the composite robot end in the task space coordinate system {W}, where represents a set of real numbers, m represents the degrees of freedom of the task space; represents the generalized joint space position, n represents the joint space degree of freedom of the composite robot manipulator, represents the generalized joint space velocity, represents the generalized joint space acceleration, where W x O 、 W y O 、 W φ O Represent the actual x, y coordinate position and rotation angle of the mobile platform, θ1,…,θ n Indicates the joint rotation angle of each link of the operating arm; represents the generalized Jacobian matrix, where They represent the inertia matrix, the Coriolis force and centrifugal force coefficient matrix, and the gravitational moment vector respectively; Represents the unknown torque caused by uncertain dynamics and external interference, represents the control torque, where τ O1 , τ O2 , τ O3 , τ O4 represents the driving torque of the Mecanum wheel set of the mobile platform, τ1,…,τ n Indicates the driving torque of each joint of the manipulator; represents the input torque conversion matrix; Defining operability metrics for composite robot terminals as follows: In formula (3), det(·) represents the matrix determinant operator, It is proportional to the vehicle-arm coordination operability.

3. The method for coordinated active disturbance rejection control of a composite robot vehicle-arm based on an optimal operating area according to claim 1, characterized in that: In step S2, a nonlinear extended state observer of the robot is constructed as follows: Define the state variables x1=q of the composite robot system. x3=f(t), where represents the generalized dynamical uncertainty and satisfies |f i (t)|≤f i , known supremum i=1,…,n+3, represents the generalized joint space position, n represents the joint space degree of freedom of the composite robot manipulator, represents the generalized joint space velocity, where W x O 、 W y O 、 W φ O Represent the actual x, y coordinate position and rotation angle of the mobile platform, θ1,…,θ n Indicates the joint rotation angle of each link of the operating arm; They represent the inertia matrix, the Coriolis force and centrifugal force coefficient matrix, and the gravitational moment vector respectively; Represents the unknown torque caused by uncertain dynamics and external interference, represents the control torque, where τ O1 , τ O2 , τ O3 , τ O4 represents the driving torque of the Mecanum wheel set of the mobile platform, τ1,…,τ n Indicates the driving torque of each joint of the manipulator; Represents the input torque conversion matrix, then the state space expression of the composite robot dynamics is: in, They represent the differentials of the state variables x1, x2, and x3 of the composite robot system respectively; The extended state observer is designed for the generalized uncertainty of the above system as follows: In formula (6), z1, z2, and z3 are the estimated values of the system state variables x1, x2, and x3 respectively, and the nonlinear error function and its constant coefficients δ>0, 0<λ1<1, 0<λ2<1; represents the positive definite diagonal gain matrix of the observer, ε 1i , i=1,…,n+3 represent the elements of the observer error vector ε1; the extended state z3 is the estimated value of the generalized dynamics uncertainty of the system.

4. The method for coordinated active disturbance rejection control of a composite robot vehicle-arm based on an optimal operating area according to claim 3, characterized in that: In step S2, the robot non-singular fast terminal sliding mode manifold is constructed as follows: Design a non-singular fast terminal sliding surface s(t) = 0 as follows: e=qq in formula (7) d and Represent the position tracking error and velocity tracking error of the task trajectory, q d represents the nominal trajectory of the generalized joint space, k1=diag{k 11 ,k 12 ,…,k 1(n+3) } and k2=diag{k 21 ,k 22 ,…,k 2(n+3) } represents the positive definite diagonal gain matrix; The normal coefficients γ1 and γ2 satisfy 1<γ2<2, γ1>γ2.

5. The method for coordinated active disturbance rejection control of a composite robot vehicle-arm based on an optimal operating area according to claim 4, characterized in that: In step S2, an ADRC motion controller is constructed as follows: In formula (8) is the nominal acceleration in joint space, sgn(s)=[sign(s1),…,sign(s n+3 )] T , the constant coefficients satisfy σ1>0, σ2>0, 0<σ3<1.

6. The method for coordinated active disturbance rejection control of a composite robot vehicle-arm based on an optimal operating area according to claim 1, characterized in that: The method further comprises step S3: constructing a dynamic equation of a nonlinear extended state observer, using a pole placement method to construct an observer gain matrix for obtaining a bounded region of observer error convergence; Based on the non-singular fast terminal sliding mode manifold and the active disturbance rejection motion controller, the Lyapunov function is constructed, and the active disturbance rejection motion controller is obtained to meet the global finite-time stability criterion of the observation-control closed-loop system to control the dynamic tracking of the task trajectory.

7. The method for coordinated active disturbance rejection control of a composite robot vehicle-arm based on an optimal operating area according to claim 6, characterized in that: In step S3, the observer gain matrix is constructed as follows: The dynamic equations for constructing the nonlinear extended state observer are: In formula (9), ε1=z1-q, ε3=f(t)-z3 is the estimation error of the extended state observer, and the state variable of the composite robot system is represents the generalized dynamical uncertainty and satisfies |f i (t)|≤f i , known supremum i=1,…,n+3, represents the generalized joint space position, n represents the joint space degree of freedom of the composite robot manipulator, represents the generalized joint space velocity, where W x O 、 W y O 、 W φ O Represent the actual x, y coordinate position and rotation angle of the mobile platform, θ1,…,θ n represents the joint rotation angle of each link of the manipulator; z1, z2, z3 are the estimated values of the system state variables x1, x2, x3 respectively; Based on this, the pole placement method is used to design the observer gain matrix as follows: The constant coefficient β0 in formula (10) is greater than 0; the observer error satisfies The supremum is f j , β0, ε ij ,i=1,2,3,j=1,…,n+3 represent the elements of the observer error vector ε1, ε2, ε3 respectively; The bounded region of error convergence of the extended state observer is obtained, which can effectively estimate and compensate the ungeneralized determinism of the composite robot system.

8. The method for coordinated active disturbance rejection control of a composite robot vehicle-arm based on an optimal operating area according to claim 6, characterized in that: In step S3, the Lyapunov function is constructed as follows: Design of Lyapunov function And deduce: In formula (11) The ADRC motion controller satisfies the global finite-time stability of the observation-control closed-loop system, that is, the error e will converge to zero quickly in a finite time; where s represents the non-singular fast terminal sliding surface, e = qq d and Represent the position tracking error and velocity tracking error of the task trajectory respectively. The normal coefficients γ1 and γ2 satisfy 1<γ2<2, γ1>γ2. k1 and k2 represent the positive definite diagonal gain matrix. represents the inertia matrix, q represents the generalized joint space position, represents the generalized joint space velocity, represents a set of real numbers, n represents the degrees of freedom of the joint space of the composite robot manipulator, represents the input torque conversion matrix, τ represents the control torque, q d represents the nominal trajectory in the generalized joint space, represents the nominal trajectory velocity in the generalized joint space, The nominal trajectory acceleration in the generalized joint space, f(t), represents the generalized dynamic uncertainty, and the constant coefficients satisfy σ1>0, σ2>0, 0<σ3<1.

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