Multi-robot cooperative artificial potential field control method and system for heavy workpiece carrying

Abstract

The invention discloses a multi-robot cooperative artificial potential field control method and system for heavy workpiece carrying. The control method comprises the steps that a dynamic model of differential drive heavy robots is established; transforming the dynamical model of the differential drive heavy-duty robot to obtain a time-delay-free equivalent dynamical model; designing a fixed time non-linear disturbance observer of the differential drive heavy-duty robot based on the time-delay-free equivalent kinetic model, and outputting an estimated value of lumped disturbance; the method comprises the steps of constructing a dynamic model of a virtual leader, constructing a distributed formation controller based on the dynamic model of the virtual leader and an estimated value of lumped disturbance output by a fixed-time nonlinear disturbance observer, and controlling the virtual leader and a plurality of followers by using the distributed formation controller so as to achieve and maintain an expected formation. According to the invention, the influence of system disturbance and input time delay is effectively overcome through the distributed formation controller, and stable and robust cooperative handling control is realized.

Description

Technical Field

[0001] This invention relates to the field of robot formation control technology, and in particular to a multi-robot collaborative artificial potential field control method and system for handling heavy workpieces. Background Technology

[0002] In manufacturing, logistics, and aerospace industries, the handling of heavy workpieces (such as drone wings) typically requires the collaborative operation of multiple mobile robots. Multi-robot cooperative handling systems (DHMRs) have broad application prospects in such tasks due to their high load-bearing capacity and flexible motion characteristics. However, multi-robot cooperative handling faces numerous challenges, including the nonlinear dynamics of the robots themselves, strong dynamic coupling with the workpiece, and the effects of internal friction and external disturbances. Furthermore, when using networks for cooperative control, input delays are inevitably introduced, which can, in severe cases, lead to system performance degradation or even instability.

[0003] Existing research on multi-robot cooperative handling often involves simplifications in dynamic modeling. For example, robots are treated as point masses, ignoring the impact of center-of-mass shift, or the cooperative system is decoupled into multiple independent tracking problems, thus avoiding the internal force / torque coupling between robots and between robots and the load. While this simplification facilitates controller design, it introduces model errors in high-dynamic, high-precision tasks, limiting the overall system performance. Furthermore, some studies only design distributed cooperative control laws at the kinematic level, failing to fully consider the formation problem under the constraint of heavy workpieces, making them difficult to directly apply to practical handling scenarios.

[0004] In terms of control methods, the artificial potential field method has attracted attention due to its simple structure and ease of achieving real-time obstacle avoidance and formation maintenance. However, traditional methods often remain at the kinematic level or oversimplify the dynamics, lacking the ability to uniformly handle nonlinear dynamics, input delay, and lumped disturbances. For input delay in network control, existing technologies often employ strategies such as the Pade approximation and predictive control for compensation. However, most methods separate delay compensation from dynamic controller design, lacking a unified framework that guarantees stability under conditions of coexisting delay and nonlinear coupling.

[0005] Furthermore, nonlinear disturbance observers are widely used to estimate and compensate for disturbances in order to suppress internal and external disturbances of the system. However, traditional observers generally only guarantee asymptotic convergence, and their convergence speed depends on the initial state and the observer gain. When the disturbance is large or changes drastically, it may lead to a prolonged transient process, which is not conducive to tasks with high safety requirements, such as handling heavy workpieces.

[0006] Therefore, existing technologies still lack a collaborative control method that can simultaneously and accurately model the dynamics of multi-robot-load coupling, effectively compensate for network latency, quickly estimate and compensate for disturbances, and ensure formation maintenance and system connectivity. Further research and improvement are urgently needed. Summary of the Invention

[0007] This invention provides a multi-robot collaborative artificial potential field control method and system for handling heavy workpieces, in order to solve the technical problems mentioned in the background art.

[0008] To achieve the above objectives, the technical solution of the present invention is implemented as follows: This invention provides a multi-robot cooperative artificial potential field control method for handling heavy workpieces, comprising the following steps: S1. Establish a dynamic model of a multi-robot collaborative handling system, which includes multiple differentially driven heavy robots, a flexible pallet, and an overweight workpiece. The overweight workpiece is placed on multiple differentially driven heavy robots through the flexible pallet. Then, construct a dynamic model of the differentially driven heavy robots based on the dynamic model of the multi-robot collaborative handling system. S2. By introducing the input delay in the network control system, the dynamic model of the differentially driven heavy robot is transformed to obtain an equivalent dynamic model without delay. S3. Based on the time-delay-free equivalent dynamic model, design a fixed-time nonlinear disturbance observer for the differential-driven heavy robot, and use the fixed-time nonlinear disturbance observer to output the estimated value of the lumped disturbance. S4. Construct a dynamic model of the virtual leader, design an artificial potential field function, and construct a distributed formation controller based on the dynamic model of the virtual leader, the artificial potential field function, and the estimated value of the lumped disturbance. Treat all differentially driven heavy robots as followers and use the distributed formation controller to control the virtual leader and multiple followers to achieve and maintain the desired formation.

[0009] Furthermore, step S1 specifically includes the following steps: S11, Calculate the... i The linear velocity of the geometric center of the heavy robot is driven by a differential mechanism. and angular velocity ;in, ; S12, Constructing the first i The velocity vector of the differential-driven heavy robot The angular velocity of the drive wheel on the differential-driven heavy robot Conversion formulas between; S13, Constructing the first i Nonholonomic constraint equations for a differential-driven heavy-duty robot; S14. Construct a dynamic model of a multi-robot cooperative handling system based on the Euler-Lagrange principle and in conjunction with nonholonomic constraint equations; S15, Constructing the first i An unsimplified dynamic model of a differential-driven heavy-duty robot; S16, Based on the dynamic model in S14, the first... i The dynamic model of the differential-driven heavy robot is simplified to obtain the first... i A dynamic model of a differentially driven heavy-duty robot.

[0010] Furthermore, in S11, the first... i The linear velocity of the geometric center of the heavy robot is driven by a differential mechanism. and angular velocity The specific calculation formula is as follows: (1) in, For the first i The radius of the drive wheels on a differentially driven heavy-duty robot For the first i The distance between two drive wheels on a differential-driven heavy-duty robot; and The first i The angular velocities of the left and right drive wheels on a differential-driven heavy-duty robot; The S12 in i The velocity vector of the differential-driven heavy robot The angular velocity of the drive wheels on the differential-driven heavy robot The conversion formulas between them are as follows: (2) in, Transformation matrix; Specifically: (3) in, Indicates the first i In the differential-driven heavy robot and inertial coordinate system The included angle of the axis; In S13, the first i The nonholonomic constraint equations for a differential-driven heavy-duty robot are: (4) in, To constrain the Jacobian matrix; Indicates the first i The state of a differentially driven heavy robot; Indicates the firsti A differential-driven generalized coordinate system for heavy-duty robots; They represent the first i The rotation angle of the left and right drive wheels on a differential-driven heavy robot; T Indicates transpose; the dot sign on the parameter indicates the first derivative of that parameter; The dynamic model of the multi-robot cooperative handling system in S14 is as follows: (5) in, For the first i The control input for a differential-driven heavy-duty robot They represent the first i The rotational torque of the left and right drive wheels on a differentially driven heavy-duty robot For the Lagrange multipliers of the binding force, For the first i A differentially driven gravitational acceleration vector for a heavy-duty robot; Indicates the first i Lumped disturbances, burst friction, and external disturbances in a differentially driven heavy robot; The number of differentially driven heavy-duty robots, To constrain the Jacobian matrix number of rows; Indicates the sign of the partial derivative; This represents the total kinetic energy of a multi-robot collaborative handling system; t Indicates time; Among them, total kinetic energy Including the kinetic energy of differentially driven heavy robots Drive wheel kinetic energy omnidirectional wheel kinetic energy kinetic energy of load ; The S15 in i The specific dynamic model of the differential-driven heavy robot is as follows: (6) in, The inertia matrix, The matrix represents the centrifugal force and the Coriolis force. For the input matrix, Torque is controlled for the drive wheels; represents the set of real numbers; the symbol · on the parameter indicates the second derivative of that parameter; In S16, the first i The specific dynamic model of the differential-driven heavy robot is as follows: (7) Among them, the first intermediate matrix Second intermediate matrix The third intermediate matrix , Represents the parameter matrix, Indicates the control torque of the drive wheels; Indicates the first i Lumped perturbation of a differentially driven heavy-duty robot It is the first The speed of the differential-driven heavy robot, including the first Linear velocity of a differential-driven heavy robot and angular velocity ; parameter matrix The formula for calculation is: (8).

[0011] Furthermore, step S2 specifically includes the following steps: S21. Calculate the delayed control input torque by introducing the input delay in the network control system, and then adjust the control input torque based on the delayed torque. i The dynamic model of the differential-driven heavy robot is transformed to obtain the transformed dynamic model. S22. Perform a Laplace transform on the control input torque with time delay to obtain the transformed control input torque; S23. Define auxiliary variables and perform a Laplace transform on the auxiliary variables to obtain the transformed auxiliary variables; S24. Substitute the transformed control input torque into the transformed auxiliary variable to obtain the differential equation of the auxiliary variable; S25. Perform an inverse Laplace transform on the differential equation of the auxiliary variable to obtain the differential equation of the auxiliary variable. S26. Combining the transformed dynamic model and the differential equations of the auxiliary variables, an equivalent dynamic model without time delay is constructed.

[0012] Furthermore, the transformed dynamic model in S21 is as follows: (9) in, It is a control input torque with a time delay; This indicates the input delay in a networked control system; The transformed control input torque in S22 is specifically as follows: (10) in, It is a Laplace variable. Represents the Laplace transform; The auxiliary variable in S23 is: (11) in, Indicates auxiliary variables; The transformed auxiliary variable in S23 is: (12) The differential equation for the auxiliary variable in S24 is: (13) The differential equation for the auxiliary variable in S25 is: (14) The time-delay-free equivalent dynamic model in S26 is as follows: (15) in, This represents an intermediate variable related to the delay parameter; and .

[0013] Furthermore, step S3 specifically includes the following steps: S31, Design observation error; S32. Design of the first step based on the time-delay-free equivalent dynamic model. A fixed-time nonlinear disturbance observer for a differential-driven heavy-duty robot; S33, Combining the time-delay-free equivalent dynamic model, the first A fixed-time nonlinear disturbance observer for a differential-driven heavy robot is constructed, and the observation error is used to build the observer's error dynamic equation. It is then determined whether the observer's error dynamic equation has converged. If it has, proceed to S34; otherwise, return to S31. S34, through the first The lumped perturbation output of the fixed-time nonlinear disturbance observer for a differentially driven heavy-duty robot. The estimated value .

[0014] Furthermore, the observation error in S31 is: (16) in, and These are the system states. and aggregate disturbance The estimated value; It is the state estimation error; It is the disturbance estimation error; the disturbance estimation error includes the external disturbance estimation error of the channel for each differentially driven heavy robot's left and right drive wheels; The S32 in The fixed-time nonlinear disturbance observer for a differential-driven heavy-duty robot is: (17) in, It is a sliding mode item; and These are the positive constant parameters to be designed; These are observer parameters used to adjust convergence performance; It is the gain function to be designed; The error dynamic equation of the observer in S33 is: (18).

[0015] Furthermore, step S4 specifically includes the following steps: S41. Construct a dynamic model of the virtual leader; treat all differentially driven heavy robots as followers; S42. Define the first [unclear] based on the dynamic model of the virtual leader. i The state error and velocity error of each follower; S43, Definition of the i The equivalent variables for the state and velocity of the first follower are defined, and the first follower's state and velocity are defined. i The equivalent variables of the state error and velocity error of each follower; S44, regarding the first i The equivalent variables of the state error of each follower are differentiated, and combined with the time-delay-free equivalent dynamic model, the equivalent state error derivative equation is obtained. The equivalent state error derivative equation shows that the dynamics of the equivalent variables of the state error are determined by the equivalent variables of the velocity error. S45. Treat the equivalent variable of each follower's state as a point in the potential energy field, and use the function... sum function Design an artificial potential field function for each pair of adjacent followers. ; S46, Solving the function Regarding the Euclidean distance between two adjacent followers The partial derivatives; S47. Using functions Regarding the Euclidean distance between two adjacent followers Solving for the artificial potential function using partial derivatives Regarding the first i The equivalent variable of the state of each follower The partial derivatives; S48. Dynamic model based on virtual leader, estimate of lumped disturbance output by fixed-time nonlinear disturbance observer, artificial potential field function. Regarding the firsti The equivalent variable of the state of each follower The partial derivatives are used to construct a distributed formation controller; S49. Use a distributed formation controller to control a virtual leader and multiple followers to achieve and maintain the desired formation.

[0016] Furthermore, the dynamic model of the virtual leader in S41 is as follows: (19) in, The status of the virtual leader. Generalized coordinates representing the virtual leader; Represents the virtual leader in the inertial coordinate system The included angle of the axis; These represent the rotation angles of the left and right drive wheels on the virtual leader, respectively. For the speed of the virtual leader, including the linear speed of the virtual leader. and angular velocity ; For the control input of the virtual leader, These represent the control torques of the left and right drive wheels of the virtual leader, respectively. For the inertia matrix of the virtual leader, For the centrifugal and Coriolis force matrices of the virtual leader, The input matrix for the virtual leader; In S42, the first i The expressions for the state error and velocity error of each follower are: (20) in, Indicates the first i The state error of each follower; Indicates the first i The speed error of each follower; In S43, the first i The equivalent variables for the state and velocity of each follower are expressed as follows: (twenty one) in, Indicates the first i The equivalent variable of the state of each follower; Indicates the first i The equivalent variable for the speed of each follower; In S43, the first i The equivalent variables for the state error and velocity error of each follower are expressed as follows: (twenty two) in, Indicates the first i Equivalent variables of the state error of each follower; Indicates the first i The equivalent variable of the speed error of each follower; The equivalent state error derivative equation in S44 is: (twenty three) The expression for the artificial potential field function in S45 is as follows: (twenty four) in, and It is a positive integer and satisfies , ;function Used to achieve formation control objectives, when the desired relative position is reached, the function... Find the minimum value; function Used to ensure network connectivity among followers; function Select as: (25) in, It is the first The first follower and the first The expected relative distance vector between each follower; function Select as: (26) in, This represents the equivalent state error between two adjacent followers, and , Indicates the first j Equivalent variables of the state error of each follower; Represents the maximum range of perception for followers; It is a positive constant and satisfies , Indicates the first i A collection of neighbors of a follower; The function in S46 Regarding the Euclidean distance between two adjacent followers The partial derivatives are: (27) The artificial potential field function in S47 Regarding the first i The equivalent variable of the state of each follower The partial derivatives are: (28) in, Represents the artificial potential field function About functions The partial derivatives, Represents the artificial potential field function Regarding the Euclidean distance between two adjacent followers The partial derivatives of, and , , ; The distributed formation controller in S48 is: (29) in, Artificial potential field function Regarding the first i Partial derivatives of the equivalent variables of the state error of each follower; These are the adjacency matrix elements of a multi-robot collaborative handling system; It is the controller gain.

[0017] Another aspect of the present invention discloses a multi-robot collaborative artificial potential field control system, including a multi-robot collaborative handling system and a network control system. The multi-robot collaborative handling system is controlled by the network control system, and the multi-robot collaborative handling system and the network control system are configured or execute the above-described multi-robot collaborative artificial potential field control method.

[0018] The beneficial effects of this invention are: 1. This invention discloses a multi-robot collaborative artificial potential field control method for handling heavy workpieces. It internally discloses a distributed formation controller, which naturally integrates formation maintenance and collision avoidance functions through the artificial potential field function, and combines a fixed-time nonlinear disturbance observer for feedforward compensation, effectively overcoming the influence of system disturbances and input time delay, and realizing stable and robust collaborative handling control. Attached Figure Description

[0019] Figure 1 This is a logic block diagram of the multi-robot collaborative artificial potential field control method in this invention; Figure 2 This is a schematic diagram of the multi-robot collaborative handling system in this invention; Figure 3 This refers to the relative distance error between the various differentially driven heavy-duty robots in this embodiment of the invention. Figure 4 This refers to the angular error between each differentially driven heavy robot relative to the virtual leader in this embodiment of the invention. Figure 5This refers to the linear velocity tracking error between each differentially driven heavy robot relative to the virtual leader in this embodiment of the invention. Figure 6 This refers to the angular velocity tracking error between each differentially driven heavy robot relative to the virtual leader in this embodiment of the invention. Figure 7 This refers to the external interference estimation error of the channel on the left drive wheel of each differentially driven heavy robot in the embodiments of the present invention; Figure 8 This refers to the external interference estimation error of the channel on the right drive wheel of each differentially driven heavy robot in the embodiments of the present invention; Figure 9 This refers to the control torque of the left drive wheel on each differential-driven heavy robot in the embodiments of the present invention; Figure 10 This refers to the control torque of the right drive wheel on each differentially driven heavy robot in the embodiments of the present invention. Detailed Implementation

[0020] To facilitate understanding of the present invention, a more complete description will be given below with reference to the accompanying drawings. Preferred embodiments of the invention are shown in the drawings. However, the invention can be implemented in many other different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided to provide a thorough and complete understanding of the disclosure of the invention.

[0021] It should also be noted that in the embodiments of this application, the same reference numerals are used to represent the same component or part. For the same part in the embodiments of this application, the reference numerals may only be used to mark one part or component as an example in the figure. It should be understood that the reference numerals are also applicable to other identical parts or components.

[0022] Reference Figure 1 This application provides a multi-robot collaborative artificial potential field control method for handling heavy workpieces, including the following steps: S1. Establish a dynamic model of the multi-robot cooperative handling system. The multi-robot cooperative handling system (Differential-driven Heavy-duty Multi-mobile Robots, DHMRs) includes multiple differentially driven heavy-duty robots, flexible pallets, and heavy-duty workpieces. The heavy-duty workpieces are placed on multiple differentially driven heavy-duty robots through flexible pallets. Then, based on the dynamic model of the multi-robot cooperative handling system, construct a dynamic model of the differentially driven heavy-duty robots. Each differential-driven heavy robot is equipped with a pair of drive wheels and two pairs of omnidirectional wheels at its bottom, with the pair of drive wheels positioned between the two pairs of omnidirectional wheels; multiple followers are supported by flexible trays, with the heavy workpieces placed on top of the flexible trays. Definition of the first The centroid of a follower is The coordinates of the four followers in the machine's coordinate system are as follows: , , , ; S2. By introducing the input delay in the network control system, the dynamic model of the differentially driven heavy robot is transformed to obtain an equivalent dynamic model without delay. S3. Based on the time-delay-free equivalent dynamic model, design a fixed-time nonlinear disturbance observer for the differential-driven heavy robot, and use the fixed-time nonlinear disturbance observer to output the estimated value of the lumped disturbance. S4. Construct a dynamic model of the virtual leader, design an artificial potential field function, and construct a distributed formation controller based on the dynamic model of the virtual leader, the artificial potential field function, and the estimated value of the lumped disturbance. Treat all differentially driven heavy robots as followers and use the distributed formation controller to control the virtual leader and multiple followers to achieve and maintain the desired formation.

[0023] In some embodiments, S1 specifically includes the following steps: S11, Calculate the... i The linear velocity of the geometric center of the heavy robot is driven by a differential mechanism. and angular velocity ;in, ; S12, Constructing the first i The velocity vector of the differential-driven heavy robot The angular velocity of the drive wheel on the differential-driven heavy robot The conversion formula between; where, They represent the first i The derivatives of the coordinate values ​​of a differentially driven heavy-duty robot in the body coordinate system, where the origin of the body coordinate system is located at the geometric center of the differentially driven heavy-duty robot. The origin of the body coordinate system x The axis points in the forward direction of the differentially driven heavy robot. y The axes follow the principles of the Cartesian coordinate system; Indicates the first i Geometric center of a differential-driven heavy-duty robot angular velocity; They represent the first i The angular velocities of the left and right drive wheels on a differential-driven heavy robot; S13, Constructing the first i Nonholonomic constraint equations for a differential-driven heavy-duty robot; S14. Since the differential-driven heavy robot is connected to the super-heavy workpiece, the differential-driven heavy robot is constrained by the super-heavy workpiece during the motion. The constraint can be introduced by the Lagrange multiplier method. The motion of the super-heavy workpiece is determined by the resultant force of all differential-driven heavy robots. Therefore, based on the Euler-Lagrange principle and combined with nonholonomic constraint equations, a dynamic model of a multi-robot cooperative handling system is constructed. S15, Constructing the first i An unsimplified dynamic model of a differential-driven heavy-duty robot; S16, Based on the dynamic model in S14, the first... i The dynamic model of the differential-driven heavy robot is simplified to obtain the first... i A dynamic model of a differentially driven heavy-duty robot.

[0024] In some embodiments, the S11 in the first i The linear velocity of the geometric center of the heavy robot is driven by a differential mechanism. and angular velocity The specific calculation formula is as follows: (1) in, For the first i The radius of the drive wheels on a differentially driven heavy-duty robot For the first i The distance between two drive wheels on a differential-driven heavy-duty robot; and The first i The angular velocities of the left and right drive wheels on a differential-driven heavy-duty robot; The S12 in i The velocity vector of the differential-driven heavy robot The angular velocity of the drive wheels on the differential-driven heavy robot The conversion formulas between them are as follows: (2) in, Transformation matrix; Specifically: (3) in, Indicates the first i In the differential-driven heavy robot and inertial coordinate system The included angle of the axis; In S13, the first i The nonholonomic constraint equations for a differential-driven heavy-duty robot are: (4) in, To constrain the Jacobian matrix; Indicates the first i The state of a differentially driven heavy robot; Indicates the first i A differential-driven generalized coordinate system for heavy-duty robots; They represent the first i The rotation angle of the left and right drive wheels on a differential-driven heavy robot; T ⊥ denotes transpose; the · sign on the parameter indicates the first derivative of that parameter; at the kinematic level, each differential-driven heavy robot is modeled independently, and its speed is determined only by its own drive wheel, without considering the motion effect of the super-heavy workpiece. The dynamic model of the multi-robot cooperative handling system in S14 is as follows: (5) in, For the first i The control input for a differential-driven heavy-duty robot They represent the first i The rotational torque of the left and right drive wheels on a differentially driven heavy-duty robot For the Lagrange multipliers of the binding force, For the first i A differentially driven gravitational acceleration vector for a heavy-duty robot; Indicates the first i Lumped disturbances, burst friction, and external disturbances in a differentially driven heavy robot; The number of differentially driven heavy-duty robots, To constrain the Jacobian matrix number of rows; Indicates the sign of the partial derivative; This represents the total kinetic energy of a multi-robot collaborative handling system; t Indicates time; Among them, total kinetic energy Including the kinetic energy of differentially driven heavy robots Drive wheel kinetic energy omnidirectional wheel kinetic energy kinetic energy of load The specific expression is as follows: Kinetic energy of each differentially driven heavy robot for: The first differential-driven heavy robot's body kinetic energy for: The second differential-driven heavy robot's body kinetic energy for: The third differential-driven heavy robot's body kinetic energy for: The fourth differential-driven heavy robot's body kinetic energy for: in, For the differential-driven heavy robot body mass, It is the moment of inertia; Drive wheel kinetic energy The expression is as follows: in, These are the mass of the driving wheel, the moment of inertia of the driving wheel about its axis, and the moment of inertia of the driving wheel about its point mass. The moment of inertia.

[0025] Universal wheel kinetic energy The expression is as follows: in, Indicates the first i The sum of the squares of the linear velocities of the omnidirectional wheels on a differentially driven heavy-duty robot, and , Indicates the first i The sum of the squares of the angular velocities of the omnidirectional wheels on a differentially driven heavy-duty robot, and , This is the moment of inertia of the caster wheel about its axle. For the universal wheel surrounding the point mass Moment of inertia of rotation. They represent the first i The linear velocity of the four omnidirectional wheels on a heavy-duty robot is determined by differential drive. , , They represent the first i The angular velocity of the four omnidirectional wheels on the heavy-duty robot is differentially driven; Load kinetic energy The expression is as follows: in, For heavy workpiece quality, The moment of inertia of the heavy workpiece about the multi-robot system. These are the linear velocity and angular velocity of the heavy workpiece, respectively.

[0026] The S15 in i The specific dynamic model of the differential-driven heavy robot is as follows: (6) in, The inertia matrix, The matrix represents the centrifugal force and the Coriolis force. For the input matrix, Torque is controlled for the drive wheels; represents the set of real numbers; the symbol · on the parameter indicates the second derivative of that parameter; In S16, the first i The specific dynamic model of the differential-driven heavy robot is as follows: (7) Among them, the first intermediate matrix Second intermediate matrix The third intermediate matrix , Represents the parameter matrix, Indicates the control torque of the drive wheels; Indicates the first i Lumped perturbation of a differentially driven heavy-duty robot It is the first The speed of the differential-driven heavy robot, including the first Linear velocity of a differential-driven heavy robot and angular velocity ; parameter matrix The formula for calculation is: (8).

[0027] In some embodiments, since the multi-robot cooperative handling system is controlled via a network, it is affected by input delay. Based on the dynamic model established in S1, this invention introduces network-induced input delay and compensates for this delay using the Pade approximation method, thereby obtaining a delay-free equivalent dynamic model. This lays the foundation for the subsequent controller design. Specifically, S2 includes the following steps: S21. Calculate the delayed control input torque by introducing the input delay in the network control system, and then adjust the control input torque based on the delayed torque. i The dynamic model of the differential-driven heavy robot is transformed to obtain the transformed dynamic model. S22. Perform a Laplace transform on the control input torque with time delay to obtain the transformed control input torque; S23. Define auxiliary variables and perform a Laplace transform on the auxiliary variables to obtain the transformed auxiliary variables; S24. Substitute the transformed control input torque into the transformed auxiliary variable to obtain the differential equation of the auxiliary variable; S25. Perform an inverse Laplace transform on the differential equation of the auxiliary variable to obtain the differential equation of the auxiliary variable. S26. Combining the transformed dynamic model and the differential equations of the auxiliary variables, an equivalent dynamic model without time delay is constructed.

[0028] In some embodiments, the transformed dynamic model in S21 is: (9) in, It is a control input torque with a time delay; This indicates the input delay in a networked control system; The transformed control input torque in S22 is specifically as follows: (10) in, It is a Laplace variable. Represents the Laplace transform; The auxiliary variable in S23 is: (11) in, Indicates auxiliary variables; The transformed auxiliary variable in S23 is: (12) The differential equation for the auxiliary variable in S24 is: (13) The differential equation for the auxiliary variable in S25 is: (14) The time-delay-free equivalent dynamic model in S26 is as follows: (15) in, This represents an intermediate variable related to the delay parameter; and The time-delay-free equivalent dynamic model uses auxiliary variables. Explicit time delay terms in the control input are eliminated. Furthermore, the analysis and design problem of a time-delayed control system can be transformed into the analysis and design problem of the time-delay-free equivalent system using a time-delay-free equivalent dynamic model.

[0029] In some embodiments, during the collaborative handling of heavy workpieces, the multi-robot collaborative handling system is subject to internal and external disturbances such as internal friction and changes in external loads. To overcome these disturbances and improve the robustness of the system, a fixed-time nonlinear disturbance observer (Fixed-time NDO) needs to be designed in S3 to accurately estimate and compensate for lumped disturbances in the system. The observer is characterized by its observation error converging to zero within a fixed time independent of the initial state, thus providing the controller with fast and accurate disturbance estimation. Specifically, S3 includes the following steps: S31, Design observation error; S32. Design of a fixed-time nonlinear disturbance observer based on a time-delay-free equivalent dynamic model. A fixed-time nonlinear disturbance observer for a differential-driven heavy-duty robot; S33, Combining the time-delay-free equivalent dynamic model, the first A fixed-time nonlinear disturbance observer for a differentially driven heavy robot is constructed, along with the observation error, to establish the observer's error dynamic equation. The convergence of the observer's error dynamic equation is determined; if convergent, proceed to step S34; otherwise, return to step S31. By proving that the observer's error dynamic equation is convergent, the first step can be verified. A fixed-time nonlinear disturbance observer for a differential-driven heavy robot can accurately estimate unknown external disturbances. S34, through the first The lumped perturbation output of the fixed-time nonlinear disturbance observer for a differentially driven heavy-duty robot. The estimated value .

[0030] In some embodiments, the observation error in S31 is: (16) in, and These are the system states. and aggregate disturbance The estimated value; It is the state estimation error; It is the disturbance estimation error; the disturbance estimation error includes the external disturbance estimation error of the channel for each differentially driven heavy robot's left and right drive wheels; The S32 in The fixed-time nonlinear disturbance observer for a differential-driven heavy-duty robot is: (17) in, It is a sliding mode item; and These are the positive constant parameters to be designed; These are observer parameters used to adjust convergence performance; It is the gain function to be designed; The error dynamic equation of the observer in S33 is: (18).

[0031] The following is about the first Stability analysis of a fixed-time nonlinear disturbance observer for a differentially driven heavy-duty robot: To conduct a rigorous stability analysis, the following assumptions are made: Assumption 1: Assume all sliding mode terms and the derivatives of all perturbations It is uniformly bounded; that is, there exist known positive constants. This makes for (representing linear velocity and angular velocity channels respectively), satisfying: in, Represents the sliding mode term with respect to velocity; Indicates the first i External disturbance observation error of differential-driven heavy robots; Indicates the first i Speed ​​observation error of differential-driven heavy-duty robots; Assumption 1 is reasonable because of the sliding mode term. It can be designed to be bounded, and the rate of change of external physical disturbances cannot be infinite.

[0032] Theorem 1: If Assumption 1 holds, and the time-varying gain function... satisfy: in, It is a fixed convergence time. It is the specified switching time, and , , , Observer parameters satisfy , (in , Even number, (Integers), and select appropriate parameters. and The observation error in the observer's error dynamic equation and It will converge within a fixed time.

[0033] Proof: (1) State Transition: The following state transition is introduced to simplify the analysis: in, , They represent the first i Equivalent velocity observation error and equivalent external disturbance observation error of a differentially driven heavy robot; Using the previous formula to transform the observer's error dynamic equation, we obtain the following formula: Due to the gain function to be designed The boundedness of, when and When convergence occurs within a fixed time, the original observation error and It will also converge within a fixed time.

[0034] (2) Lyapunov function: The Lyapunov function is defined as follows: in, The vector represents the first One element, . , Represent the fundamental Lyapunov function, the first Lyapunov function, and the second Lyapunov function, respectively. i Lyapunov functions for differential-driven heavy-duty robots; Indicates the first i An additional Lyapunov function for a differential-driven heavy-duty robot; (3) Derivative analysis and convergence: For By taking the derivative and using Assumption 1 and scaling inequalities, and through formula derivation, it is finally possible to prove the Lyapunov function of the multi-robot cooperative handling system. The derivative satisfies the following inequality: in, It is a constant. , According to the fixed-time stability theory, this inequality guarantees that the observer's error dynamic equation is fixed-time stable, i.e., the state estimation error... and disturbance estimation error It will converge to zero within a fixed time.

[0035] In some embodiments, S4 specifically includes the following steps: S41. Construct a dynamic model of the virtual leader; treat all differentially driven heavy robots as followers; S42. Define the first [unclear] based on the dynamic model of the virtual leader. i The state error and velocity error of each follower; S43, Definition of the i The equivalent variables for the state and velocity of the first follower are defined, and the first follower's state and velocity are defined. i The equivalent variables of the state error and velocity error of each follower; S44, regarding the first i The equivalent variables of the state error of each follower are differentiated, and combined with the time-delay-free equivalent dynamic model, the equivalent state error derivative equation is obtained. The equivalent state error derivative equation shows that the dynamics of the equivalent variables of the state error are determined by the equivalent variables of the velocity error. S45. Treat the equivalent variable of each follower's state as a point in the potential energy field, and use the function... sum function Design an artificial potential field function for each pair of adjacent followers. ; S46, Solving the function Regarding the Euclidean distance between two adjacent followers The partial derivatives; S47. Using functions Regarding the Euclidean distance between two adjacent followers Solving for the artificial potential function using partial derivatives Regarding the first i The equivalent variable of the state of each follower The partial derivatives; S48. A distributed formation controller is constructed based on the dynamic model of the virtual leader and the estimated value of the lumped disturbance output by the fixed-time nonlinear disturbance observer. S49. Use a distributed formation controller to control a virtual leader and multiple followers to achieve and maintain the desired formation.

[0036] In some embodiments, the dynamic model of the virtual leader in S41 is as follows: (19) in, The status of the virtual leader. Generalized coordinates representing the virtual leader; Represents the virtual leader in the inertial coordinate system The included angle of the axis; These represent the rotation angles of the left and right drive wheels on the virtual leader, respectively. For the speed of the virtual leader, including the linear speed of the virtual leader. and angular velocity ; For the control input of the virtual leader, These represent the control torques of the left and right drive wheels of the virtual leader, respectively. For the inertia matrix of the virtual leader, For the centrifugal and Coriolis force matrices of the virtual leader, The input matrix for the virtual leader; In S42, the first i The expressions for the state error and velocity error of each follower are: (20) in, Indicates the first i The state error of each follower; Indicates the first i The speed error of each follower; In S43, the first i The equivalent variables for the state and velocity of each follower are expressed as follows: (twenty one) in, Indicates the first i The equivalent variable of the state of each follower; Indicates the first i The equivalent variable for the speed of each follower; In S43, the first i The equivalent variables for the state error and velocity error of each follower are expressed as follows: (twenty two) in, Indicates the first i Equivalent variables of the state error of each follower; Indicates the first i The equivalent variable of the speed error of each follower; The equivalent state error derivative equation in S44 is: (twenty three) The expression for the artificial potential field function in S45 is as follows: (twenty four) in, and It is a positive integer and satisfies , ;function Used to achieve formation control objectives, when the desired relative position is reached, the function... Find the minimum value; function Used to ensure network connectivity among followers; function Select as: (25) in, It is the first The first follower and the first The expected relative distance vector between each follower; function Select as: (26) in, This represents the equivalent state error between two adjacent followers, and , Indicates the first j Equivalent variables of the state error of each follower; Represents the maximum perception range (communication radius) of the follower; It is a positive constant and satisfies , Indicates the first i A collection of neighbors of a follower; The function in S46 Regarding the Euclidean distance between two adjacent followers The partial derivatives are: (27) The artificial potential field function in S47 Regarding the first i The equivalent variable of the state of each follower The partial derivatives are: (28) in, Represents the artificial potential field function About functions The partial derivatives, Represents the artificial potential field function Regarding the Euclidean distance between two adjacent followers The partial derivatives of, and , , From the artificial potential field function From the specific form, we can know that , and when (i.e., when followers tend to disconnect) Its potential energy is infinite, thus preventing the formation from breaking up.

[0037] The distributed formation controller in S48 is: (29) in, Artificial potential field function Regarding the first i Partial derivatives of the equivalent variables of the state error of each follower; These are the adjacency matrix elements of a multi-robot collaborative handling system; It is the controller gain.

[0038] The following verifies the effectiveness of the distributed formation controller: Assumption 2: At the initial moment, the multiple followers in the multi-robot cooperative handling system can communicate with each other, that is, the undirected graph is connected and satisfies: Theorem 2: Under assumptions 1 and 2, for the time-delay-free equivalent dynamic model, in the distributed formation controller and the... Under the action of a fixed-time nonlinear disturbance observer with one follower, the following description applies: (1) Undirected graph Always maintain connectivity.

[0039] (2) The formation of multiple followers used for the coordinated handling of heavy workpieces will asymptotically converge to the desired formation and operate in coordination at the desired speed.

[0040] Proof: (1) Connectivity proof: Define the Lyapunov function of the multi-robot cooperative handling system as follows: Lyapunov functions for multi-robot cooperative handling systems Taking the derivative and substituting it into the distributed formation controller, we can derive the following: because If there is a tendency for robots to disconnect ( or ),but ,lead to This is related to Contradiction. Therefore, undirected graphs Always connected.

[0041] (2) Proof of formation convergence: Depend on and According to the Russell invariance principle and Barbalat's lemma, when At that time, there were: By constructing auxiliary functions And using artificial potential field function Regarding the first i The equivalent variable of the state of each follower The property of the partial derivatives can be used to prove that when hour: because And undirected graph Connectivity, as in the above equation, means that all robots have reached the desired relative position, that is, the formation of multiple followers will asymptotically converge to the desired formation.

[0042] The distributed formation controller naturally integrates formation maintenance and collision avoidance functions through an artificial potential field function, and combines a disturbance observer for feedforward compensation, effectively overcoming the effects of system disturbances and input delays, and achieving stable and robust cooperative transport control.

[0043] In some embodiments, S4 is followed by: S5, performing numerical simulation using MATLAB.

[0044] Specifically, step S5 includes the following steps: S51, Simulation parameter settings; S51 specifically includes: S511, Robot geometric and dynamic parameters; The geometric dimensions and dynamic parameters of the follower used in the simulation are set as follows: Geometric dimensional parameters: Spacing between the two drive wheels: Universal wheel installation spacing: The distance between the front and rear driven wheels Drive wheel radius: swivel wheel radius: Centroid offset: .

[0045] Mass and moment of inertia parameters: Follower body mass: Drive wheel mass: Caster wheel mass: Mass of heavy workpieces: Moment of inertia of the follower body: Moment of inertia of the driving wheel about its axle: The moment of inertia of the driving wheel about its center of mass: Moment of inertia of the caster wheel about its axle: The moment of inertia of the omnidirectional wheel about its center of mass: Moment of inertia of heavy workpieces: .

[0046] S512, Simulation Scenario and Initial Conditions; Initial conditions: The initial positions of the 4 followers (DHMR) are set as follows: , , , The initial angle is set as follows: , , , The initial position, angle, and speed of the virtual leader are as follows: , , , .

[0047] Control parameters: The parameters of the artificial potential field function are as follows: , , The follower's perception radius is The adjacency matrix weights of the communication graph are: The controller gain is ;No. The parameters of the fixed-time nonlinear disturbance observer for each follower are: , , , , , , The sliding mode is designed as follows: , , , Delay set to To simulate real-world working conditions, an external disturbance of 10 N is set for the multi-robot collaborative handling system, and the simulation step size is [missing value]. Control torque limit .

[0048] Step S52, Simulation Results and Analysis; To verify the effectiveness of the multi-robot cooperative artificial potential field control method for handling heavy workpieces proposed in this application, a simulation study was conducted in MATLAB software. Consider a group of four followers modeled on a two-dimensional plane, one extremely heavy workpiece, and a flexible pallet. The structure of the multi-robot cooperative handling system is as follows: Figure 2 As shown.

[0049] Numerical simulation results are as follows Figure 3-10 As shown. Figure 3-4 The figures show the curves of relative distance error and angular error as a function of time in a multi-robot collaborative handling system. Figure 3 Parameters in This represents the relative distance error between the first follower and the second follower; Figure 3The definitions of other parameters are similar; Figure 4 middle Indicates the first i The angular error of each follower relative to the virtual leader; Figure 4 The definitions of other parameters are similar; as shown in the figure, all formation distance errors can converge to near 0 in 10s, and angle errors can converge to near 0 in 4s, realizing the rapid and accurate formation of 4 followers and completing the collaborative handling of heavy workpieces.

[0050] Figure 5-6 The curve showing the relative speed error of a multi-robot collaborative handling system as a function of time. Figure 5 middle Indicates the first i The linear velocity tracking error of each follower relative to the virtual leader; Figure 5 The definitions of other parameters are similar; Figure 6 middle Indicates the first i The angular velocity tracking error of each follower relative to the virtual leader; Figure 6 The definitions of other parameters are similar; as shown in the figure, the linear velocity and angular velocity of the multi-robot collaborative handling system can quickly achieve accurate tracking of the virtual leader, and the curves are very smooth.

[0051] Figure 7-8 The curve showing the time-varying estimation error of the designed fixed-time disturbance observer for external disturbances to the system. Figure 7 middle Indicates the first i Estimation error of external interference in the left drive wheel channel of the follower; Figure 7 and Figure 8 The definitions of other parameters are similar; as shown in the figure, the interference estimation error of the multi-robot cooperative handling system converges to near 0 within about 5 seconds, which can quickly and effectively estimate external interference.

[0052] Figure 9-10 For the control torque of a multi-robot collaborative handling system, Figure 9 and Figure 10 middle Indicates the first i The control torque of the left drive wheel of the follower. Figure 9 and Figure 10 The definitions of other parameters are similar. As shown in the figure, the control torque reaches its maximum limit in the initial stage and then converges to near 0 within 3 seconds, and the overall curve is relatively smooth.

[0053] Another aspect of the present invention discloses a multi-robot collaborative artificial potential field control system, including a multi-robot collaborative handling system and a network control system. The multi-robot collaborative handling system is controlled by the network control system, and the multi-robot collaborative handling system and the network control system are configured or execute the above-described multi-robot collaborative artificial potential field control method.

[0054] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Furthermore, the technical solutions of the various embodiments of the present invention can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A multi-robot collaborative artificial potential field control method for handling heavy workpieces, characterized in that, Includes the following steps: S1. Establish a dynamic model of a multi-robot collaborative handling system, which includes multiple differentially driven heavy robots, a flexible pallet, and an overweight workpiece. The overweight workpiece is placed on multiple differentially driven heavy robots through the flexible pallet. Then, construct a dynamic model of the differentially driven heavy robots based on the dynamic model of the multi-robot collaborative handling system. S2. By introducing the input delay in the network control system, the dynamic model of the differentially driven heavy robot is transformed to obtain an equivalent dynamic model without delay. S3. Based on the time-delay-free equivalent dynamic model, design a fixed-time nonlinear disturbance observer for the differential-driven heavy robot, and use the fixed-time nonlinear disturbance observer to output the estimated value of the lumped disturbance. S4. Construct a dynamic model of the virtual leader, design an artificial potential field function, and construct a distributed formation controller based on the dynamic model of the virtual leader, the artificial potential field function, and the estimated value of the lumped disturbance. Treat all differentially driven heavy robots as followers and use the distributed formation controller to control the virtual leader and multiple followers to achieve and maintain the desired formation.

2. The multi-robot collaborative artificial potential field control method for handling heavy workpieces according to claim 1, characterized in that, S1 specifically includes the following steps: S11, Calculate the... i The linear velocity of the geometric center of the heavy robot is driven by a differential mechanism. and angular velocity ;in, ; S12, Constructing the first i The velocity vector of the differential-driven heavy robot The angular velocity of the drive wheel on the differential-driven heavy robot Conversion formulas between; S13, Constructing the first i Nonholonomic constraint equations for a differential-driven heavy-duty robot; S14. Construct a dynamic model of a multi-robot cooperative handling system based on the Euler-Lagrange principle and in conjunction with nonholonomic constraint equations; S15, Constructing the first i An unsimplified dynamic model of a differential-driven heavy-duty robot; S16, Based on the dynamic model in S14, the first... i The dynamic model of the differential-driven heavy robot is simplified to obtain the first... i A dynamic model of a differentially driven heavy-duty robot.

3. The multi-robot collaborative artificial potential field control method for handling heavy workpieces according to claim 2, characterized in that, The S11 in the i The linear velocity of the geometric center of the heavy robot is driven by a differential mechanism. and angular velocity The specific calculation formula is as follows: （1） in, For the first i The radius of the drive wheels on a differentially driven heavy-duty robot For the first i The distance between two drive wheels on a differential-driven heavy-duty robot; and The first i The angular velocities of the left and right drive wheels on a differential-driven heavy-duty robot; The S12 in i The velocity vector of the differential-driven heavy robot The angular velocity of the drive wheels on the differential-driven heavy robot The conversion formulas between them are as follows: （2） in, Transformation matrix; Specifically: （3） in, Indicates the first i In the differential-driven heavy robot and inertial coordinate system The included angle of the axis; In S13, the first i The nonholonomic constraint equations for a differential-driven heavy-duty robot are: （4） in, To constrain the Jacobian matrix; Indicates the first i The state of a differentially driven heavy robot; Indicates the first i A differential-driven generalized coordinate system for heavy-duty robots; They represent the first i The rotation angle of the left and right drive wheels on a differential-driven heavy robot; T Indicates transpose; the dot sign on the parameter indicates the first derivative of that parameter; The dynamic model of the multi-robot cooperative handling system in S14 is as follows: （5） in, For the first i The control input for a differential-driven heavy-duty robot They represent the first i The rotational torque of the left and right drive wheels on a differentially driven heavy-duty robot For the Lagrange multipliers of the binding force, For the first i A differentially driven gravitational acceleration vector for a heavy-duty robot; Indicates the first i Lumped disturbances, burst friction, and external disturbances in a differentially driven heavy robot; The number of differentially driven heavy-duty robots, To constrain the Jacobian matrix number of rows; Indicates the sign of the partial derivative; This represents the total kinetic energy of a multi-robot collaborative handling system; t Indicates time; Among them, total kinetic energy Including the kinetic energy of differentially driven heavy robots Drive wheel kinetic energy omnidirectional wheel kinetic energy kinetic energy of load ; The S15 in i The specific dynamic model of the differential-driven heavy robot is as follows: （6） in, The inertia matrix, The matrix represents the centrifugal force and the Coriolis force. For the input matrix, Torque is controlled for the drive wheels; represents the set of real numbers; the symbol · on the parameter indicates the second derivative of that parameter; In S16, the first i The specific dynamic model of the differential-driven heavy robot is as follows: （7） Among them, the first intermediate matrix Second intermediate matrix The third intermediate matrix , Represents the parameter matrix, Indicates the control torque of the drive wheels; Indicates the first i Lumped perturbation of a differentially driven heavy-duty robot It is the first The speed of the differential-driven heavy robot, including the first Linear velocity of a differential-driven heavy robot and angular velocity ; parameter matrix The formula for calculation is: （8）。 4. The multi-robot collaborative artificial potential field control method for handling heavy workpieces according to claim 3, characterized in that, S2 specifically includes the following steps: S21. Calculate the delayed control input torque by introducing the input delay in the network control system, and then adjust the control input torque based on the delayed torque. i The dynamic model of the differential-driven heavy robot is transformed to obtain the transformed dynamic model. S22. Perform a Laplace transform on the control input torque with time delay to obtain the transformed control input torque; S23. Define auxiliary variables and perform a Laplace transform on the auxiliary variables to obtain the transformed auxiliary variables; S24. Substitute the transformed control input torque into the transformed auxiliary variable to obtain the differential equation of the auxiliary variable; S25. Perform an inverse Laplace transform on the differential equation of the auxiliary variable to obtain the differential equation of the auxiliary variable. S26. Combining the transformed dynamic model and the differential equations of the auxiliary variables, an equivalent dynamic model without time delay is constructed.

5. The multi-robot cooperative artificial potential field control method for handling heavy workpieces according to claim 4, characterized in that, The transformed dynamic model in S21 is as follows: （9） in, It is a control input torque with a time delay; This indicates the input delay in a networked control system; The transformed control input torque in S22 is specifically as follows: （10） in, It is a Laplace variable. Represents the Laplace transform; The auxiliary variable in S23 is: （11） in, Indicates auxiliary variables; The transformed auxiliary variable in S23 is: （12） The differential equation for the auxiliary variable in S24 is: （13） The differential equation for the auxiliary variable in S25 is: （14） The time-delay-free equivalent dynamic model in S26 is as follows: （15） in, This represents an intermediate variable related to the delay parameter; and .

6. The multi-robot cooperative artificial potential field control method for handling heavy workpieces according to claim 5, characterized in that, S3 specifically includes the following steps: S31, Design observation error; S32. Design of the first step based on the time-delay-free equivalent dynamic model. A fixed-time nonlinear disturbance observer for a differential-driven heavy-duty robot; S33, Combining the time-delay-free equivalent dynamic model, the first A fixed-time nonlinear disturbance observer for a differential-driven heavy robot is constructed, and the observation error is used to build the observer's error dynamic equation. It is then determined whether the observer's error dynamic equation has converged. If it has, proceed to S34; otherwise, return to S31. S34, through the first The lumped perturbation output of the fixed-time nonlinear disturbance observer for a differentially driven heavy-duty robot. The estimated value .

7. The multi-robot cooperative artificial potential field control method for handling heavy workpieces according to claim 6, characterized in that, The observation error in S31 is: （16） in, and These are the system states. and aggregate disturbance The estimated value; It is the state estimation error; It is the disturbance estimation error; the disturbance estimation error includes the external disturbance estimation error of the channel for each differentially driven heavy robot's left and right drive wheels; The S32 in The fixed-time nonlinear disturbance observer for a differential-driven heavy-duty robot is: （17） in, It is a sliding mode item; and These are the positive constant parameters to be designed; These are observer parameters used to adjust convergence performance; It is the gain function to be designed; The error dynamic equation of the observer in S33 is: （18）。 8. The multi-robot cooperative artificial potential field control method for handling heavy workpieces according to claim 7, characterized in that, S4 specifically includes the following steps: S41. Construct a dynamic model of the virtual leader; treat all differentially driven heavy robots as followers; S42. Define the first [unclear] based on the dynamic model of the virtual leader. i The state error and velocity error of each follower; S43, Definition of the i The equivalent variables for the state and velocity of the first follower are defined, and the first follower's state and velocity are defined. i The equivalent variables of the state error and velocity error of each follower; S44, regarding the first i The equivalent variables of the state error of each follower are differentiated, and combined with the time-delay-free equivalent dynamic model, the equivalent state error derivative equation is obtained. The equivalent state error derivative equation shows that the dynamics of the equivalent variables of the state error are determined by the equivalent variables of the velocity error. S45. Treat the equivalent variable of each follower's state as a point in the potential energy field, and use the function... sum function Design an artificial potential field function for each pair of adjacent followers. ; S46, Solving the function Regarding the Euclidean distance between two adjacent followers The partial derivatives; S47. Using functions Regarding the Euclidean distance between two adjacent followers Solving for the artificial potential function using partial derivatives Regarding the first i The equivalent variable of the state of each follower The partial derivatives; S48. Dynamic model based on virtual leader, estimate of lumped disturbance output by fixed-time nonlinear disturbance observer, artificial potential field function. Regarding the first i The equivalent variable of the state of each follower The partial derivatives are used to construct a distributed formation controller; S49. Use a distributed formation controller to control a virtual leader and multiple followers to achieve and maintain the desired formation.

9. A multi-robot cooperative artificial potential field control method for handling heavy workpieces according to claim 8, characterized in that, The dynamic model of the virtual leader in S41 is as follows: （19） in, The status of the virtual leader. Generalized coordinates representing the virtual leader; Represents the virtual leader in the inertial coordinate system The included angle of the axis; These represent the rotation angles of the left and right drive wheels on the virtual leader, respectively. For the speed of the virtual leader, including the linear speed of the virtual leader. and angular velocity ; For the control input of the virtual leader, These represent the control torques of the left and right drive wheels of the virtual leader, respectively. For the inertia matrix of the virtual leader, For the centrifugal and Coriolis force matrices of the virtual leader, The input matrix for the virtual leader; In S42, the first i The expressions for the state error and velocity error of each follower are: （20） in, Indicates the first i The state error of each follower; Indicates the first i The speed error of each follower; In S43, the first i The equivalent variables for the state and velocity of each follower are expressed as follows: （21） in, Indicates the first i The equivalent variable of the state of each follower; Indicates the first i The equivalent variable for the speed of each follower; In S43, the first i The equivalent variables for the state error and velocity error of each follower are expressed as follows: （22） in, Indicates the first i Equivalent variables of the state error of each follower; Indicates the first i The equivalent variable of the speed error of each follower; The equivalent state error derivative equation in S44 is: （23） The expression for the artificial potential field function in S45 is as follows: （24） in, and It is a positive integer and satisfies , ;function Used to achieve formation control objectives, when the desired relative position is reached, the function... Find the minimum value; function Used to ensure network connectivity among followers; function Select as: （25） in, It is the first The first follower and the first The expected relative distance vector between each follower; function Select as: （26） in, This represents the equivalent state error between two adjacent followers, and , Indicates the first j Equivalent variables of the state error of each follower; Represents the maximum range of perception for followers; It is a positive constant and satisfies , Indicates the first i A collection of neighbors of a follower; The function in S46 Regarding the Euclidean distance between two adjacent followers The partial derivatives are: （27） The artificial potential field function in S47 Regarding the first i The equivalent variable of the state of each follower The partial derivatives are: （28） in, Represents the artificial potential field function About functions The partial derivatives, Represents the artificial potential field function Regarding the Euclidean distance between two adjacent followers The partial derivatives of, and , , ; The distributed formation controller in S48 is: （29） in, Artificial potential field function Regarding the first i Partial derivatives of the equivalent variables of the state error of each follower; These are the adjacency matrix elements of a multi-robot collaborative handling system; It is the controller gain.

10. A multi-robot cooperative artificial potential field control system, characterized in that, The system includes a multi-robot collaborative handling system and a network control system. The multi-robot collaborative handling system is controlled by the network control system. The multi-robot collaborative handling system and the network control system are configured to execute the multi-robot collaborative artificial potential field control method according to any one of claims 1 to 9.

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