Adaptive impedance-based multi-mobile-robot collaborative transportation control method

Abstract

An adaptive impedance-based multi-mobile-robot collaborative transportation control method. Each mobile robot estimates the actual pose and ideal pose of a reference point and the first and second derivatives of the ideal pose by means of two finite-time fully-distributed observers, respectively; and then, on the basis of the estimated poses of the reference point, the pose of an end-effector of a mechanical arm, and closed-chain constraints for collaborative transportation, an ideal trajectory of the end-effector of the mobile robot, and an estimated value of a pose deviation between the end-effector of the mobile robot and the reference point are obtained. An adaptive impedance system of each mobile robot is interconnected with a virtual energy tank, and the energy tank is used to guide the updating of impedance parameters, thereby ensuring the passivity of the entire collaborative adaptive impedance system. To process unknown system dynamics of mobile robots, an asymptotic tracking adaptive neural network controller is designed using a neural network, thereby asymptotically achieving an ideal adaptive impedance relationship. The operational accuracy of multi-robot collaborative transportation systems is improved while ensuring safe collaboration.

Description

A multi-mobile robot cooperative carrying control method based on adaptive impedance

[0001] The present application claims priority to the Chinese patent application No. 2024110092840, filed on July 26, 2024, and entitled "A multi-mobile robot cooperative carrying control method based on adaptive impedance", the whole content or part of which is incorporated herein by reference. TECHNICAL FIELD

[0002] The present application belongs to the field of robot control technology, in particular relates to a multi-mobile robot cooperative carrying control method based on adaptive impedance. BACKGROUND

[0003] Modern large-scale complex equipment manufacturing core technology is an important factor to measure the development level of a country's manufacturing industry, and has a profound impact on national security and economic construction. In the field of industrial production, there are a large number of small batch, multi-variety production tasks. Robots or robotized equipment has many advantages, such as large workspace, strong parallel coordination work ability, etc., which can adapt to complex processing environment. However, the workspace range of fixed or track type robots is limited, and cannot handle large complex parts such as aircraft wings, barrel segments, turbine blades, etc. Mobile robots have super large range of work space by skillfully combining the mobility of mobile chassis and the dexterity of mechanical arm, and are an effective tool to realize large-scale complex equipment manufacturing.

[0004] Most of the current mobile robot systems are single robot systems, but single robots face problems such as low load capacity and easy to suffer from single machine failure, so that the manufacturing mode based on single robot can not meet the high-quality and efficient manufacturing demand of large and complex equipment. Multi-mobile robot system can improve the adaptability, robustness and load capacity of the system through cooperation between each other, and is an effective tool to realize the carrying of large and heavy parts. Although some scholars have carried out certain research on multi-robot cooperative carrying, they usually need each robot to know the ideal trajectory of the object and the pose deviation of the mechanical arm end to the reference point or the mass center of the object in advance, and obtain the ideal trajectory of the mobile robot end and the grasping matrix through the two information. However, due to the limited perception ability of the robot system, not every robot can obtain the actual pose and ideal pose of the reference point. In addition, if the value of the pose deviation is directly set in the controller design stage, it requires the robot to achieve accurate grasping of the given grasping point when grasping the object. This operation is usually very time-consuming and affects the manufacturing efficiency. More importantly, when the object shape is complex and there is occlusion, the robot may not be able to directly obtain the pose of the reference point, so it is impossible to calculate the position of the grasping point according to the pose of the reference point and the value of the pose deviation between the robot end and the reference point set. Therefore, for the multi-mobile robot cooperative carrying system, if it can obtain the ideal pose of the mobile robot end and the pose deviation of the mechanical arm end relative to the reference point through the estimated information, there is no special requirement for the grasping point when the robot grasps the object, so as to realize fast grasping and improve the flexibility of the robot and the manufacturing efficiency of large and complex equipment.

[0005] The dynamics parameters of the multi-robot system and the object to be carried usually have uncertainties. When the system has uncertainties, impedance control is an effective method to realize safe operation, but the parameters of the impedance system depend on the specific task. Adaptive impedance control can update the impedance parameters online according to the specific task, which is an effective method to realize safe operation on unknown objects. However, changing the stiffness value of the adaptive impedance system may inject energy into the adaptive impedance system, which may cause the adaptive impedance system to not satisfy the passivity, so that the system may diverge. Therefore, ensuring that the adaptive impedance system satisfies the passivity condition is the key to guarantee safe cooperation. If the adaptive impedance system does not satisfy the passivity condition, the cooperative carrying task may fail.

[0006] Therefore, the present application proposes a multi-mobile robot cooperative carrying control method based on adaptive impedance. SUMMARY

[0007] In view of the above technical problems, the present application provides a multi-mobile robot cooperative carrying control method based on adaptive impedance.

[0008] The technical scheme adopted by the present application to solve its technical problems is:

[0009] A multi-mobile robot cooperative carrying control method based on adaptive impedance, the method comprising the following steps:

[0010] S100: a dynamic model of a mobile robot and a dynamic model of an object are established, and a dynamic system model of multi-mobile robot cooperative carrying is established in combination with kinematic constraints;

[0011] S200: two finite-time full-distributed observers are designed by using information interaction between the multi-mobile robots to estimate the actual pose and the ideal pose and the first two-order derivatives of the reference point, so as to obtain the estimated value of the actual pose of the reference point, the estimated value of the ideal pose of the reference point and the first two-order derivatives thereof;

[0012] S300: according to the estimated value of the actual pose of the reference point, the actual pose of the end of the mobile robot and the closed-chain constraint of cooperative carrying, the estimated value of the pose deviation between the reference point and the end of the mobile robot is obtained, and based on the estimated value of the pose deviation and the estimated value of the ideal pose of the reference point and the first two-order derivatives thereof, the estimated value of the grasping matrix of the mobile robot about the reference point and the ideal pose of the end of the mobile robot and the first two-order derivatives thereof are obtained;

[0013] S400: an internal force tracking error is defined, a dynamic model of a distributed adaptive impedance system based on a virtual energy tank is established in combination with the actual pose of the end of the mobile robot, the internal force tracking error and the ideal pose of the end of the mobile robot obtained, the stiffness of the dynamic model of the impedance system is updated online according to the internal force error, the position tracking error of the end of the mobile robot and the value of the energy tank, and the updated ideal pose, velocity and acceleration of the end of the mobile robot are obtained according to the dynamic model of the adaptive impedance system;

[0014] S500: according to the updated ideal pose, velocity and acceleration of the end of the mobile robot, the pose tracking error and the velocity tracking error of the end of the mobile robot in the Cartesian space are obtained in combination with the actual position and velocity of the end of the mobile robot, the ideal velocity and acceleration of the generalized joint of the mobile robot are obtained by using inverse kinematics in combination with the updated ideal velocity and acceleration of the end of the mobile robot, the dynamic system model is introduced into a torque controller through a Lyapunov function according to the ideal velocity of the generalized joint of the mobile robot and the current joint velocity, the system coupling dynamic term is obtained, a neural network adaptive update law based on an integral bounded function is designed to adaptively compensate the system coupling dynamic term in the torque controller, a control signal is sent to a robot actuator to drive the end of the mobile robot to gradually track the updated ideal trajectory, an ideal adaptive impedance relationship is established, and the control of the end of the mobile robot is realized.

[0015] Preferably, S100 includes:

[0016] S110: Consider the i-th mobile robot system whose robotic arm carries n... i,m The dynamic model of the i-th mobile robot system is as follows: (The system has several links.)

[0017] in, M is the mass inertia matrix of the i-th mobile robot. i,p M is the mass inertia matrix of the i-th mobile platform. i,m M is the mass inertia matrix of the i-th robotic arm. i,pm and M i,mp Let be the coupling mass inertia matrix between the mobile platform and the robotic arm; The matrix representing the centripetal and Coriolis forces of a mobile robot, C i,p C is the centripetal force and Coriolis force matrix of the i-th mobile platform. i,m C is the centripetal force and Coriolis force matrix of the i-th robotic arm. i,pm and C i,mp The centripetal force and Coriolis force matrix represents the coupling between the mobile platform and the robotic arm; Let be the dimension of the generalized coordinates of the i-th mobile robot. The gravity vector representing the mobile robot. and Let be the gravity vectors of the moving platform and the robotic arm of the i-th mobile robot, respectively. H i,p J is the constraint matrix for the i-th mobile robot; i,p and J i,m Let be the Jacobian matrices of the i-th mobile platform and the robotic arm, respectively; B is the input transformation matrix of the mobile robot. i,p and B i,m Let p be the input transformation matrix for the i-th mobile platform and the robotic arm, respectively. i To control input dimensionality and Let be the input torque vectors of the i-th mobile platform and the robotic arm, respectively. Where F i,p and F i,e These represent the nonholonomic constraint forces acting on the end effector of the mobile robot and the spinor of the external forces acting on the end effector of the mobile robot, respectively. Let be the generalized joint coordinates of the mobile robot, where Let p be the pose of the mobile platform p of the i-th mobile robot. Let m be the joint angle position of the robotic arm m of the i-th mobile robot. They represent q respectivelyi The first and second derivatives, Represents the number of mobile robots; Joint velocity Ratio of reduced joint velocities Multiple dimensions, n i,p Let n be the dimension of the pose of the mobile platform p of the i-th mobile robot. i,m Let be the degree of freedom of the i-th robotic arm;

[0018] Consider the nonholonomic constraints of the i-th mobile platform as follows: Reduced joint velocities can be obtained. Make:

[0019] Among them, A i,p (q i,p )satisfy Therefore, multiplying both sides of the dynamic model of the mobile robot in S110 by... Its dynamic model can be rewritten as:

[0020] in,

[0021] and

[0022] F i,e The external force spinor at the end effector of the mobile robot;

[0023] S120: Consider the dynamic model of the object, specifically:

[0024] in, It is the mass-inertia matrix of the object. The matrix representing the centripetal and Coriolis forces of an object. It is the gravitational vector of the object, F. o x is the resultant force of multiple mobile robots acting on the center of mass of an object. o and v o These are the pose and velocity spinor of the object's center of mass, respectively;

[0025] Consider the velocity v of the object's center of mass. o relative to the velocity v at the reference point r Relationship: v o =J r,o v r and the net force F acting on the center of mass of the object. o and the external force spindle F at the end of the i-th mobile robot i,e Relationship: wherein, is the grasp matrix of the mobile robot with respect to the object mass center, J r,o is the Jacobian matrix between the object mass center and the object reference point, J o,i is the Jacobian matrix between the object mass center and the i-th mobile robot end-effector, the dynamic model of the object can be rewritten as:

[0026] wherein, is the grasp matrix of the mobile robot with respect to the reference point s(·) is the skew-symmetric matrix operator, is the position error between the reference point and the mobile robot end-effector in the inertial frame;

[0027] S130: considering the load distribution coefficient Δ i ≥ 0 corresponding to the i-th mobile robot r , the indirect force F i,r exerted by the end of the i-th mobile robot on the object reference point x and F i,r can be decomposed into the operational force F i,E and the internal force F i,I , i.e. F i,r = F i,E + F i,I , thus the coupling dynamic equation of the i-th mobile robot and the object is:

[0028] wherein, Φ A,i is the transformation matrix between the geometric Jacobian and the analytical Jacobian, J i,e is the Jacobian matrix between the i-th mobile robot end-effector velocity and the reduced joint velocity , i.e. is the pseudo-inverse matrix of J r,i .

[0029] Preferably, S200 comprises:

[0030] S210: designing an observer to estimate the actual pose of the reference point, defining as the observation value of the i-th mobile robot to the actual pose x r of the reference point, the synchronization error δ x,ir of the estimated value of the actual pose of the reference point of the i-th mobile robot can be defined as:

[0031] Among them, b i =1 indicates that the mobile robot i can measure or directly obtain the actual pose x of the reference point. r Otherwise b i =0, j∈N i This means that mobile robot i can receive information from mobile robot j. It is obtained from a finite-time fully distributed observer, specifically as follows:

[0032] Where, k 2,i,r For positive integers, for The first derivative, p i,e and o i,e Let represent the actual position and orientation of the i-th mobile robot's end effector, respectively; o i,e The first derivative, k 3,i,r For adaptive parameters, the update law is as follows:

[0033] Among them, Γ i,r It is a positive definite matrix;

[0034] S220: Design an observer to estimate the ideal pose of the reference point and its first two derivatives, defining the ideal trajectory of the reference point as x. d And its first two derivatives are respectively and When b i When x = 0, design a fully distributed observer to estimate x. d , and Specifically:

[0035] in, and For the i-th mobile robot, x d , The estimated value, α i ,β i ,γ i ∈(0.5,1) are positive constants; and The consistency error of the observations is specifically as follows:

[0036] In addition, k x,i k v,i and k a,i It is derived from the adaptive law, specifically as follows:

[0037] Among them, Γ 1,i ,Γ 2,i ,Γ 3,i It is a positive definite matrix;

[0038] S230: Define observation error and Based on the closed-chain constraint x i,e =x r +π ri , can be obtained in i p ri Let x be a constant vector, and let x be the reference point. r With the i-th mobile robot end effector x i,e The relative positions between them are represented in the coordinate system of the i-th mobile robot end effector. Let k represent the relative attitude between the coordinate system attached to the reference point and the coordinate system of the i-th mobile robot end effector in the inertial coordinate system. 3,i,r > i p ri At that time, the observation error e x,ir It converges to zero within a finite amount of time.

[0039] Preferably, S300 includes:

[0040] S310: Estimated value considering the actual pose of the reference point and closed-chain constraint π ri =x i,e -x r ,available:

[0041] in, and Let be the estimated values ​​of the i-th mobile robot's position and orientation at the reference point, respectively. From this, the estimated value of the position deviation can be obtained. and the estimated value of relative attitude Specifically:

[0042] because It converges to x in a finite time. r ,so and They converge to in finite time respectively i p ri and w η ri ;

[0043] S320: Based on the estimated value of the position deviation Estimates of the ideal trajectory of the reference point By closed-chain constraint x i,ed =x i,d +π ri,d The ideal trajectory design for the i-th mobile robot end effector is as follows:

[0044] in, and and Let these represent the ideal position and orientation of the i-th mobile robot end effector, respectively. i p ri and w η ri It is a constant vector. first derivative Designed as follows:

[0045] in, for The first derivative;

[0046] The second derivative Designed as follows:

[0047] in,

[0048] S330: Defines the estimation error of the ideal trajectory of the mobile robot's end effector as... and As can be seen from S310, and They converge to in finite time respectively i p ri and w η ri Therefore, it can be concluded that within a limited time... Converging to zero, It converges to zero in a finite amount of time, while Depend on and If it converges to zero in a finite amount of time, then we know that It converges to zero within a finite amount of time. and The ideal trajectory of the designed mobile robot end effector converges to zero within a finite time, and the ideal trajectory of the mobile robot end effector converges to the actual ideal trajectory of the mobile robot end effector within a finite time.

[0049] Preferably, S400 includes:

[0050] S410: Define the internal force tracking error F i,Ie =F i,I -F i,Id Fi,Id For ideal internal forces, the following adaptive impedance model is established:

[0051] Among them, M 3,i , and K 3,i (t) is a positive definite diagonal matrix, representing the inertia matrix, damping matrix, and stiffness matrix, respectively. Let M be the pose tracking error of the i-th mobile robot end effector. 3,i B 3,i (t) and K 3,i (t) is a positive definite diagonal matrix;

[0052] The adaptive impedance model is decomposed into multiple one-dimensional adaptive impedance systems, where the number of one-dimensional adaptive impedance systems for each mobile robot is equal to the dimension of its control input. The j-th one-dimensional adaptive impedance system is represented as:

[0053] Among them, F ij,Ie M 3,ij B 3,ij (t) and K 3,ij (t), Δx i,j , and F respectively i,Ie M 3,i B 3,i (t), K 3,i (t), Δx i , and The element in the j-th row;

[0054] S420: Considering that a large stiffness value for an impedance system helps reduce the tracking error of the impedance system, the growth rate of the impedance system stiffness is determined by the internal force tracking error, the position tracking error, and the value of the virtual energy tank, specifically:

[0055] Among them, Γ F,ij Let γ be a positive constant, Proj(·) be the projection operator, and γ be a positive constant. s,ij The method used to limit the growth rate of stiffness is as follows:

[0056] Among them, s i,j ≥0 represents the maximum allowable power corresponding to the energy injected into the j-th one-dimensional adaptive impedance system.

[0057] δ 2,ij Used to maintain the value of the energy tank Not lower than the predetermined lower limit of the energy tank Specifically:

[0058] S430: The dynamics of designing the virtual energy tank are as follows:

[0059] in, 0≤μ i ≤1 is a constant;

[0060] δ 1,i Used to maintain the value of the energy tank Not higher than the predetermined upper limit Specifically:

[0061] S440: To prove that the adaptive impedance system interconnected with the virtual energy tank satisfies passivity, consider the following Lyapunov function for the entire multi-robot cooperative transport adaptive impedance system:

[0062] Dynamically substituting the adaptive impedance model from S410 From this, we can obtain:

[0063] It can be seen that when δ 1,i When = 1, we have When δ 1,i When = 0, we have Therefore, It is always true, therefore:

[0064] For the entire adaptive impedance system of multi-robot cooperative handling, Satisfies passivity;

[0065] S450: Considering the asymptotic realization of the ideal adaptive impedance model, an impedance error Δe is required. imp It asymptotically converges to zero, specifically as follows:

[0066] To achieve this goal, an updated reference trajectory x for the mobile robot's end effector is designed. i,c , And x i,c , and The following relationship must be satisfied:

[0067] Substituting the above equation into the impedance error Δe imp From the equation, we can obtain:

[0068] Therefore, when x i,e asymptotic tracking x i,c as well as asymptotic tracking When, Δe imp It converges asymptotically to zero.

[0069] Preferably, S500 includes:

[0070] S510: Define tracking error And the following cross-coupling errors:

[0071] in, For the estimation of the ideal relative pose between the i-th and j-th mobile robot end effectors, l 3,i It is a positive constant;

[0072] Taking the derivative of the above equation, we can obtain Specifically:

[0073] To achieve the control objective, the ideal joint velocities of a mobile robot can be designed as follows:

[0074] Among them, Λ i Let be a positive definite diagonal constant matrix; differentiating both sides of the above equation, the ideal joint acceleration can be designed as follows:

[0075] S520: Defines the joint space velocity tracking error of a mobile robot. Therefore, the tracking error dynamic model of the i-th mobile robot can be written as:

[0076] in, Using neural networks to approximate unknown function vectors Right now in Let be the optimal weight vector matrix of the neural network. For the basis function vector, To approximate the error vector, define and

[0077] By incorporating a neural network, the following asymptotic tracking adaptive controller is designed:

[0078] in, To be Replace J σ,i In i p ri The obtained information about Jσ,i The estimate, k i =k 1,i +k 2,i ||F i,I ||and k 1,i and k 2,i For positive constants, continuous functions satisfy in It is a positive constant. for Based on the estimated value, the update law of the neural network is designed as follows:

[0079] in, It is a positive integer;

[0080] S530: Define estimation error To confirm the stability and asymptotic tracking performance of the proposed controller, the candidate Lyapunov is:

[0081] Differentiating with respect to V, we get:

[0082] consider From the expression for τ, we get:

[0083] in, because It is by Caused by, and When there is a boundary, It is also bounded, because It is bounded, therefore It is also bounded, when hour, Therefore z i and It is bounded, and further we can obtain It is also bounded because the control input τ i It is a function of a bounded signal, so τ i It is also bounded; therefore, all closed-loop signals are bounded.

[0084] Furthermore, because It converges to zero in a finite amount of time, so Converging to zero in a finite amount of time means that It converges to zero in a finite amount of time, so there exists a positive constant. Make In summary, for time t→∞, we have:

[0085] According to Barbara's lemma, as time t→∞, That is, as time t→∞, and In summary, as time t→∞, the impedance error Converging to zero;

[0086] S540: Write distributed control programs to control the end effector of the mobile robot.

[0087] The aforementioned multi-robot cooperative handling control method based on adaptive impedance obtains the ideal pose of the robot's end effector, its second-order derivative, and the pose deviation of the end effector relative to a reference point by designing two fully distributed observers and simultaneously incorporating kinematic constraints. Furthermore, a virtual energy tank is interconnected with the adaptive impedance system to guide the parameter updates of the adaptive impedance system, thereby ensuring the passivity of the adaptive impedance system. This method can maximize the operational accuracy of the multi-robot cooperative handling system while ensuring safe collaboration. Attached Figure Description

[0088] Figure 1 is a flowchart of a multi-mobile robot cooperative handling control method based on adaptive impedance in one embodiment of the present invention;

[0089] Figure 2 is a block diagram of a multi-mobile robot cooperative handling control method based on adaptive impedance in one embodiment of the present invention;

[0090] Figure 3 is a schematic diagram of collaborative handling by multiple mobile robots;

[0091] Figure 4 shows the actual pose of the mobile robot of the present invention at the reference point. r The estimation error diagram;

[0092] Figure 5 shows the ideal pose of the mobile robot of the present invention at the reference point x. d The estimation error diagram;

[0093] Figure 6 shows the ideal pose of the mobile robot of the present invention at the reference point x. d first derivative The estimation error diagram;

[0094] Figure 7 shows the ideal pose of the mobile robot of the present invention at the reference point x. d The second derivative The estimation error diagram;

[0095] Figure 8 shows the positional deviation between the end effector of the mobile robot and the reference point in the end effector coordinate system of the mobile robot according to the present invention. picture;

[0096] Figure 9 shows the norm and sum of the position and velocity tracking errors of the mobile robot end effector of the present invention. picture;

[0097] Figure 10 shows the values ​​of the virtual energy tank interconnected with the adaptive impedance system in this invention;

[0098] Figure 11 shows the Lyapunov function V of the entire multi-robot cooperative transport adaptive impedance system of the present invention. 2I The value;

[0099] Figure 12 is a simulation diagram of the process of multiple mobile robots collaboratively transporting objects according to the present invention.

[0100] Figure 13 shows the control performance of the proposed method and the control method based on adaptive law estimation of position deviation in the xy plane. Detailed Implementation

[0101] To enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings.

[0102] In one embodiment, as shown in Figures 1 and 2, a multi-mobile robot cooperative handling control method based on adaptive impedance includes the following steps:

[0103] S100: Establish the dynamic model of the mobile robot and the dynamic model of the object, and combine kinematic constraints to establish a dynamic system model of cooperative handling by multiple mobile robots.

[0104] S200: By utilizing the information interaction between multiple mobile robots, two finite-time fully distributed observers are designed to estimate the actual pose and ideal pose of the reference point and its first two derivatives, respectively, to obtain the estimated value of the actual pose of the reference point, the estimated value of the ideal pose of the reference point and its first two derivatives.

[0105] S300: Based on the estimated actual pose of the reference point, the actual pose of the multiple mobile robot end effectors, and the closed-loop constraints of cooperative handling, the estimated pose deviation between the reference point and the mobile robot end effector is obtained. Based on the estimated pose deviation and the estimated ideal pose of the reference point and its first two derivatives, the estimated grasping matrix of the mobile robot with respect to the reference point and the ideal pose of the mobile robot end effector and its first two derivatives are obtained.

[0106] S400: Define the internal force tracking error, combine the actual pose of the mobile robot end effector, the internal force tracking error, and the obtained ideal pose of the mobile robot end effector to establish a dynamic model of the distributed adaptive impedance system based on the virtual energy tank. According to the internal force error, the position tracking error of the mobile robot end effector, and the value of the energy tank, update the stiffness of the dynamic model of the impedance system online, and obtain the updated ideal pose, velocity, and acceleration of the mobile robot end effector based on the dynamic model of the adaptive impedance system.

[0107] S500: Based on the updated ideal pose and velocity of the mobile robot end effector and its actual position and velocity, the pose tracking error and velocity tracking error of the mobile robot end effector in Cartesian space are obtained. Combined with the updated ideal velocity and acceleration of the mobile robot end effector, the ideal velocity and acceleration of the generalized joints of the mobile robot are obtained using inverse kinematics. Based on the ideal velocity and current joint velocity of the generalized joints of the mobile robot, the dynamic system model is introduced into the torque controller through Lyapunov functions to obtain the system coupling dynamic terms. An adaptive update law based on an integral bounded function is designed to adaptively compensate the system coupling dynamic terms in the torque controller. The control signal is sent to the robot actuator to drive the mobile robot end effector to progressively track the updated ideal trajectory, establish an ideal adaptive impedance relationship, and realize the control of the mobile robot end effector.

[0108] The above-mentioned multi-mobile robot cooperative handling control method based on adaptive impedance addresses the following problems in the cooperative handling process of multi-mobile robot systems: (1) It is necessary to know the reference point or the pose of the object's center of mass in advance and require the mobile robot to accurately grasp the given grasping point when grasping the object, which affects the cooperation efficiency; (2) When the parameters of the object being transported are unknown, adaptive impedance control is often used to achieve the adaptive impedance parameters, but the change in impedance parameters may cause the system to diverge; (3) When using neural networks to model the unknown dynamics of the mobile robot and the object, due to the approximation error, the neural network controller is difficult to achieve accurate tracking, thus failing to achieve the practical problem of the ideal adaptive impedance relationship.

[0109] Each mobile robot estimates the actual pose and ideal pose of the reference point and its first two derivatives using two finite-time fully distributed observers. Then, based on the estimated pose of the reference point, the pose of the end effector of the robotic arm, and the closed-chain constraints of the cooperative transport, it obtains the ideal trajectory of the end effector of the mobile robot and the estimated value of the pose deviation between the end effector of the mobile robot and the reference point. The designed observers can ensure the finite-time convergence of the estimation error, thereby avoiding the need to know the grasping point in advance and realizing the rapid grasping of unknown objects by the mobile robotic arm during cooperative transport. (2) The adaptive impedance system of each mobile robot is interconnected with a virtual energy tank. The energy tank is used to guide the updating of impedance parameters, thereby ensuring the passivity of the entire cooperative adaptive impedance system. (3) The unknown system dynamics of the mobile robot are handled by using a neural network with high computational efficiency and few training parameters to design an asymptotic tracking adaptive neural network controller, thereby asymptotically realizing the ideal adaptive impedance relationship. As shown in Figure 3, only mobile robot 1 can directly obtain the actual pose and ideal pose of the reference point and its first two derivatives, i.e., b1 = 1, b2 = b3 = b4 = 0. The communication topology between mobile robots is represented using graph theory, and their adjacency matrix is ​​a. 2,1 =a 3,2 =a 4,1 =1, other a i,j =0, where a i,j =1 indicates that the i-th mobile robot can receive the information from the j-th mobile robot; otherwise, a i,j =0.

[0110] In one embodiment, S100 includes:

[0111] S110: Consider the i-th mobile robot system whose robotic arm carries n... i,m The dynamic model of the i-th mobile robot system is as follows: (The system has several links.)

[0112] in, M is the mass inertia matrix of the i-th mobile robot. i,p M is the mass inertia matrix of the i-th mobile platform. i,m M is the mass inertia matrix of the i-th robotic arm. i,pm and M i,mp Let be the coupling mass inertia matrix between the mobile platform and the robotic arm; The matrix representing the centripetal and Coriolis forces of a mobile robot, C i,p C is the centripetal force and Coriolis force matrix of the i-th mobile platform. i,m C is the centripetal force and Coriolis force matrix of the i-th robotic arm. i,pm and C i,mp The centripetal force and Coriolis force matrix represents the coupling between the mobile platform and the robotic arm; Let be the dimension of the generalized coordinates of the i-th mobile robot. The gravity vector representing the mobile robot. and Let be the gravity vectors of the moving platform and the robotic arm of the i-th mobile robot, respectively. H i,p J is the constraint matrix for the i-th mobile robot; i,p and J i,m Let be the Jacobian matrices of the i-th mobile platform and the robotic arm, respectively; B is the input transformation matrix of the mobile robot. i,p and B i,m Let p be the input transformation matrix for the i-th mobile platform and the robotic arm, respectively. i To control input dimensionality and Let be the input torque vectors of the i-th mobile platform and the robotic arm, respectively. Where F i,p and F i,e These represent the nonholonomic constraint forces acting on the end effector of the mobile robot and the spinor of the external forces acting on the end effector of the mobile robot, respectively. Let be the generalized joint coordinates of the mobile robot, where Let p be the pose of the mobile platform p of the i-th mobile robot. Let m be the joint angle position of the robotic arm m of the i-th mobile robot. They represent q respectively i The first and second derivatives, Represents the number of mobile robots; Joint velocity Ratio of reduced joint velocities Multiple dimensions, n i,p Let n be the dimension of the pose of the mobile platform p of the i-th mobile robot. i,m Let be the degree of freedom of the i-th robotic arm;

[0113] Consider the nonholonomic constraints of the i-th mobile platform as follows: Reduced joint velocities can be obtained. Make:

[0114] Among them, A i,p (q i,p )satisfy Therefore, multiplying both sides of the dynamic model of the mobile robot in S110 by... Its dynamic model can be rewritten as:

[0115] in, and

[0116] S120: Consider the dynamic model of the object, specifically:

[0117] in, It is the mass-inertia matrix of the object. The matrix representing the centripetal and Coriolis forces of an object. It is the gravitational vector of the object, F. o x is the resultant force of multiple mobile robots acting on the center of mass of an object. o and v o These are the pose and velocity spinor of the object's center of mass, respectively;

[0118] Consider the velocity v of the object's center of mass. o relative to the velocity v at the reference point r Relationship: v o =J r,o v r and the net force F acting on the center of mass of the object. o and the external force spindle F at the end of the i-th mobile robot i,e Relationship: in, This is the matrix for capturing the center of mass of the object. J r,o J is the Jacobian matrix between the object's center of mass and its reference point. o,i Let be the Jacobian matrix between the object's center of mass and the i-th mobile robot end effector. Then, the object's dynamic model can be rewritten as:

[0119] in, Mobile robot's grasping matrix about reference points s(·) is an antisymmetric matrix operator. This represents the positional deviation between the reference point and the end effector of the mobile robot in the inertial coordinate system.

[0120] S130: Consider the load distribution coefficient Δ corresponding to the i-th mobile robot i ≥0 and the end effector of the i-th mobile robot acts on the object reference point x. r Indirect force F i,r ,in, and Moreover F i,r It can be decomposed into operating force F i,E and internal force F i,I That is, Fi,r =F i,E +F i,I Therefore, the coupling dynamic equation between the i-th mobile robot and the object is:

[0121] in, Φ A,i J is the transformation matrix between the geometric Jacobian and the analytic Jacobian. i,e Let the end effector velocity of the i-th mobile robot be... With reduced joint velocity The Jacobian matrix between them, i.e. For J r,i The pseudo-inverse matrix.

[0122] In one embodiment, S200 includes:

[0123] S210: Design an observer to estimate the actual pose of the reference point, define... Let x be the actual pose of the i-th mobile robot relative to the reference point. r If the observed value is given, then the synchronization error δ of the estimated actual pose of the i-th mobile robot to the reference point is... x,ir It can be defined as:

[0124] Among them, b i =1 indicates that the mobile robot i can measure or directly obtain the actual pose x of the reference point. r Otherwise b i =0, j∈N i This means that mobile robot i can receive information from mobile robot j. It is obtained from a finite-time fully distributed observer, specifically as follows:

[0125] Where, k 2,i,r For positive integers, for The first derivative, p i,e and o i,e Let represent the actual position and orientation of the i-th mobile robot's end effector, respectively; o i,e The first derivative, k 3,i,r For adaptive parameters, the update law is as follows:

[0126] Among them, Γ i,r It is a positive definite matrix;

[0127] S220: Design an observer to estimate the ideal pose of the reference point and its first two derivatives, defining the ideal trajectory of the reference point as x.d And its first two derivatives are respectively and When b i When x = 0, design a fully distributed observer to estimate x. d , and Specifically:

[0128] in, and For the i-th mobile robot, x d , The estimated value, α i ,β i ,γ i ∈(0.5,1) are positive constants; and The consistency error of the observations is specifically as follows:

[0129] In addition, k x,i k v,i and k a,i It is derived from the adaptive law, specifically as follows:

[0130] Among them, Γ 1,i ,Γ 2,i ,Γ 3,i It is a positive definite matrix;

[0131] S230: Define observation error and Based on the closed-chain constraint x i,e =x r +π ri , can be obtained in i p ri Let x be a constant vector, and let x be the reference point. r With the i-th mobile robot end effector x i,e The relative positions between them are represented in the coordinate system of the i-th mobile robot end effector. Let k represent the relative attitude between the coordinate system attached to the reference point and the coordinate system of the i-th mobile robot end effector in the inertial coordinate system. 3,i,r > i p ri At that time, the observation error e x,ir It converges to zero within a finite amount of time.

[0132] Specifically, as shown in Figure 4, the i-th mobile robot's actual pose x at the reference point... r estimation error It converges to zero within a finite time; as shown in Figure 5, the i-th mobile robot's ideal pose x at the reference point. d estimation error It converges to zero within a finite time; as shown in Figure 6, the i-th mobile robot's ideal pose x at the reference point. d first derivative estimation error It converges to zero within a finite time; as shown in Figure 7, the i-th mobile robot's ideal pose x at the reference point. d The second derivative estimation error It converges to zero within a finite amount of time.

[0133] In one embodiment, S300 includes:

[0134] S310: Estimated value considering the actual pose of the reference point and closed-chain constraint π ri =x i,e -x r ,available:

[0135] in, and Let be the estimated values ​​of the i-th mobile robot's position and orientation at the reference point, respectively. From this, the estimated value of the position deviation can be obtained. and the estimated value of relative attitude Specifically:

[0136] because It converges to x in a finite time. r ,so and They converge to in finite time respectively i p ri and w η ri ;

[0137] S320: Based on the estimated value of the position deviation Estimates of the ideal trajectory of the reference point By closed-chain constraint x i,ed =x i,d +π ri,d The ideal trajectory design for the i-th mobile robot end effector is as follows:

[0138] in, and and Let these represent the ideal position and orientation of the i-th mobile robot end effector, respectively. i p ri and w η ri It is a constant vector. first derivative Designed as follows:

[0139] in, for The first derivative;

[0140] The second derivative Designed as follows:

[0141] in,

[0142] S330: Defines the estimation error of the ideal trajectory of the mobile robot's end effector as... and As can be seen from S310, and They converge to in finite time respectively i p ri and w η ri Therefore, it can be concluded that within a limited time... Converging to zero, and It converges to zero in a finite amount of time, while Depend on and If it converges to zero in a finite amount of time, then we know that It converges to zero within a finite amount of time. and The ideal trajectory of the designed mobile robot end effector converges to zero within a finite time, and the ideal trajectory of the mobile robot end effector converges to the actual ideal trajectory of the mobile robot end effector within a finite time.

[0143] Specifically, as shown in Figure 8, since the i-th mobile robot's actual pose x at the reference point... r estimation error e x,ir It converges to zero within a finite amount of time. Converges to within a finite time i p ri =R w,i (o ie ) T (p i,e -p i,r ),Right now and Because the i-th mobile robot estimates the ideal pose of the reference point and position offset estimation They converge to their actual values ​​in a finite amount of time. Based on kinematic constraints, the expected pose of the i-th mobile robot end effector and the parameters of the grasping matrix can be obtained in a finite amount of time.

[0144] In one embodiment, S400 includes:

[0145] S410: Define the internal force tracking error F i,Ie =F i,I -F i,Id F i,Id For ideal internal forces, the following adaptive impedance model is established:

[0146] Among them, M 3,i , and K 3,i (t) is a positive definite diagonal matrix, representing the inertia matrix, damping matrix, and stiffness matrix, respectively. Let M be the pose tracking error of the i-th mobile robot end effector. 3,i B 3,i (t) and K 3,i (t) is a positive definite diagonal matrix;

[0147] The adaptive impedance model is decomposed into multiple one-dimensional adaptive impedance systems, where the number of one-dimensional adaptive impedance systems for each mobile robot is equal to the dimension of its control input. The j-th one-dimensional adaptive impedance system is represented as:

[0148] Among them, F ij,Ie M 3,ij B 3,ij (t) and K 3,ij (t), Δx i,j , and F respectively i,Ie M 3,i B 3,i (t), K 3,i (t), Δx i , and The element in the j-th row;

[0149] S420: Considering that a large stiffness value for an impedance system helps reduce the tracking error of the impedance system, the growth rate of the impedance system stiffness is determined by the internal force tracking error, the position tracking error, and the value of the virtual energy tank, specifically:

[0150] Among them, Γ F,ij Let γ be a positive constant, Proj(·) be the projection operator, and γ be a positive constant. s,ij The method used to limit the growth rate of stiffness is as follows:

[0151] Among them, s i,j ≥0 represents the maximum allowable power corresponding to the energy injected into the j-th one-dimensional adaptive impedance system.

[0152] δ 2,ij Used to maintain the value of the energy tank Not lower than the predetermined lower limit of the energy tank Specifically:

[0153] S430: The dynamics of designing the virtual energy tank are as follows:

[0154] in, 0≤μ i ≤1 is a constant;

[0155] δ 1,i Used to maintain the value of the energy tank Not higher than the predetermined upper limit Specifically:

[0156] S440: To prove that the adaptive impedance system interconnected with the virtual energy tank satisfies passivity, consider the following Lyapunov function for the entire multi-robot cooperative transport adaptive impedance system:

[0157] Dynamically substituting the adaptive impedance model from S410 From this, we can obtain:

[0158] It can be seen that when δ 1,i When = 1, we have When δ 1,i When = 0, we have Therefore, It is always true, therefore:

[0159] For the entire adaptive impedance system of multi-robot cooperative handling, Satisfies passivity;

[0160] S450: Considering the asymptotic realization of the ideal adaptive impedance model, an impedance error Δe is required. imp It asymptotically converges to zero, specifically as follows:

[0161] To achieve this goal, an updated reference trajectory x for the mobile robot's end effector is designed. i,c , And x i,c , and The following relationship must be satisfied:

[0162] Substituting the above equation into the impedance error Δe imp From the equation, we can obtain:

[0163] Therefore, when x i,e asymptotic tracking x i,c as well as asymptotic tracking When, Δe imp Asymptotically converges to zero. In one embodiment, S500 includes:

[0164] S510: Define tracking error And the following cross-coupling errors:

[0165] in, For the estimation of the ideal relative pose between the i-th and j-th mobile robot end effectors, l 3,i It is a positive constant;

[0166] Taking the derivative of the above equation, we can obtain Specifically:

[0167] To achieve the control objective, the ideal joint velocities of a mobile robot can be designed as follows:

[0168] Among them, Λ i Let be a positive definite diagonal constant matrix; differentiating both sides of the above equation, the ideal joint acceleration can be designed as follows:

[0169] S520: Defines the joint space velocity tracking error of a mobile robot. Therefore, the tracking error dynamic model of the i-th mobile robot can be written as:

[0170] in, Using neural networks to approximate unknown function vectors Right now in Let be the optimal weight vector matrix of the neural network. For the basis function vector, To approximate the error vector, define and

[0171] By incorporating a neural network, the following asymptotic tracking adaptive controller is designed:

[0172] in, To be Replace J σ,i In i p ri The obtained information about J σ,i The estimate, k i =k 1,i +k 2,i ||F i,I ||and k 1,i and k 2,i For positive constants, continuous functions satisfy in It is a positive constant. for Based on the estimated value, the update law of the neural network is designed as follows:

[0173] in, It is a positive integer;

[0174] S530: Define estimation error To confirm the stability and asymptotic tracking performance of the proposed controller, the candidate Lyapunov is:

[0175] Differentiating with respect to V, we get:

[0176] consider From the expression for τ, we get:

[0177] in, because It is by Caused by, and When there is a boundary, It is also bounded, because It is bounded, therefore It is also bounded, when hour, Therefore z i and It is bounded, and further we can obtain It is also bounded because the control input τ iIt is a function of a bounded signal, so τ i It is also bounded; therefore, all closed-loop signals are bounded.

[0178] Furthermore, because It converges to zero in a finite amount of time, so Converging to zero in a finite amount of time means that It converges to zero in a finite amount of time, so there exists a positive constant. Make In summary, for time t→∞, we have:

[0179] According to Barbara's lemma, as time t→∞, That is, as time t→∞, and In summary, as time t→∞, the impedance error Converging to zero;

[0180] S540: Write distributed control programs to control the end effector of the mobile robot.

[0181] Specifically, as shown in Figure 9, the impedance error Δe imp Asymptotic convergence to zero requires the position tracking error of the mobile robot's end effector. and speed error It asymptotically converges to zero. It asymptotically converges to zero. It can be seen that the developed distributed neural adaptive impedance controller method can guarantee... The asymptotic convergence to zero guarantees the desired adaptive impedance relationship. As shown in Figure 10, since variable stiffness may inject energy into the impedance system, this energy can be considered as extracted from the virtual energy tank to ensure the passivity of the entire system; therefore, the value of the virtual energy tank decreases. Since the energy dissipated by damping can be partially collected, the value of the virtual energy tank increases. When the value of the energy tank reaches a predetermined lower limit, further energy extraction from the energy tank is prohibited. Therefore, the interconnected adaptive impedance system with the energy tank can guarantee passivity; as shown in Figure 11, the Lyapunov function V of the entire interconnected adaptive impedance system... 2I The value of is bounded, so the entire interconnected adaptive impedance system is stable.

[0182] Figure 12 shows the poses of multiple mobile robots collaboratively transporting objects at times t=6s, t=19.2s, and t=30s, from left to right. The dashed lines represent the ideal trajectory of the object reference point; the solid lines represent the actual trajectory of the object reference point when the proposed method is applied. As shown in Figure 13, the tracking performance degrades due to estimation errors in the position offset design of the controller based on adaptive law estimation of position deviation. (The short-interval dashed lines represent the ideal trajectory of the object reference point; the solid lines represent the actual trajectory of the object reference point when the proposed method is applied; the long-interval dashed lines represent the actual trajectory of the object reference point when the control method based on adaptive law estimation of position deviation is applied.)

[0183] Compared with the prior art, the advantages of the present invention are as follows:

[0184] (1) This paper innovatively employs two observers to estimate the actual and ideal poses of the reference point, and obtains the positional deviation between the robot end effector and the reference point and the ideal trajectory of the mobile robot end effector based on the estimated poses. Simultaneously, a distributed adaptive impedance control scheme based on an energy tank is combined to design a controller for multi-mobile robotic arm collaborative handling, ensuring safe cooperation during multi-robot collaborative handling. The main contribution of this work is that the positional deviation between the mobile robot end effector and the reference point is estimated in real time, eliminating the need for the mobile robot to achieve precise grasping of a given grasping point when grasping an object, and minimizing tracking errors while ensuring safe cooperation.

[0185] (2) The designed finite-time observer is fully distributed, which can guarantee that the observation error converges to zero in finite time, and does not require global information, making it easy to apply and expand. The distributed adaptive impedance control based on the energy tank can ensure that the system satisfies the passivity requirement, and adaptively updates the impedance parameters, so that the proposed control scheme can adapt to different cooperative tasks.

[0186] (3) An adaptive neural network controller was developed using neural networks to compensate for uncertain dynamics and achieve asymptotic tracking of the updated reference position and velocity, thereby realizing ideal adaptive impedance dynamics. In addition, the number of neural network update laws proposed by the neural network control method is independent of the dimension of the neural network weight vector and the number of degrees of freedom of the mobile robot, and has high computational efficiency.

[0187] The above provides a detailed description of a multi-mobile robot cooperative handling control method based on adaptive impedance. Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of these embodiments are merely for the purpose of helping to understand the core ideas of this invention. It should be noted that those skilled in the art can make various improvements and modifications to this invention without departing from its principles, and these improvements and modifications also fall within the protection scope of the claims of this invention.

Claims

1. A method for adaptive impedance-based multi-mobile robot cooperative handling control, characterized by, The method comprises the following steps: S100: a dynamic model of a mobile robot and a dynamic model of an object are established, kinematic constraints are combined, and a dynamic system model of cooperative carrying of multiple mobile robots is established; S200: two finite-time full-distributed observers are designed by using information interaction among the multiple mobile robots to estimate actual poses and ideal poses and their second-order derivatives of a reference point, so as to obtain an estimated value of the actual pose of the reference point, an estimated value of the ideal pose of the reference point and its second-order derivative; S300: according to the estimated value of the actual pose of the reference point, actual poses of the ends of the multiple mobile robots and closed-chain constraints of cooperative carrying, an estimated value of a pose deviation between the reference point and the end of the mobile robot is obtained, based on the estimated value of the pose deviation and the estimated value of the ideal pose of the reference point and its second-order derivative, an estimated value of a grasping matrix of the mobile robot about the reference point and an ideal pose of the end of the mobile robot and its second-order derivative are obtained; S400: an internal force tracking error is defined, a dynamic model of a distributed adaptive impedance system based on a virtual energy tank is established by combining the actual pose of the end of the mobile robot, the internal force tracking error and the ideal pose of the end of the mobile robot obtained, the stiffness of the dynamic model of the impedance system is updated online according to the internal force error, the position tracking error of the end of the mobile robot and the value of the energy tank, and the ideal pose, velocity and acceleration of the end of the mobile robot after updating are obtained according to the dynamic model of the adaptive impedance system; S500: according to the ideal pose, velocity and acceleration of the end of the mobile robot after updating and the actual position and velocity of the end of the mobile robot, pose tracking errors and velocity tracking errors of the end of the mobile robot in the Cartesian space are obtained, ideal velocities and accelerations of generalized joints of the mobile robot are obtained by using inverse kinematics in combination with the ideal velocity and acceleration of the end of the mobile robot after updating, the dynamic system model is introduced into a torque controller through a Lyapunov function according to the ideal velocities of the generalized joints of the mobile robot and current joint velocities, a neural network adaptive update law based on an integral bounded function is designed to adaptively compensate for the system coupling dynamic items in the torque controller, control signals are sent to a robot actuator to drive the end of the mobile robot to gradually track the ideal trajectory after updating, an ideal adaptive impedance relationship is established, and control of the end of the mobile robot is realized.

2. The method of claim 1, wherein, S100 comprises: S110: considering that the manipulator of the ith mobile robot system has n i,m links, the dynamics model of the ith mobile robot system is: wherein is the mass inertia matrix of the ith mobile robot, M i,p is the mass inertia matrix of the ith mobile platform, M i,m is the mass inertia matrix of the ith mobile platform, M i,pm and M i,mp is the coupling mass inertia matrix between the mobile platform and the manipulator; is the centripetal and Coriolis force matrix of the i-th mobile platform, C i,p is the centripetal and Coriolis force matrix of the i-th mobile platform, C i,m is the centripetal and Coriolis force matrix of the i-th mobile platform, C i,pm and C i,mp is the centripetal and Coriolis force matrix of the coupling between the mobile platform and the manipulator; the dimension of the generalized coordinates for the i-th mobile robot, a gravity vector representative of the mobile robot, and a gravity vector of the mobile platform and the robot arm of the i-th mobile robot, respectively, H i,p constraint matrix for the ith mobile robot; J i,p and J i,m Jacobian matrices for the ith mobile platform and manipulator, respectively; is the input transformation matrix of the mobile robot, B i,p and B i,m are the input transformation matrices of the ith mobile platform and the manipulator, respectively, p i is the control input dimension of the vector, and input torque vector of the i-th mobile platform and the robot arm, respectively, where F i,p and F i,e are the nonholonomic constraint forces and the mobile robot end-effector external force wrench, respectively, for the generalized joint coordinates of the mobile robot, wherein a pose of a mobile platform p for the i-th mobile robot, joint angle position of the mechanical arm m for the i-th mobile robot, respectively representing the first derivative and the second derivative of q i , a number of representative mobile robots; For joint velocity Slope order joint velocity a high number of dimensions, n i,p a number of dimensions, n, of the pose of the mobile platform p of the i-th mobile robot i,m a number of degrees of freedom of the i-th robot arm Consider the nonholonomic constraint for the i-th mobile platform as Reduced joint velocities are available such that: wherein A i,p (q i,p ) satisfies Thus, the dynamics model of the mobile robot in S110 is multiplied by The kinetic model can be rewritten as: wherein, J i,e = [J i,p A i,p , J i,m ], and F i,e Wextis the external wrench vector at the end of the mobile robot; S120: Consider the dynamics model of the object, which is specifically: wherein is the mass inertia matrix of the object, a centripetal force representative of the object and a coriolis force matrix, is the gravity vector of the object, F o is the resultant force acting on the object's center of mass by the mobile robots, x o and v o are the object's center of mass pose and velocity screw, respectively; Consider the velocity v of the center of mass of the object o The relationship between the velocity v of the reference point and the velocity v of the center of mass of the object: r o = J r,o v r , and the relationship between the total force F experienced by the center of mass of the object and the i-th mobile robot end-external force wrench F o i,e ​​​ wherein for the grasp matrix with respect to the center of mass of the object, J r,o J is the Jacobian matrix between the object mass center and the object reference point, o,i J is the Jacobian matrix between the object mass center and the i-th mobile robot end, then the dynamics model of the object can be rewritten as: wherein Mobile robot grasp matrix with respect to a reference point s(·) is the anti-symmetric matrix operator, is a representation of a position deviation between the reference point and the end of the mobile robot in an inertial coordinate system; S130: Consider the load distribution coefficient Δ corresponding to the i-th mobile robot i ≥ 0 and the end of the i-th mobile robot acting on the object reference point x r indirect force F i,r wherein, and And F i,r The operation force F i,E And the internal force F i,I That is, F i,r =F i,E +F i,I Therefore, the coupling dynamic equation of the ith mobile robot and the object is: wherein Φ A,i is the transformation matrix between the geometric Jacobian and the analytical Jacobian, J i,e is the end velocity of the ith mobile robot Joint velocities with reduced order the Jacobian matrix between the two, i.e. For J r,i the pseudo-inverse matrix.

3. The method of claim 2, wherein, S200 comprises: S210: design an observer to estimate the actual pose of the reference point, define The observation value of the actual pose x r of the reference point by the i-th mobile robot is xi, then the synchronization error δ x,ir of the estimated value of the actual pose of the reference point by the i-th mobile robot can be defined as: where b i = 1 means that mobile robot i can measure or directly obtain the actual pose x r of the reference point, otherwise b i = 0, j e N i means that mobile robot i can receive information from mobile robot j, The finite-time global distributed observer is obtained, which is specifically as follows: wherein k 2,i,r is a normal number, For a first derivative of the function f(x), p i,e and o i,e Pi and θi represent the actual position and pose of the end of the i-th mobile robot, respectively; For o i,e the first derivative, k 3,i,r is an adaptive parameter, whose update law is specified as: where Γ i,r is a positive definite matrix; S220: design the ideal pose of the observer-estimated reference point and its first two derivatives, define the ideal trajectory of the reference point as x d and its first two derivatives as and When b i = 0, the full-distributed observer estimates x d , and In particular, wherein, and respectively, the i-th mobile robot pair x d , an estimated value of a, a i , b i , g i ∈(0.5, 1) is a normal number; and For the consistency error of the observed value, it is specifically: Furthermore, k x,i , k v,i and k a,i are obtained from an adaptive law, which is specified as: where Γ 1,i ,Γ 2,i ,Γ 3,i are positive definite matrices; S230: define observation error and According to the closed chain constraint x i,e = x r + π ri , we obtain wherein i p ri is a constant vector, which is the reference point x r is the relative position between the end of the ith mobile robot x i,e in the coordinate system of the end of the ith mobile robot, is the representation of the relative pose between the coordinate system attached to the reference point and the coordinate system of the end of the i-th mobile robot in the inertial coordinate system, when k 3,i,r i p ri is the observation error x,ir which converges to zero in finite time.​ 4. The method of claim 3, wherein, S300 comprises: S310: Consider the estimated value of the actual pose of the reference point and closed chain constraints π ri = x i,e - x r , we obtain wherein and respectively, the i-th mobile robot's estimate of the position and pose of the reference point, respectively, and thus, the estimate of the position error and an estimate of the relative pose In particular, Because Converge to x in finite time r So and converge to i p ri and w η ri ; S320: According to the estimated value of the positional deviation and an estimated value of an ideal trajectory of the reference point x = x i,ed = x i,d + π ri,d The ideal trajectory of the end of the ith mobile robot is designed as: wherein and and respectively represent the ideal position and attitude of the end of the i-th mobile robot, i p ri and w η ri is a constant vector, first derivative of the function designed to: wherein For a first-order derivative of second derivative of the function designed to: wherein S330: define the estimation error of the ideal trajectory of the end of the mobile robot as and From S310, it is known that and converge to i p ri and w η ri respectively in finite time converges to zero, and converges to zero in finite time, and By and Converges to zero in finite time, it is known that converge to zero in finite time, and converges to zero in a finite time, and the ideal trajectory of the end of the mobile robot designed converges to the actual ideal trajectory of the end of the mobile robot in a finite time.

5. The method of claim 4, wherein, S400 comprises: S410: define internal force tracking error F i,Ie = F i,I - F i,Id where F i,Id is the ideal internal force, an adaptive impedance model is established as follows: M 3,i , and K 3,i (t) are positive definite diagonal matrices representing the mass, damping and stiffness matrices, respectively, The pose tracking error for the end of the i-th mobile robot is given by 3,i , B 3,i (t) and K 3,i (t) are positive definite diagonal matrices. The adaptive impedance model is decomposed into a plurality of one-dimensional adaptive impedance systems, wherein the number of one-dimensional adaptive impedance systems of each mobile robot is equal to the dimension of its control input, and the jth one-dimensional adaptive impedance system is represented as: where F ij,Ie , M 3,ij , B 3,ij (t) and K 3,ij (t) are as defined above, Δx i,j , and F i,Ie , M 3,i , B 3,i (t), K 3,i (t), Δx i , and a jth row element of S420: Considering that a large stiffness value for the impedance system helps to reduce the tracking error of the impedance system, the growth rate of the impedance system stiffness is determined by the values of the internal force tracking error, the position tracking error, and the virtual energy tank, specifically: where Γ F,ij is a constant, Proj(·) is a projection operator, γ s,ij is a constant used to limit the rate of stiffness growth, which is given by: where s i,j ≥ 0 is the maximum allowed power corresponding to the energy injected into the jth one-dimensional adaptive impedance system, δ 2,ij values for securing the energy tank No less than the predetermined lower bound of the energy tank In particular, S430: design the dynamics of the virtual energy tank, which specifically is: wherein, is a constant; δ 1,i values for securing the energy tank not higher than a predetermined upper bound In particular, S440: To prove that the adaptive impedance system interconnected with the virtual energy tank satisfies passivity, for the whole multi-robot cooperative carrying adaptive impedance system, the following Lyapunov function is considered: Substitute the dynamics of the adaptive impedance model in S410 In the above equation, the variables are defined as follows: It is known that when δ 1,i = 1, there are When δ 1,i = 0, there is Thus, it is possible to obtain It is always true, therefore, that: For an adaptive impedance system for entire multi-robot cooperative handling, input-output pair satisfies passivity; S450: Considering the asymptotically ideal adaptive impedance model, the impedance error Ae is needed imp converges asymptotically to zero, which is specifically: To achieve this goal, the reference trajectory x of the updated end of the mobile robot is designed i,c , and x i,c , With satisfies the following relationship: Substituting the above equation into the equation for the impedance error Δe imp we obtain Thus, it is known that when x i,e Asymptotic tracking of x i,c and Asymptotic tracking At time Δe imp Asymptotically converges to zero.

6. The method of claim 5, wherein, S500 comprises: S510: define tracking error and cross-coupling errors as follows: wherein, an estimate of an ideal relative pose of the end of the i-th mobile robot to the end of the j-th mobile robot, is a constant; Taking the derivative of the above equation, we obtain In particular, To achieve the control objective, the ideal joint velocity of the mobile robot can be designed as follows: where Λ i is a positive definite diagonal constant matrix; the ideal joint acceleration can be designed as follows by taking the derivative of the above equation: S520: define joint space velocity tracking error of the mobile robot So, the tracking error dynamics model of the ith mobile robot is written as: wherein, Approximating an unknown function vector using neural networks That is wherein for the optimal weight vector matrix of the neural network, for the basis function vector, To approximate the error vector, define and In combination with the neural network, an asymptotic tracking adaptive controller is designed as follows: wherein To facilitate Instead of J σ,i in i p ri the estimate for J σ,i is obtained, k i = k 1,i + k 2,i ||F i,I || and k 1,i and k 2,i are normal numbers, continuous functions satisfy wherein is a constant, For The estimated value of the neural network is designed as the update law: wherein is a constant; S530: define an estimation error To confirm the stability and asymptotic tracking performance of the proposed controller, the candidate Lyapunov function is: Taking the derivative of V with respect to t, we get: Consider and the expression for τ, we obtain: wherein Due to is by caused, and is bounded, is also bounded, since is bounded, so is also bounded, when Time, So z i and is bounded, further obtainable Also bounded because the control input τ i is a function of a bounded signal, so τ i is also bounded, and in summary, all closed loop signals are bounded; Furthermore, because converges to zero in finite time, so Converges to zero in finite time, which means converges to zero in finite time, so there exists a positive constant such that In summary, the inequality, when time t→∞, has: According to Barbara's lemma, we can get that when time t→∞, That is, at time t→∞, and In summary, when time t→∞, impedance error converges to zero; S540: a distributed control program is written to realize control of the end of the mobile robot.

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