Spatial flexible multi-arm robot cooperative control method and system using stress stiffening effect

Abstract

The invention discloses a spatial flexible multi-arm robot cooperative control method and system using a stress stiffening effect, and relates to the field of spatial flexible multi-arm robot cooperative control. The problems that in the prior art, robot research considering flexibility mainly focuses on a single mechanical arm, and for a multi-arm space robot, especially the situation that configuration can be switched between an open chain and a closed chain, current research is still few are solved. The method comprises the steps that based on the open chain topological configuration and the self-closed chain topological configuration of the space flexible multi-arm robot, kinetic models, considering joint flexibility, of the space multi-arm robot in the open chain state and the self-closed chain state are established respectively; an internal force stiffening effect is introduced, whether internal stress exists or not is determined, and rigidity analysis of the space multi-arm robot considering the flexible joint under the self-closed chain configuration is completed; a composite control law is designed for the space multi-arm robot considering the flexible joint based on a singular perturbation method, and the method is also suitable for the field of improving the control precision in the orbit service and orbit capturing process.

Description

Technical Field

[0001] The present invention relates to the technical field of coordinated control of space flexible multi-arm robots, and in particular to a coordinated control method and system of space flexible multi-arm robots utilizing stress stiffening effect. Background Art

[0002] There are currently hundreds of high-value spacecraft in geosynchronous orbit. However, these spacecraft often fail due to structural failures, control system failures, fuel exhaustion, and other reasons. Due to the lack of effective on-orbit maintenance methods, they can only be replaced by launching new satellites, which seriously increases the cost of development and launch. Therefore, how to stably capture failed spacecraft and perform space operations such as disassembly, maintenance, and life extension has become the focus of future space technology research in various countries. As a new type of on-orbit capture tool, space multi-arm robots have stronger stability, flexibility, and reliability compared to traditional single-arm robots. Current research focuses on the fields of collaborative motion planning, collaborative force control, and collaborative perception of space multi-arm robots, and has achieved rich research results.

[0003] In the study of the dynamics of space multi-arm robots, space robots are classified as a type of floating base system, in which the motion and force of the manipulator, actuator and base will affect each other, which is called the "dynamic coupling" effect. It derives a generalized form of Jacobian matrix suitable for space floating manipulators, which is used to solve the problem of satellite attitude control. In the prior art, a generalized relative Jacobian method is proposed for the relative motion planning of two arms in inertial space. The situation that the space multi-arm robot forms a closed-loop system when capturing the target is further considered, and the dynamic coupling effect of the open-loop system and the closed-loop system is analyzed. According to the kinematic and dynamic formulas of the free-floating multi-arm space robot with closed-loop constraints, the mapping relationship from the joint space to the task space is described. The impact dynamics, post-capture stability and maneuver transfer of the space multi-arm robot system during the capture process are unified into a dynamic framework. The flexibility of the space manipulator, especially the joint flexibility, cannot be ignored in actual tasks, especially when capturing large loads with unknown dynamic properties, the joint flexibility will greatly affect the capture accuracy. In this regard, the prior art has gradually improved the dynamic model of flexible joints and proposed a modeling method that is more in line with the actual system.

[0004] In summary, the existing research on flexible robots mainly focuses on single robotic arms. For multi-arm space robots, especially those that can switch configurations between open and closed chains, there is still little research.

[0005] In the study of control methods of space multi-arm robots, since space multi-arm robots are complex nonlinear systems, many scholars have applied nonlinear control methods to them, such as adaptive control, robust control, sliding mode control, etc., and achieved good results. Furthermore, some scholars have considered the closed-loop kinematic constraints of multi-arm systems and proposed a series of coordinated control methods to improve the control effect of multi-arm robots. In the prior art, a dual-arm coordinated motion planning and compliant control method is proposed, which has a unique zero space projection relative Jacobian matrix and a relative operating force between the two arms. Based on model predictive control, a dual-arm collaborative gripping control method is proposed, and a dual-arm coordinated "regional directional capture" method is proposed to capture non-cooperative tumbling targets. However, most of the above studies regard space multi-arm robots as rigid bodies and do not consider the control errors caused by flexibility. In the study of control methods of space robots considering flexibility, due to the modeling of flexible joints, the dynamic model of the multi-arm system becomes a more complex high-order model, which poses great challenges and requirements to the control system. PD control with flexibility compensation regards the error caused by flexibility as an interference term, which can suppress the control error of flexible joints to a certain extent, but does not consider the dynamic model of flexible joints, and its tracking dynamic performance is poor. Singular perturbation control decouples the flexible joint model into a system with two time scales, fast and slow, and has the advantage of model reduction. However, the research objects of the above methods are mainly single flexible joints or single robotic arms with multiple flexible joints, and there is little research on spatial multi-arm robots.

[0006] In summary, the existing technology research mainly focuses on multiple robotic arms acting on the target satellite at the same time, such as multi-arm clamping and hugging the target. In some tasks, such as when the target has only one nozzle for docking or the target is small, the action point available for the robotic arm to operate is single. Summary of the invention

[0007] The present invention aims to solve the problem that the research on flexible robots in the prior art mainly focuses on a single robotic arm, and there is still little research on multi-arm space robots, especially those that can switch configurations between open and closed chains.

[0008] To solve the above technical problems, the present invention is achieved through the following technical solutions:

[0009] Solution 1: The present invention proposes a method for collaborative control of a space flexible multi-arm robot using a stress stiffening effect, the method comprising the following steps:

[0010] S1. Based on the two topological configurations of the space flexible multi-arm robot, the dynamic models of the space multi-arm robot in the open chain and self-closed chain states considering the joint flexibility are established respectively;

[0011] S2. Introduce the internal force stiffening effect in the dynamic model of the open chain and self-closed chain states described in S1, and determine whether there is internal stress to complete the stiffness analysis of the spatial multi-arm robot considering flexible joints in the self-closed chain configuration;

[0012] S3. Based on the singular perturbation method, a composite control law is designed for the space multi-arm robot considering flexible joints as described in S2. The composite control law includes collaborative control of the stiffness of the space flexible robot system on both slow and fast time scales, i.e., collaborative control of the space flexible multi-arm robot that achieves the internal force stiffening effect.

[0013] Furthermore, a preferred embodiment is provided, in which the stiffness analysis method of the spatial multi-arm robot with flexible joints in a closed chain configuration when there is no internal stress in S2 is implemented by determining the stiffness matrix of the kth robot arm in a state without pre-internal force.

[0014] Furthermore, a preferred embodiment is provided, wherein the method for determining the stiffness matrix of the kth mechanical arm in a state without pre-internal force specifically comprises:

[0015] When considering the elastic deformation of the flexible joint, the pose x based on the Combine Body CB Expressed as the generalized motor angle of the kth robot arm and the deformation of the kth generalized joint spring of the robot arm Function:

[0016] x CB =f(Θ k ,ε k ) (twenty one)

[0017] Taking the derivative on both sides we get:

[0018]

[0019] In the formula, Used to describe the posture changes of the Combinaine Body. is the vector formed by the differential of the angle variable of the generalized joint motor of the kth robot arm, is the vector formed by the differential deformation of the joint hinge on the kth robot arm, δε0=0 6×1 , the kinematic Jacobian matrix of the k-th robot arm is Respectively represent the generalized joint motor speed And the deformation speed of the flexible joint spring Combine Body Speed The impact of

[0020]

[0021] Where: is the torque column vector of the flexible hinge on the kth robot arm, where is the torque column vector on the i-th flexible hinge on the k-th robot arm, δε k is the deformation of the joint spring;

[0022] The control torque applied by the joint motor is

[0023]

[0024] In the formula, To control the equivalent stiffness;

[0025] When Combine Body is subjected to external force f e When it works, δx is generated at the end of Combine Body CB The corresponding joint change is (δΘ, δε), and the virtual work done by the external force is equal to the sum of the virtual work done by the internal force of the mechanism:

[0026]

[0027] Substituting (22) into (25) we obtain

[0028]

[0029] Equation (26) holds true for any virtual displacement, thus the static equilibrium equation can be obtained:

[0030]

[0031] Substituting (23), (24) and (27) into (22), we obtain

[0032]

[0033] Further we get:

[0034] f e =K k δx CB (29)

[0035] In the formula, is the stiffness matrix of the kth robot arm without pre-internal force.

[0036] Furthermore, a preferred embodiment is provided, wherein the Combine Body dynamics equation is obtained using the Newton-Euler formula.

[0037] Further, a preferred embodiment is provided, in which a stiffness analysis method of a spatial multi-arm robot with flexible joints in a self-closing chain configuration is performed by determining the internal force f I The system stiffness matrix under action accomplish.

[0038] Further, a preferred embodiment is provided, by determining the pre-internal force f I The system stiffness matrix under action The specific implementation method is:

[0039] Define the potential energy function And taking the differentiation of each term in (27) we get:

[0040]

[0041] In the formula, is the Hessian matrix of the potential energy function ζ, where

[0042] Solving equation (31) yields

[0043]

[0044] In the formula,

[0045] Substituting (32) into (22), we can obtain

[0046]

[0047] In the formula,

[0048]

[0049] In the formula, For the pre-loaded internal force f I The stiffness matrix of the kth robot arm in the case of is the stiffness coefficient.

[0050] Further, a preferred embodiment is provided, wherein There is a pre-loaded internal force f I The stiffness matrix of the kth robot arm in this case is given by f I The direction and size of the system are determined by the system configuration.

[0051] Solution 2: A space flexible multi-arm robot collaborative control system utilizing stress stiffening effect, the system comprising:

[0052] The model building module is used to build the dynamic models of the space multi-arm robot in the open chain and self-closed chain states considering the joint flexibility based on the two topological configurations of the space multi-arm robot.

[0053] The stiffness analysis module is used to introduce the internal force stiffening effect into the dynamic model of the open chain and self-closed chain states described in the model building module, and to determine whether there is internal stress to complete the stiffness analysis of the spatial multi-arm robot considering flexible joints in the self-closed chain configuration;

[0054] A collaborative control module is used to design a composite control law for the space multi-arm robot considering flexible joints described in the stiffness analysis module based on a singular perturbation method. The composite control law includes collaborative control of the stiffness of the space flexible robot system on two time scales, slow and fast, that is, collaborative control of the space flexible multi-arm robot that completes the internal force stiffening effect.

[0055] The present invention is beneficial in that:

[0056] The collaborative control method of a spatial flexible multi-arm robot utilizing stress stiffening effect described in the present invention improves the system stiffness from both dynamics and control perspectives by using an internal force interaction mechanism and a coordinated control algorithm under a closed chain configuration, in order to reduce control errors caused by inaccurate modeling of joint flexibility and dynamics during docking and capture.

[0057] The present invention proposes a design scheme of a fast locking and releasing device for a space multi-arm robot. The device can realize switching between an open chain and a self-closing chain structure, so as to improve the adaptability of the robot in different tasks.

[0058] The present invention introduces the "stress stiffening" effect in material mechanics and establishes the dynamic models of the space multi-arm robot in the open chain and self-closed chain states considering joint flexibility. This effect describes the relationship between the internal stress of the structure and the lateral stiffness. It points out and proves that by changing the internal stress distribution in the self-closed chain system of the space multi-arm robot, the system stiffness of the space multi-arm robot can be improved from the dynamic level.

[0059] Based on the singular perturbation theory, the present invention designs a composite control law for a space multi-arm robot taking into account joint flexibility. The control law performs control on slow and fast time scales, taking into account both capture compliance and suppressing the vibration of flexible joints, thus improving the equivalent stiffness of the system from the control level.

[0060] The present invention is also applicable to the field of improving control accuracy during orbital service and orbital capture. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1Schematic diagram of two topological configurations of the space multi-arm robot described in Implementation Mode 1.

[0062] Figure 1 In the figure, (a) is a schematic diagram of the topological configuration of the open chain state, and (b) is a schematic diagram of the topological configuration of the closed chain state;

[0063] Figure 1 In the figure, 1 is the base, 2 is the No. 1 robot arm, 3 is the cone-rod docking mechanism, 4 is the target, 5 is the quick-install and quick-change device, and 6 is the No. 2 robot arm.

[0064] Figure 2 This is a schematic diagram of the open-chain coordinate system definition described in Implementation Example 11.

[0065] Figure 3 This is a schematic diagram of the open-chain coordinate system definition described in Implementation Example 11.

[0066] Figure 4 This is a schematic diagram of the flexible joint model described in Implementation Example 11.

[0067] Figure 5 Schematic diagram of the interaction force in the closed chain state described in Implementation Example 11.

[0068] Figure 6 This is a schematic diagram of the terminal deformation under stress stiffening described in the eleventh embodiment.

[0069] Figure 7 This is the original block diagram of the spatial flexible multi-arm robot collaborative control system utilizing the internal force stiffening effect as described in Implementation Example 8.

[0070] Figure 8 This is a schematic diagram of the simulation process described in Implementation Method 11.

[0071] Figure 8 In the figure, (a) is a simulation diagram of the open chain control stage at 0-5s, (b) is a simulation diagram of the closed chain formation stage at 5-10s, (c) is a simulation diagram of the closed chain docking stage at 10-15s, and (d) is a simulation diagram of the assembly control stage at 15-30s.

[0072] Fig. 9 Schematic diagram of the expected trajectory of the end of the robot arm in the open chain stage described in the eleventh embodiment.

[0073] Fig. 9 In the figure, (a) is a schematic diagram of the desired position trajectory of the end of the robotic arm, and (b) is a schematic diagram of the desired posture trajectory of the end of the robotic arm.

[0074] Fig.10 This is a schematic diagram of the expected trajectory of the Combined Body at the end of the closed-loop chain stage described in Implementation Example 11.

[0075] Fig.10 In the figure, (a) is a schematic diagram of the expected position trajectory of the Combined Body, and (b) is a schematic diagram of the expected posture trajectory of the Combined Body.

[0076] Fig.11 It is a schematic diagram comparing the terminal error results of Arm_1 and Arm_2 under two controllers in the open chain stage described in Implementation Example 11.

[0077] Fig.11 In the figure, (a) is a schematic diagram of the position error in the x direction of the end of Arm_1, (b) is a schematic diagram of the position error in the x direction of the end of Arm_2, (c) is a schematic diagram of the position error in the y direction of the end of Arm_1, (d) is a schematic diagram of the position error in the y direction of the end of Arm_2, (e) is a schematic diagram of the position error in the z direction of the end of Arm_1, and (f) is a schematic diagram of the position error in the z direction of the end of Arm_2.

[0078] Fig.12 Schematic diagram of control error of Combined Body in the self-closing chain state described in Implementation Example 11.

[0079] Fig.12 In the figure, (a) is a schematic diagram of the combined body x-direction position error, (b) is a schematic diagram of the combined body quaternion error q1, (c) is a schematic diagram of the combined body y-direction position error, (d) is a schematic diagram of the combined body quaternion error q2, (e) is a schematic diagram of the combined body z-direction position error, and (f) is a schematic diagram of the combined body quaternion error q3.

[0080] Fig.13 This is a schematic diagram of the joint angle of the robot arm when the compressive stress is 300N as described in the eleventh embodiment.

[0081] Fig.13 In the figure, (a) is the rotation angle q of the connecting rod of Arm_1 1 Schematic diagram, (b) is the rotation angle θ of the Arm_1 motor 1 Schematic diagram, (c) is the rotation angle q of the Arm_2 connecting rod 2 Schematic diagram, (d) is the rotation angle θ of the Arm_2 motor 2 Schematic diagram.

[0082] Fig.14 This is a schematic diagram of the output torque τ of the robot arm when the compressive stress is 300N as described in the eleventh embodiment.

[0083] Fig.14In the figure, (a) is the output torque τ of the Arm_1 motor 1 Schematic diagram, (b) is the output torque τ of the Arm_2 motor 2 Schematic diagram.

[0084] Fig.15 This is a schematic diagram of the Base posture error described in Implementation Example 11.

[0085] Fig.15 In the figure, (a) is a schematic diagram of the Base x-direction position error, (b) is a schematic diagram of the Base attitude quaternion error q1, (c) is a schematic diagram of the Base y-direction position error, (d) is a schematic diagram of the Base attitude quaternion error q2, (e) is a schematic diagram of the Base z-direction position error, and (f) is a schematic diagram of the Base attitude quaternion error q3.

[0086] Fig.16 This is a physical picture of the ground experiment setup of the space multi-arm robot described in Implementation Mode 11.

[0087] Fig.17 This is a schematic diagram of a physical simulation verification based on a ground experiment of a space multi-arm robot for the verification described in Implementation Mode 11.

[0088] Fig.17 In the figure, (a) is a simulation diagram of the movement from the open-chain configuration to the docking state at 0 s, (b) is a simulation diagram of the movement from the open-chain configuration to the docking state at 200 s, (c) is a simulation diagram of the movement from the open-chain configuration to the docking state at 255 s, and (d) is a simulation diagram of the movement from the open-chain configuration to the docking state at 375 s.

[0089] Fig.18 Schematic diagram of the comparison of the spatial distance error curve of the end of the robot arm moving under load state described in the eleventh embodiment.

[0090] Fig.19 This is a schematic diagram of the change of internal force and torque over time in the self-closed chain configuration formed by the space robot through topology change as described in the eleventh embodiment.

[0091] Fig.19 In the figure, (a) is a schematic diagram of the variation of internal force in the closed chain configuration with time, and (b) is a schematic diagram of the variation of torque in the closed chain configuration with time. DETAILED DESCRIPTION

[0092] In order to make the purpose, technical solutions and advantages of the implementation methods of the present application clearer, the technical solutions in the implementation methods of the present application will be clearly and completely described below in conjunction with the drawings in the implementation methods of the present application. Obviously, the described implementation methods are only part of the implementation methods of the present application, not all of the implementation methods.

[0093] Embodiment 1: This embodiment provides a space flexible multi-arm robot collaborative control method using stress stiffening effect, the space flexible multi-arm robot collaborative control method comprises the following steps:

[0094] S1. Based on the two topological configurations of the space flexible multi-arm robot, the dynamic models of the space multi-arm robot in the open chain and self-closed chain states considering the joint flexibility are established respectively;

[0095] S2. Introduce the internal force stiffening effect in the dynamic model of the open chain and self-closed chain states described in S1, and determine whether there is internal stress to complete the stiffness analysis of the spatial multi-arm robot considering flexible joints in the self-closed chain configuration;

[0096] S3. Based on the singular perturbation method, a composite control law is designed for the space multi-arm robot considering flexible joints as described in S2. The composite control law includes collaborative control of the stiffness of the space flexible robot system on both slow and fast time scales, i.e., collaborative control of the space flexible multi-arm robot that achieves the internal force stiffening effect.

[0097] Implementation method 2. This implementation method is a further limitation of the collaborative control method of the space flexible multi-arm robot utilizing the stress stiffening effect described in implementation method 1. In S2, the stiffness analysis method of the space multi-arm robot considering flexible joints in a closed chain configuration when there is no internal stress is implemented by determining the stiffness matrix of the kth robotic arm in the state without pre-internal force.

[0098] Embodiment 3: This embodiment further limits the method for collaborative control of a space flexible multi-arm robot using stress stiffening effect described in Embodiment 2. The method for determining the stiffness matrix of the kth mechanical arm in a state without pre-internal force specifically includes:

[0099] When considering the elastic deformation of the flexible joint, the pose x based on the Combine Body CB Expressed as the generalized motor angle of the kth robot arm and the deformation of the kth generalized joint spring of the robot arm Function:

[0100] x CB =f(Θ k ,ε k ) (twenty one)

[0101] Taking the derivative on both sides we get:

[0102]

[0103] In the formula, Used to describe the posture changes of the Combinaine Body. is the vector formed by the differential of the angle variable of the generalized joint motor of the kth robot arm, is the vector formed by the differential deformation of the joint hinge on the kth robot arm, δε0=0 6×1 , the kinematic Jacobian matrix of the k-th robot arm is Respectively represent the generalized joint motor speed And the deformation speed of the flexible joint spring Combine Body Speed The impact of

[0104]

[0105] Where: is the torque column vector of the flexible hinge on the kth robot arm, where is the torque column vector on the i-th flexible hinge on the k-th robot arm, δε k is the deformation of the joint spring;

[0106] The control torque applied by the joint motor is

[0107]

[0108] In the formula, To control the equivalent stiffness;

[0109] When Combine Body is subjected to external force f e When it works, δx is generated at the end of Combine Body CB The corresponding joint change is (δΘ, δε), and the virtual work done by the external force is equal to the sum of the virtual work done by the internal force of the mechanism:

[0110]

[0111] Substituting (22) into (25) we obtain

[0112]

[0113] Equation (26) holds true for any virtual displacement, thus the static equilibrium equation can be obtained:

[0114]

[0115] Substituting (23), (24) and (27) into (22), we obtain

[0116]

[0117] Further we get:

[0118] f e =K k δx CB (29)

[0119] In the formula, is the stiffness matrix of the kth robot arm without pre-internal force.

[0120] Embodiment 4: This embodiment further limits the collaborative control method of the space flexible multi-arm robot using the stress stiffening effect described in embodiment 3, and the Combine Body dynamics equation is obtained using the Newton-Euler formula.

[0121] Embodiment 5. This embodiment is a further limitation of the coordinated control method of the space flexible multi-arm robot using the stress stiffening effect described in Embodiment 1. When there is an internal force in S2, the stiffness analysis method of the space multi-arm robot considering the flexible joints in the self-closed chain configuration is determined by determining the pre-internal force f I The system stiffness matrix under action accomplish.

[0122] Embodiment 6: This embodiment further limits the collaborative control method of the space flexible multi-arm robot using the stress stiffening effect described in Embodiment 5. By determining the pre-internal force f I The system stiffness matrix under action The specific implementation method is:

[0123] Define the potential energy function And taking the differentiation of each term in (27) we get:

[0124]

[0125] In the formula, is the Hessian matrix of the potential energy function ζ, where

[0126] Solving equation (31) yields

[0127]

[0128] In the formula,

[0129] Substituting (32) into (22), we can obtain

[0130]

[0131] In the formula,

[0132]

[0133] In the formula, For the pre-loaded internal force f I The stiffness matrix of the kth robot arm in the case of is the stiffness coefficient.

[0134] Embodiment 7: This embodiment further limits the method for collaborative control of a space flexible multi-arm robot using stress stiffening effect described in Embodiment 5. There is a pre-loaded internal force f I The stiffness matrix of the kth robot arm in this case is given by f I The direction and size of the system are determined by the system configuration.

[0135] Embodiment 8: This embodiment proposes a spatial flexible multi-arm robot collaborative control system using stress stiffening effect, the system comprising:

[0136] The model building module is used to build the dynamic models of the space multi-arm robot in the open chain and self-closed chain states considering the joint flexibility based on the two topological configurations of the space multi-arm robot.

[0137] The stiffness analysis module is used to introduce the internal force stiffening effect into the dynamic model of the open chain and self-closed chain states described in the model building module, and to determine whether there is internal stress to complete the stiffness analysis of the spatial multi-arm robot considering flexible joints in the self-closed chain configuration;

[0138] A collaborative control module is used to design a composite control law for the space multi-arm robot considering flexible joints described in the stiffness analysis module based on a singular perturbation method. The composite control law includes collaborative control of the stiffness of the space flexible robot system on two time scales, slow and fast, that is, collaborative control of the space flexible multi-arm robot that completes the internal force stiffening effect.

[0139] Embodiment 9. This embodiment proposes a computer device, including a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes the method described in any one of embodiments 1 to 7.

[0140] Embodiment 10: This embodiment proposes a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, the steps of the method described in any one of embodiments 1 to 7 are implemented.

[0141] Implementation 11: This implementation proposes an example, which is used to explain the above-mentioned implementations 1 to 8. The specific example is as follows:

[0142] See also Figures 1 to 19 In this embodiment, the space multi-arm robot capture scene consists of two parts, namely the space multi-arm robot and the target, i.e., the satellite. The target is used to simulate a communication satellite in geosynchronous orbit. The space dual-arm robot uses two seven-degree-of-freedom robotic arms to approach the target spacecraft in an open-chain configuration. Fig.19 (a) shows a self-closing chain configuration formed above the target, and the nozzle of the target spacecraft is docked and fixed by using the docking cone rod, as shown in Fig.19 (b) as shown.

[0143] The space multi-arm robot consists of four parts: a base, a quick locking and releasing device, two 7-DOF robotic arms, and a cone-rod docking device. Figure 2 The base is a cube satellite with a sailboard, which has the ability of attitude change and orbit transfer, and is controlled by the attitude and orbit control system. It is a controlled space flight robot.

[0144] like Figure 3 and Figure 4 As shown, the center of mass coordinate system ∑0 of the space multi-arm robot base is in the inertial coordinate system ∑ I In free flight, the generalized coordinates of the base mass center coordinate system ∑0 can be expressed as Among them, r0∈R 3 represents the position vector of the matrix in the inertial system, It represents the attitude of the base coordinate system relative to the inertial system, expressed by the Euler angle of the zyx rotation order. In general, assuming that the space robot system has N manipulators, the number of degrees of freedom of the kth (k = 1, ..., N) manipulator is n k , that is, with n k The base is represented as the 0th rigid body, and the path direction from the base to the end is defined as the positive direction, and the i-th axis Connected to the i-th link body, represents the joint node connecting link i-1 and link i in arm k, where represents the root joint node of arm k. According to graph theory, node Is the parent node of the i rigid body, node It is the child node of the i rigid body.

[0145] like Figure 3 and Figure 4 As shown, the definition is the coordinate system of the center of mass of rod i located at arm k; represents the center of mass of the i-th rod of arm k; Indicates connection arrive A vector of Indicates connection arrive A vector of Indicates connection arrive A vector of Indicates the connection base centroid to Vector.

[0146] 1. Dynamic modeling of a spatial dual-arm robot with flexible joints in an open-chain state

[0147] use Represents the position vector of the end of the robot k in the inertial system, r0∈R 3 It represents the position vector of the base mass center in the inertial system. Definition use express The antisymmetric matrix of .

[0148] Derived to obtain the projection of the kth robot arm end velocity in the inertial system The conversion relationship between the k joint speed of the robot arm is:

[0149]

[0150] In the formula, Represents the projection of the position and attitude vector of the base body's center of mass in the inertial system. represents the Jacobian matrix of the base at the end of the k-th robot arm. represents the Jacobian matrix of the k-th robotic arm, where represents the Jacobian matrix of the linear velocity at the end of the k-th robotic arm, Represents the Jacobian matrix of the angular velocity at the end of the k-th robotic arm. represents the column vector of the joint velocity of the k-th robot arm, represents the velocity of the i-th joint of robot k.

[0151] The velocity of the floating base in the inertial system The end speed of all robots is combined Expressed in one equation, we can get

[0152]

[0153] Where, the velocity set in the joint space is expressed as The Jacobian matrix of the floating base space robot represents the mapping relationship between the base velocity and joint velocity in the joint space and the base velocity and the end-of-arm velocity in the Cartesian space.

[0154] The dynamic model of the space robot is derived using the Lagrange method. Let L be the Lagrange function. is the generalized force vector corresponding to the non-conservative active force of the system

[53] , T is kinetic energy, V is potential energy, and the generalized coordinates of the system are So the Lagrange function is

[0155] L=TV (3)

[0156] Taking the derivative of formula (3) with respect to time, we can get

[0157]

[0158] The total kinetic energy of the space multi-arm robot system is the sum of the kinetic energy of the base and the kinetic energy of each robotic arm.

[37] :

[0159]

[0160] In the formula, is the generalized inertia matrix, H0∈R 6 × 6 is the inertia matrix of the floating matrix, is the inertia matrix of the robot arm link, is the coupling term of the inertia matrix of the base and the connecting rod.

[0161] The generalized force Q is mainly composed of the external forces / torques on multiple end effectors according to the external forces on the space multi-arm robot system. composition, When the base body is performing attitude and orbit control, the projection of the control force / torque in the inertial system is: It represents the projection of the external force on the end of the k-th robotic arm in the inertial system. Q can be expressed as follows:

[0162]

[0163] This implementation is the flexibility of the robot joints, which is mainly caused by the harmonic reducer and torque sensor.

[27] Assuming that , the flexible joint can be simplified to a linear spring with negligible mass, such as Figure 5 shown.

[0164] Flexible joint dynamics model:

[0165]

[0166] In the formula, Represents the inertia matrix of the motor rotor. Among them, represents the main inertia of the i-th motor rotor of the k-th robot arm, represents the motor angle column vector, represents the generalized torsional stiffness coefficient matrix of the joint, where represents the torsional stiffness coefficient of the i-th joint of the k-th robotic arm, Control torque of the robot joint.

[0167] Furthermore, since the matrix does not contain elastic elements and moves freely in 6-dimensional space, consider adding a 6-dimensional virtual flexible joint with a stiffness of 0 to the matrix. Write the potential energy V in matrix form:

[0168]

[0169] make represents the generalized motor rotation angle of the system, represents the generalized torsional stiffness coefficient of the system. Then equation (8) can be expressed by generalized coordinates express

[0170]

[0171] Substituting equations (5), (9) and (6) into (4), we can obtain the dynamic model of the spatial multi-arm robot with flexible joints:

[0172]

[0173] In the formula, is the inertia force term, is a nonlinear term, is the Coriolis force, For the centrifugal force.

[0174] In order to unify the dimensions of equations (7) and (10), we replace represents the main inertia of the inertial shaft of the generalized motor rotor of the system, represents the system generalized motor control torque, then (7) can be rewritten as

[0175]

[0176] Now, by combining equations (10) and (11), we can obtain the dynamic equation of the spatial multi-arm robot with flexible joints in the open chain state:

[0177]

[0178] In the capture task, we are more concerned about the dynamic characteristics in the operation space, so (12) is rewritten as the dynamic equation in the operation space,

[0179]

[0180] In the formula, represents the system mass matrix in the operating space, represents the Coriolis force and centrifugal force matrix in the operating space, Represents the generalized coordinate column vector composed of the base body posture and each robot end posture in the operation space.

[0181] 2. Dynamic modeling of the self-closed chain state of a spatial multi-arm robot considering flexible joints

[0182] After forming a self-closing chain structure, Figure 1 As shown in (b), it can be regarded as that the i-th robot arm and the j-th robot arm are constrained together on a rigid body, which is called CombinedBody. The motion state of CombinedBody is jointly determined by the ends of the two robot arms. According to Assumption 1, there is no relative velocity between the two constrained objects. represents the projection of the combined body's center of mass velocity in the inertial system, and There are the following relations

[0183]

[0184] In the formula, Represents the set of end velocities of the robot arm in the closed chain state. It represents the conversion matrix of the end velocity of each manipulator and the Combined Body contact point and the Combined Body center of mass velocity in the closed chain state. Usually, T Ce is called the contact matrix. Is a vector The antisymmetric matrix of .

[0185] For each end of the robot connected to the Combined Body, there is a speed constraint, that is, the relative speed is 0. Take the first and second robot arms connected to the Combined Body as an example, they satisfy the following kinematic constraint relationship:

[0186]

[0187] in is the constraint Jacobian matrix between robot arms i and j, where yes The antisymmetric matrix of .

[0188] Introducing the constraints of the base to construct a more complete system constraint equation, equation (15) can be written as

[0189]

[0190] in, represents the generalized constraint matrix of the system, Denotes the Jacobian matrix J G The pseudo-inverse of . Formula (16) represents the velocity constraint relationship of the end of the space robot when the system is in a closed chain state.

[0191] The end of the kth robot arm interacts with the Combined Body at the constraint point It is equivalent to the end contact force in the open chain state, which is (10) The two are mutually acting and reacting. Using the Newton-Euler formula, we can get the Combined Body dynamics equation:

[0192]

[0193] Among them, H CB ∈R 6×6 represents the mass matrix of the Combined Body, C CB ∈R 6 represents the combined body centrifugal force and Coriolis term, f CB ∈R 6 Represents the resultant force applied to the Combined Body, F CBext ∈R 6 Represents the resultant force of the external forces acting on the CombinedBody.

[0194] f CB It is the multiple contact forces applied by multiple arms to the Combined Body when the two arms form a closed chain structure. The control force formed together satisfies

[0195]

[0196] in, express If only one robot is operating, a closed chain state cannot be formed. In the case where the projections of joint torque and force are mapped one by one, the inverse dynamics has a unique solution.

[0197] F ce The other part generates the contact internal force f of the object I ∈R 6N , f I They exist in pairs, with a resultant force of 0, and are used to generate stable internal forces, such as clamping force. Introducing the null space matrix

[39] , F ce Can be f cb and f I express:

[0198]

[0199] in, N(T ce )∈R 6N×6 T ce The null space matrix is ​​represented as follows:

[0200]

[0201] Since the null space matrix N(T ce ) exists, we can I Design and distribute, and f I It will not affect the control effect of the Combined Body in the inertial system.

[0202] Through the QLRD device, the space multi-arm robot can form a self-closed chain configuration, while satisfying the end control force, forming internal force in the link at the same time. This introduces the concept of "stress stiffening", which describes the relationship between the internal force of the structure and the lateral stiffness. Analogous to the strings of a guitar, the tighter the string, that is, the greater the axial tension, the greater the lateral stiffness. This section mainly studies the relationship between the internal force and stiffness in the link of a space multi-arm robot with flexible joints when it forms a self-closed chain state for capture.

[0203] 3. Stiffness analysis of a spatial multi-arm robot with flexible joints in a self-closing chain configuration without internal forces

[0204] When considering the elastic deformation of the joints, the pose x of the Combine Body CB It can be expressed as the generalized motor angle of the kth robot arm and the deformation of the kth generalized joint spring of the robot arm Function:

[0205] x CB =f(Θ k ,εk ) (twenty one)

[0206] Taking the derivative on both sides we get:

[0207]

[0208] Where: Used to describe the posture changes of Combine Body. is the vector formed by the differential of the angle variable of the generalized joint motor of the kth robot arm, is the vector formed by the differential deformation of the joint hinge on the kth robot arm. Since the spring on the base is a virtual hinge, δε0=0 6×1 The kinematic Jacobian matrix of the kth robot arm is Describes the generalized joint motor speed And the deformation speed of the flexible joint spring CombineBody Speed impact.

[0209] Since the deformation of the flexible joint is usually very small (the initial deformation is 0), according to the spring model mentioned above, the relationship between deformation and torque can be expressed as

[0210]

[0211] Where: is the torque column vector of the flexible hinge on the kth robot arm, where is the torque column vector on the i-th flexible hinge on the k-th robot arm, δε k is the deformation of the joint spring.

[0212] The control torque applied by the joint motor (active hinge) is

[0213]

[0214] In the formula, To control the equivalent stiffness.

[0215] When Combine Body is subjected to external force f e When the Combine Body is in action, due to the existence of flexibility, δx is generated at the end of the Combine Body. CB The corresponding joint change is (δΘ,δε). According to the virtual work principle, the virtual work done by the external force is equal to the sum of the virtual work done by the internal force of the mechanism:

[0216]

[0217] Substituting (22) into (25) we obtain

[0218]

[0219] Equation (26) holds true for any virtual displacement, thus the static equilibrium equation can be obtained:

[0220]

[0221] Substituting (23), (24) and (27) into (22), we obtain

[0222]

[0223] Further we get:

[0224] f e =K k δx CB (29) In formula, is the stiffness matrix of the kth manipulator in the state without pre-internal force, which reflects the influence of the elasticity of the kth manipulator under the action of external force on the posture of the terminal Combinebody.

[0225] Consider that all robot branches are connected to the same Combinebody and have the same posture change δx CB The stiffness matrix of the whole system without pre-stress only needs to be K k Add up to get

[0226]

[0227] 4. Stiffness analysis of a spatial multi-arm robot with flexible joints in a self-closing chain configuration with internal forces

[0228] After applying internal force f to the Combine body I Under the premise of , assuming that an external force δf is applied to the Combine body at this time, so that the Combine body undergoes a transformation of δq, satisfying For the pre-loaded internal force f I The system stiffness matrix under the action.

[0229] According to the principle of equivalence between strain energy and work

[40] , define the potential energy function And taking the differentiation of each term in (27) we get:

[0230]

[0231] In the formula, is the Hessian matrix of the potential energy function ζ, where

[0232] Solving equation (31) yields In the formula,

[0233] Substituting (32) into (22), we can obtain

[0234]

[0235] In the formula,

[0236]

[0237] In the formula, For the pre-loaded internal force f I The stiffness matrix of the kth robot arm in the case of is the stiffness coefficient. It can be found that the stiffness matrix under the pre-internal force is Received , and these parameters further depend on f I The direction and magnitude of the system configuration. This proves that the pre-internal force f I Changing the stiffness of a spatial multi-arm robot system considering joint flexibility.

[0238] Consider that all robot branches are connected to the same Combine Body and thus have the same posture change δx CB , the stiffness matrix of the entire system with pre-internal force only needs to be Add up to get

[0239]

[0240] Although the stiffness matrix expression is very complicated, by analyzing (34), it is found that the stiffness With coefficient and Negatively correlated, and and At the same time, it can be found through (31) that when f I When it is orthogonal to the impact displacement δf, the modulus of ζ has a maximum or minimum value. This shows that f I The stiffness of the CombineBody in the orthogonal direction is the most affected, showing two effects: "stress stiffening" and "stress softening", similar to the tension and relaxation of a guitar string. When designing a controller, you can use the CombineBody impact force f e The direction of f is designed and controlled according to (19) IThe size and direction of the impact are improved, thereby increasing the stiffness in the impact direction, thereby improving the control accuracy during the capture process from a dynamic level under the condition of model uncertainty (including the uncertainty of the space dual-arm robot itself and the lack of target inertia parameters).

[0241] Since the dynamic model of the space multi-arm robot with flexible joints is a high-order system, it is difficult to control it directly. The flexible joint model is reduced in order using the singular perturbation method, and the complex high-order system is decomposed into a slow subsystem and a fast subsystem, which describe the large-scale rigid body motion and joint elastic motion respectively. The slow subsystem after reduction is equivalent to the rigid body model, while the fast subsystem is a linear system. Therefore, control algorithms can be designed for these two subsystems to ensure tracking accuracy and quickly suppress the vibration of the flexible arm, which is an effective control solution.

[0242] Flexible joint torque Then (12) can be rewritten as:

[0243]

[0244] According to the singular perturbation theory, the state variable z1 = τ is selected.

[0245] Based on (36), the state space equation is obtained

[0246]

[0247] in, is called the perturbation parameter, which is a standard form of a singular perturbation system. It can be interpreted as a two-time-scale system with state variables x = [x1, x2] T is changing slowly, and the state variable z=[z1,z2] T It changes rapidly, thus dividing the system into two subsystems: fast and slow.

[0248] The kinetic equation of state at a slow time scale is:

[0249]

[0250] (38) is the form of the dynamic state equation of a space robot under rigid conditions.

[0251] Fast time scale t f Next f =(tt s ) / μ, the “boundary layer” system of the slow manifold about z can be defined as In this boundary layer system, by letting μ approach zero, a reduced-order model of the fast system can be obtained.

[0252]

[0253] in,

[0254] According to the derivation of the reduced-order model, the control input can be divided into a fast part and a slow part, and a dual-time-scale composite control law is used to apply it to the rigid dynamics part and the flexible joint dynamics part of the spatial multi-arm robot. The control input τ can be expressed as follows:

[0255]

[0256] Use Slow Control To control the slow system, use fast control To control the fast system, the original fourth-order control problem is decomposed into two second-order problems, which are handled at different time scales.

[0257] 0.3 Slow part control law

[0258] 5. Impedance control in open link state

[0259] definition Then the dynamic equation (13) in the operation space is written as:

[0260]

[0261] Among them, F τ Represents the end operation space force. The joint torque τ generated by the external force ext and the external force F e satisfy

[0262] When a spatial dual-arm robot with flexible joints is performing a capture operation on a target, it is hoped that the robot will be flexible in an unknown contact environment, that is, the robot will have a certain degree of compliance with the working environment to prevent damage to the robot body and the operated object.

[0263] The slow-speed reduced-order model of the spatial dual-arm robot considering flexible joints has the same form as the rigid dynamics model, so the controller developed for rigid manipulator control can be used for the control of the slow-speed state.

[0264] In order to realize the impedance characteristics of the end of the robot arm, the actual end position x∈R 6+6N and the virtual equilibrium point position x d ∈R 6+6N The error between The purpose of impedance control is to achieve position at the end With F e The dynamic relationship between:

[0265]

[0266] where Λ d ∈R (6+6N)×(6+6N) , D d ∈R (6+6N)×(6+6N) and K d ∈R (6+6N)×(6+6N) are the desired inertia, damping and stiffness matrices of the robot end and are symmetric and positive definite.

[0267] Substituting (42) into (41) we obtain:

[0268]

[0269] In order to avoid the external force feedback term in the control input of the closed-loop system, let Λ d =Λ(x), multiply both sides by The joint input torque based on the Cartesian spatial impedance control law is obtained when the slow part of the system is in an open chain state

[0270]

[0271] 4.1.2 Impedance control in closed chain state

[0272] After forming the self-closing chain system, the cone rod device at the end of the CombinedBody is used for docking. Therefore, it is hoped that the CombinedBody will exhibit impedance characteristics. (42) is slightly modified

[0273]

[0274] in represents the position error of the Combined Body, Λ CBd ∈R 6×6 , D CBd ∈R 6×6 and K CBd ∈R 6×6 They are the expected inertia, damping and stiffness matrices of the Combined Body, all of which are symmetric positive definite matrices.

[0275] Substitute (45) into the rigid body dynamics equation (17) of the Combined Body and let Λ CBd =H CB , and the control input force f is obtained CB ∈R 6 Expressed as

[0276]

[0277] f CBThe contact force F of the end of the manipulator in contact with the Combined Body in the space dual-arm robot ce Provided. At the same time, according to the previous research, a certain internal force f is applied I , can improve the stiffness of the end, reduce the displacement caused by the capture impact, and improve the control accuracy. According to formula (19), the expected contact force F of the end of the manipulator on the Combined Body is calculated as ced , based on the action and reaction forces, the combined body's reaction forces on the ends of each robot arm The desired end force F is quickly tracked by the robot controller ed , to achieve impedance control at the end of the Combined Body.

[0278] Based on the dynamic equation of the robot arm, the PI controller of the force is designed, and the control force / torque F of the spatial dual-arm robot is c :

[0279]

[0280] where F error =F ed -F e , K p and K I They are respectively the positive definite gain matrices of the proportional and integral links of the robot force in the closed chain state.

[0281] Multiply both sides of (47) by The joint input torque of the slow part of the system under the end Cartesian impedance control in the closed chain state and the PI control law of the manipulator spatial operation force is obtained.

[0282]

[0283] 0.4 Fast Partial Control Law

[0284] In the previous article, the closed-loop fast dynamics was approximated as a second-order system, and according to the literature

[42] A control law for the fast system is proposed, which controls the bandwidth while keeping the boundary layer system stable and is designed based on the measurable flexible joint data. Therefore, the control input for the fast part of the system is

[0285]

[0286] In the formula, They are the state variables related to the fast subsystem proposed in the previous article. and are the gain coefficients of the fast control law. Since the dynamic equations of the flexible joints of the space multi-arm robot are consistent in both the open chain state and the self-closed chain state, the input of the fast control part is the same. Based on the idea of ​​singular perturbation, the control strategy of the space multi-arm robot with joint flexibility in the open chain and self-closed chain state is considered, such as Figure 7 shown.

[0287] 0.5 Simulation Experiment

[0288] In order to verify the correctness of the "stress stiffening" effect and composite control algorithm of the space multi-arm robot considering flexible joints proposed in this paper, a simulation framework based on Matlab / Simulink was established. The planning and control algorithms of the space dual-arm robot were implemented in Matlab / Simulink, and the dynamic modeling of the robot was implemented in Smiscpae. A simulation experiment of the space dual-arm robot considering flexible joints to capture the unknown dynamic parameter space target was carried out, and the simulation results of four control strategies were compared, namely: (1) operating space impedance control law, represented by "IC" (Impedance Control); (2) composite control law based on singular perturbation, represented by "CC" Compound control, in this state there is no internal force; (3) considering the existence of 300N compressive stress in the x direction of the Combined Body in the closed chain state, that is, f I =[0,0,0,300,0,0] T The composite control law is represented by “CC(CS)” Compressive stress; (4) Considering that there is a 100N tensile stress in the x direction of the Combined Body in the closed chain state, instantaneous f I =[0,0,0,-100,0,0] T The composite control law is represented by “CC(TS)” Tensile stress.

[0289] The spatial dual-arm robot described in this embodiment adopts two seven-degree-of-freedom manipulators of the same configuration, and its improved DH parameters are shown in Table 1. The end effector of Arm_1 is a cone rod docking mechanism, which docks and locks with the nozzle of the target object. The end effector of Arm_2 is the active end of QLRD, which docks and locks with the passive end of QLRD set on the link1_6 body on Arm_1 to form a self-closed chain loop. At this time, link1_6, link1_7, cone rod docking device and passive end of QLRD on Arm_1 together constitute the Combinedbody mentioned above, which is controlled by the joint action of Arm_1 and Arm_2.

[0290] Table 1 Improved DH parameters of the space dual-arm robot

[0291]

[0292] (α i is the connecting rod rotation angle, a i is the connecting rod length, θ i is the joint angle offset, d i is the connecting rod offset)

[0293] The mass inertia parameters of each body in the space dual-arm robot are shown in Table 2. In the dynamic parameters of the flexible joint, the system generalized motor rotor shaft inertia is set System generalized torsion

[0294] Rotational stiffness

[0295] Table 2 Mass and inertia parameters of the space dual-arm robot

[0296]

[0297] Set the initial pose parameters of each body. The default position unit is m, the pose is expressed in Euler angles, the default sequence is "ZYX", and the unit is radians. The initial pose of the center of mass of the base body is In the initial configuration, the end of Arm_1, that is, the end of the cone-rod docking device, is positioned as follows: The end of Arm_2, i.e. the end of the active end of QLRD, is The initial center of mass pose of the target is The initial stage of the base body mass center velocity v0, joint angular velocity ω0, target body mass center velocity v target All are 0.

[0298] Table 3 Control system parameter settings

[0299]

[0300] The whole simulation process is as follows: 1. Open-chain control stage at 0-5s: The space dual-arm robot moves based on the open-chain state control strategy. During this process, the control base is kept stable near the initial posture, and the end of the cone rod of Arm_1 is controlled to move to the top of the nozzle of the target to prepare for docking. At the same time, the active end of the QLRD located at Arm_2 is controlled to move to the top of the passive end of the QLRD located at arm_1 to prepare for docking. The expected trajectory is: the end of Arm_1 is moved from the waypoint [-1.158, 0.108, -1.000, -0.503, 0, pi]] T Move to the waypoint [-1.158,0.108,-1.000,-pi / 2,0,pi] T, the end of Arm_2 is at the waypoint [1.155,-0.108,-0.800,2.639,0,pi] T Move to the waypoint [-1.158,0.108,-1.000,pi / 2,0,pi] T ; 2. Self-closing chain formation stage at 5-10s: Arm_2 and Arm_1 form a self-closing chain system and stabilize through the closing and locking of the QLRD jaws; 3. Self-closing chain docking stage 10-15s: operating force f based on impedance control and zero space CB Calculation and internal force f I The end of the Combinedbody is at the position [-1.158,0.108,-1.000,-pi / 2,0,pi] T Move to the pose [-1.158,0.108,-1.000,-pi / 2,0,pi] T , docking with the target's nozzle and stabilizing; 4. Assembly control phase 15-30s: Under the joint control of Arm_1 and Arm_2, the target is pulled into the vicinity of the base based on the closed-loop state control strategy, and the posture changes from [-1.158, 0.108, -1.000, -pi / 2, 0, pi] T Return to the pose [-1.158,0.108,-1.000,-pi / 2,0,pi] T Simulate the on-orbit operation process. The desired position of the base body always remains at the initial position. The trajectory sequence x is obtained by interpolating each position point with a fifth-order polynomial. e , The expected pose trajectory of Arm_1 and Arm_2 in the open chain stage after interpolation and the expected pose trajectory of Combinedbody in the closed chain stage are as follows: Fig. 9 and Fig.10 The simulation process is shown in Figure 8 shown.

[0301] Fig.11The comparison results of the control errors of the two controllers for the end of Arm_1 and Arm_2 in the open-chain control stage from 0 to 10 seconds are shown. The figure shows that during the period of 0-5 seconds, the two arms are in an independent motion state, but at the 5th second, the error increases temporarily due to the interference caused by the contact and locking of the QLRD. Compared with the controller that only uses impedance control, the controller using the composite control law makes the control error of the end of the robot arm smaller and converges faster. This is because the fast control part of the singular perturbation theory takes into account the motion state of the flexible joint and provides a suppression method, which can effectively reduce the end jitter amplitude and vibration frequency caused by the joint flexibility and improve the control accuracy. At the same time, the slow control part of the composite control law retains the compliant characteristics of the impedance control, so that the error curves of the two robotic arms show a damping attenuation trend.

[0302] Depend on Fig.12 It can be seen that after the closed chain is formed, the Combined Body is acted upon by Arm_1 and Arm_2 and moves along the -z axis along the desired trajectory. The attitude error is expressed using the error quaternion

[43] Description, its imaginary part is the posture error component of each axis. At the 15th second, the Combined Body completes docking with the target and moves in the positive direction of the z axis, pulling the target closer. It can be observed from the figure that after docking, the position error of the Combined Body in the z direction is larger than that in the x and y directions, reaching 0.03m, which is due to the impact interference from the z direction. It can be observed that compared with the case of using the "IC" controller, the end jitter of the Combined Body caused by the docking impact and joint flexibility is smaller when the "CC" control law is used, thereby obtaining higher control accuracy. When considering the existence of internal forces in the self-closed chain structure formed by the two arms, under the same control parameters, when a pressure of 300N "CC(CS)" is applied, the end posture error caused by the docking impact is smaller than that without internal forces, especially in the z direction of the impact. As shown in Figure e, the error is reduced by 0.004m and the z-direction accuracy is improved by 13.33%. This result verifies the aforementioned "stress stiffening" effect, that is, when sufficient pressure is provided in the axial direction, that is, in the x-direction, the stiffness in the lateral direction, that is, in the z-direction, that is, in the impact direction, can be increased. Similarly, under the "CC(TS)" condition, the "stress relaxation" effect is also observed. When a tensile force of 100N is applied, the lateral stiffness is significantly reduced, the control error increases by 0.002m compared to the case without internal force, the stiffness decreases by 6%, and the vibration is obvious. If the value of the internal stress is further increased, the "stress stiffening" or "stress relaxation" effect will appear more obviously, thus proving that it is feasible to use the double arms to form a self-closed chain structure to generate internal force, and to use the direction and magnitude of the internal force to change the stiffness in a certain direction.

[0303] Fig.14The motor torque output of the robot arm when a 300N pressure is applied in the self-closing chain system is shown. It can be observed that the motor output torque is small in the open chain state at 0-10s. After the self-closing chain is formed, the motor output torque increases after 10s due to the need to provide an internal force of 300N. In particular, the Jiont3, Jiont4, and Jiont5 joints bear a greater load of 200Nm. This is also to reflect the concept that the stiffness of the system can be increased when the internal stress is sufficient. Therefore, a larger internal force value is set in the simulation. However, when considering the pressure bearing capacity of the material, the range of the internal force needs to be reasonably designed.

[0304] Fig.15 The change of the position and posture error of the base Base during the entire simulation process is shown. As the support of the two robotic arms, the base will be affected by the reaction force of the robotic arms, and its equivalent stiffness will also change due to the internal force. It can be observed from the figure that in the "CC (CS)" case with a pressure of 300N, compared with other cases, the position and posture errors of the base are smaller when disturbed by the dynamic coupling of the two robotic arms and the target object. In particular, the position error in the z direction is reduced by 0.004m compared to the case without internal force. This shows that the presence of sufficiently large internal forces in the closed chain system can make the structure have higher stiffness, thereby reducing the interference of external disturbances.

[0305] The ground experiment of the space multi-arm robot is set up as shown in the figure. We built a space robot with two 7-DOF manipulators on the experimental platform. Since the research focus of this paper is on the variable topology dynamics and control of the robot, the air floating platform is not used to simulate the microgravity environment. The space robot base is fixed on the experimental platform. The end of the manipulator contains a QLRD device, which allows the robot to switch between open chain and self-closed chain configurations. The manipulator and the QLRD device are driven by servo motors. The industrial controller uses the Ethercat protocol to transmit control instructions to the motor. OptoForce Sensing Systems is also installed at the end of Arm_2 to measure the internal force / torque in the self-closed chain configuration to verify the "stress stiffening" effect. Four Optitrack visual sensors are built around the experimental platform to measure the position of the end of the manipulator.

[0306] In order to verify the effectiveness of the proposed theory and algorithm, the following experimental conditions are designed: Similar to the simulation conditions, from 0 to 255 seconds, the two manipulators first move to the docking state in an open chain configuration. From 255 seconds to 375 seconds, the end-to-end vertical motion with a load of 2.5 kg is performed in the following modes: (1) single manipulator impedance control (IC(Single)) without docking, (2) no internal force coordination (CC(Null)) in a closed chain, and (3) internal force coordination (CC(CS)) in a closed chain, to simulate the docking and transfer motion in the Z direction.

[0307] Fig.19 The spatial distance error curves of the end of the manipulator moving under load under three experimental conditions are shown. There is a fluctuating error between the actual end position and the expected motion position. The rise of the curve is due to the deviation of the load under the action of gravity, which causes the error to accumulate over time. The fluctuation of the curve is due to the flexible vibration caused by the joint and assembly gap. By comparison, it can be found that the error accumulation of the single manipulator is more obvious and the vibration is faster than that of the self-closed chain. Under the self-closed chain configuration, the error accumulation is small, and this phenomenon is more obvious in the case of internal force, reducing the error by about 0.002m. The experimental results show that this method can be used for target capture of space multi-arm robots. Accuracy. The composite control law based on singular perturbation divides the robot into slow and fast subsystems for control, while considering the flexibility of capture and the equivalent stiffness of flexible joints. The effectiveness and correctness of the proposed method are verified by simulation and experiment. The results show that compared with the simple impedance control law, the composite control law based on singular perturbation can effectively reduce the jitter caused by joint flexibility at the end of the manipulator and reduce the control error. In the closed chain state, the rigidity of the system can be increased and the control error caused by the impact during capture can be reduced by applying internal stress reasonably.

[0308] Those skilled in the art will appreciate that the above are only preferred embodiments of the present invention, and the various embodiments of the present disclosure and / or the features described in the claims may be combined or combined in various ways, even if such combinations or combinations are not explicitly described in the present disclosure. It is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art may still modify the technical solutions described in the aforementioned embodiments, or perform equivalent substitutions on some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention shall be included in the protection scope of the present invention.

[0309] Although preferred embodiments of the present invention have been described, additional changes and modifications may be made to these embodiments by those skilled in the art once the basic inventive concepts are known. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention. Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A collaborative control method for a space flexible multi-arm robot using stress stiffening effect, characterized in that: The space flexible multi-arm robot collaborative control method comprises the following steps: S1. Based on the two topological configurations of the space flexible multi-arm robot, the dynamic models of the space multi-arm robot in the open chain and self-closed chain states considering the joint flexibility are established respectively; S2. Introduce the internal force stiffening effect in the dynamic model of the open chain and self-closed chain states described in S1, and determine whether there is internal stress to complete the stiffness analysis of the spatial multi-arm robot considering flexible joints in the self-closed chain configuration; S3. Based on the singular perturbation method, a composite control law is designed for the space multi-arm robot considering flexible joints as described in S2. The composite control law includes collaborative control of the stiffness of the space flexible robot system on both slow and fast time scales, i.e., collaborative control of the space flexible multi-arm robot that achieves the internal force stiffening effect.

2. The method for collaborative control of a space flexible multi-arm robot using stress stiffening effect according to claim 1, characterized in that: In S2, the stiffness analysis method of the spatial multi-arm robot considering flexible joints in a closed chain configuration when there is no internal stress is realized by determining the stiffness matrix of the kth robotic arm in the state without pre-internal force.

3. The method for collaborative control of a space flexible multi-arm robot using stress stiffening effect according to claim 2, characterized in that: The method for determining the stiffness matrix of the kth manipulator in the state without pre-internal force specifically includes: When considering the elastic deformation of the flexible joint, the pose x based on the Combine Body CB Expressed as the generalized motor angle of the kth robot arm and the deformation of the kth generalized joint spring of the robot arm Function: x CB =f(Θ k ,he k ) (21) Taking the derivative on both sides we get: In the formula, Used to describe the posture changes of Combine Body. is the vector formed by the differential of the angle variable of the generalized joint motor of the kth robot arm, is the vector formed by the differential deformation of the joint hinge on the kth robot arm, δε0=0 6×1 , the kinematic Jacobian matrix of the k-th robot arm is Respectively represented as the generalized joint motor speed And the deformation speed of the flexible joint spring Combine Body Speed The impact of Where: is the torque column vector of the flexible hinge on the kth robot arm, where is the torque column vector on the i-th flexible hinge on the k-th robot arm, δε k is the deformation of the joint spring; The control torque applied by the joint motor is In the formula, To control the equivalent stiffness; When Combine Body is subjected to external force f e When it works, δx is generated at the end of Combine Body CB The corresponding joint change is (δΘ, δε), and the virtual work done by the external force is equal to the sum of the virtual work done by the internal force of the mechanism: Substituting (22) into (25) we obtain Equation (26) holds true for any virtual displacement, thus the static equilibrium equation can be obtained: Substituting (23), (24) and (27) into (22), we obtain Further we get: f e =K k δx CB (29) In the formula, is the stiffness matrix of the kth robot arm without pre-internal force.

4. The method for collaborative control of a space flexible multi-arm robot using stress stiffening effect according to claim 3 is characterized in that: The Combine Body dynamics equation is obtained using the Newton-Euler formula.

5. The method for collaborative control of a space flexible multi-arm robot using stress stiffening effect according to claim 1, characterized in that: The stiffness analysis method of the spatial multi-arm robot considering flexible joints in the self-closed chain configuration when there is internal force in S2 is determined by determining the pre-internal force f I The system stiffness matrix under action accomplish.

6. The method for collaborative control of a space flexible multi-arm robot using stress stiffening effect according to claim 5, characterized in that: By determining the pre-internal force f I The system stiffness matrix under action The specific implementation method is: Define the potential energy function And taking the differentiation of each term in (27) we get: In the formula, is the Hessian matrix of the potential energy function ζ, where Solving equation (31) yields In the formula, Substituting (32) into (22), we can obtain In the formula, In the formula, For the pre-loaded internal force f I The stiffness matrix of the kth robot arm in the case of is the stiffness coefficient.

7. The method for collaborative control of a space flexible multi-arm robot using stress stiffening effect according to claim 5, characterized in that: Said There is a pre-loaded internal force f I The stiffness matrix of the kth robot arm in this case is given by f I The direction and size of the system are determined by the system configuration.

8. A space flexible multi-arm robot collaborative control system utilizing stress stiffening effect, characterized in that: The system comprises: The model building module is used to build the dynamic models of the space multi-arm robot in the open chain and self-closed chain states considering the joint flexibility based on the two topological configurations of the space multi-arm robot. The stiffness analysis module is used to introduce the internal force stiffening effect into the dynamic model of the open chain and self-closed chain states described in the model building module, and to determine whether there is internal stress to complete the stiffness analysis of the spatial multi-arm robot considering flexible joints in the self-closed chain configuration; A collaborative control module is used to design a composite control law for the space multi-arm robot considering flexible joints described in the stiffness analysis module based on a singular perturbation method. The composite control law includes collaborative control of the stiffness of the space flexible robot system on two time scales, slow and fast, that is, collaborative control of the space flexible multi-arm robot that completes the internal force stiffening effect.

9. A computer device comprising a memory and a processor, characterized in that A computer program is stored in the memory. When the processor runs the computer program stored in the memory, the processor executes the method according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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