Layered passive whole-body compliance control method for multi-branch spacecraft

Abstract

The invention provides a layered passive whole-body compliant control method for a multi-branch spacecraft. The method is a spacecraft whole-body control method combining a cooperative control theory, a layered control theory, a passive control theory and an impedance control theory. The system has the advantages that multi-stage compatible control of end effector compliant contact and whole body configuration maintenance can be achieved, a self-adaptive variable impedance control strategy is introduced into an end compliant control layer, the problem of safe compliant contact with a target is solved, meanwhile, a system passive compensation controller based on an energy tank is embedded into each control layer, and the system passive compensation control is more stable. And the safety and stability of the system operation process can be ensured.

Description

Technical Field

[0001] The present invention belongs to the technical fields of on-orbit service, spacecraft control and whole-body control, and in particular relates to a multi-branch spacecraft layered passive whole-body compliant control method. Background Art

[0002] In recent years, the on-orbit construction and maintenance tasks of large space facilities such as large space stations and space solar power stations have received widespread attention. In order to meet their autonomous construction and maintenance needs, various types of control spacecraft and space robots have been developed. Compared with traditional fixed-base manipulators and single-arm and double-arm spacecraft, multi-branch spacecraft systems can complete various types of space manipulations independently with a single arm or in coordination with multiple arms, and can move flexibly on the surface of large space facilities. They are the main tools and carriers for the construction and maintenance of large space facilities in the future. In the process of operating on the surface of large facilities, multi-branch spacecraft not only need to control the force / position of the end effector of the manipulator, but also need to take into account the overall configuration maintenance control of the spacecraft, facing the challenge of multi-level coordinated control, and the traditional control method that only focuses on the end posture is difficult to achieve coordinated and compliant control of the whole body of the multi-branch spacecraft. Therefore, the present invention proposes a multi-branch spacecraft layered passive whole body compliant control method that can achieve multi-arm coordination and is compatible with end compliant control and overall configuration maintenance.

[0003] For terminal compliance control, the traditional fixed parameter impedance control method is difficult to cope with the uncertainty of target position and stiffness, while the impedance control method based on reinforcement learning has better performance, but the computation is large and requires a large amount of relevant training data. Considering the actual needs of on-orbit control, the adaptive variable impedance compliance control strategy with small computational complexity and easy to embed into the hierarchical control framework is a method with good application prospects.

[0004] In addition, both stiffness changes and the zero space projection operator of hierarchical control may produce active behaviors, leading to system instability. To address this problem, the present invention introduces a system passive recovery method based on an energy tank to ensure the safe and stable operation of multi-branch spacecraft during on-orbit control. Summary of the invention

[0005] The purpose of the present invention is to solve the problems in the prior art and propose a layered passive whole-body compliance control method for multi-branch spacecraft. A layered passive whole-body compliance control method is designed for the task requirements of multi-branch spacecraft on the surface of the space station. This method is a whole-body control method for spacecraft that combines collaborative control theory, layered control theory, passive control theory and impedance control theory. Its advantage is that it can realize multi-level compatible control of end-effector compliant contact and whole-body configuration maintenance, and introduces an adaptive variable impedance control strategy in the terminal compliance control layer to solve the problem of safe compliant contact with the target. At the same time, a system passive compensation controller based on an energy tank is embedded in each control level to ensure the safety and stability of the system operation process.

[0006] The present invention is implemented by the following technical scheme. The present invention proposes a multi-branch spacecraft layered passive whole-body compliance control method, which includes the following steps:

[0007] Step 1: Establish the coupled dynamics model of the multi-branch spacecraft and the space station as a whole;

[0008] Step 2: Using the master-slave multi-arm collaborative strategy, the expected position and posture of the master operating arm are generated according to the target position and posture, and then the expected position and posture of the slave arm are obtained according to the relative position and posture relationship between the master and slave arms;

[0009] Step 3: According to the priority of multiple control objectives, the terminal 6-DOF compliant control is set as the main control target, and the joint compliant configuration maintenance control is set as the secondary control target. A hierarchical coordination control framework based on the null space projection method is designed, and the null space matrix is ​​weighted by the system inertia to ensure that the transient kinetic energy is minimized during the robot manipulation process; the control laws of each level are designed using the PD-like classic impedance control form to obtain a basic hierarchical control system;

[0010] Step 4: Combine the coupling relationship of each level in the nonlinear term and eliminate the coupling part through the passive feedback control strategy to avoid the mutual influence of each level control;

[0011] Step 5: Modify the fixed stiffness gain of the main control level, introduce an adaptive variable impedance adjustment strategy, and adjust the stiffness gain in real time according to the position tracking error and force tracking error;

[0012] Step 6: Design a system passivity compensation subsystem based on an energy tank at each control level to compensate for the active behavior caused by the zero space projection operator and stiffness change, restore the passivity of the system, and obtain the compensated task space control instructions;

[0013] Step 7: Map the task space control instructions generated by each level of control subsystem into the joint space through the inertia weighted pseudo-inverse of the Jacobian matrix corresponding to each level to generate joint torque control instructions.

[0014] Furthermore, in step 1, for the control task of a multi-branch spacecraft with four 7-joint robotic arms anchored on the space station with one arm and three arms cooperating to grab the target, the coupling dynamics model of the multi-branch spacecraft and the space station is first established:

[0015]

[0016] in, represents the coupling inertia matrix between the multi-branch spacecraft and the space station; C = [C b C m ] represents the nonlinear term matrix; T is the space station control force and torque; τ is the manipulator joint control torque; F ext represents the external disturbance force and torque; x b represents the center of mass position and attitude of the space station; θ q Represents the joint angle.

[0017] Furthermore, the relative position and posture derivation process of the two slave operating arms and the master operating arm in step 2 is:

[0018] Step 1: The geometric relationship when the three manipulators work together to grasp the target can be obtained by expressing the motion closed chain constraint of the three arms as follows:

[0019]

[0020] Where i = [1, 2, 3] represents the labels of the three robotic arms; is the rotation matrix of the i-th terminal coordinate system relative to the target center of mass coordinate system; is the posture transformation matrix of the target relative to the i-th end effector; ρ i is the equivalent virtual rod from the end effector to the target center of mass; It is the position and posture of the target; is the position and attitude of the ith terminal in the spacecraft base coordinate system;

[0021] Step 2: Express the end position and attitude of the main manipulator arm in the space station body coordinate system, and obtain the expected position and attitude of the main arm:

[0022]

[0023] Step 3: Difference between the end positions and postures of the two slave arms and the master arm is used to derive their relative positions and postures:

[0024]

[0025] in, is the relative position and posture between the end of the i-th slave arm and the master arm.

[0026] Furthermore, the design process of the hierarchical control framework based on null space projection in step 3 is:

[0027] Step 1: For a hierarchical control task with h levels, the forward kinematics is expressed as:

[0028]

[0029] Among them, J i represents the Jacobian matrix of the i-th level; is the joint angular velocity i∈[1,2];

[0030] Step 2: Establish the mission space dynamics from the joint space dynamics of the multi-branch spacecraft:

[0031]

[0032] in A represents the joint torque caused by the external force and moment acting on the end effector; e represents the hierarchical task inertia matrix; C e is the nonlinear term of the hierarchical task; is the speed of the hierarchical task space; represents the extended Jacobian matrix, where

[0033] Step 3: Design the inertia-weighted null space projection operator as:

[0034]

[0035] Among them, U i-1 Represents the Jacobian matrix J of the previous control task i-1 The null space matrix of H is obtained by matrix singular value decomposition; m is the inertia matrix of the multi-branch spacecraft;

[0036] Step 4: Design the control laws for each level as follows:

[0037]

[0038] in, represents the error between the actual value and the expected value of the task space state at the i-th level; K i =K c_i +K v_i (t) represents the stiffness gain, which consists of a fixed gain and a time-varying gain; Di represents the damping gain; F i It is the control instruction of task space at each level.

[0039] Furthermore, the derivation process of the passive feedback control law for coupling elimination described in step 4 is described as follows:

[0040] Step 1: Substitute the nonlinear term C in formula (6) e Expands to:

[0041]

[0042] Among them, c 11 and c 22 The diagonal block matrices representing the primary control task and the secondary control task, respectively; c 21 =-c 12 A coupled block matrix representing two levels of nonlinear terms;

[0043] Step 2: Design the passive feedback control law of the nonlinear coupling part as follows:

[0044]

[0045] Among them, τ dc is the joint torque control instruction with the coupling term eliminating feedback.

[0046] Furthermore, the adaptive variable impedance control law described in step 5 is designed as follows:

[0047]

[0048] Among them, ε(t) is the adaptive adjustment coefficient with the initial value set to 0; represents the redesigned variable stiffness gain; η is the update rate; T is the sampling period of the controller; f d_i and f et_i They represent the expected contact force and actual contact force of the end effector respectively; and according to the Routh stability criterion, the value range of η is Only when the actual contact force converges to the expected value can it be guaranteed.

[0049] Furthermore, the design process of the passive compensation subsystem based on the energy tank described in step 6 is as follows:

[0050] Step 1: Rewrite formula (5) to get:

[0051]

[0052] Define an energy tank system as follows:

[0053]

[0054] Among them, ψ t is the system state of the energy tank; γ t_i and δ t_i Respectively represent the input and output of the energy tank, the specific form is:

[0055]

[0056] λ i Indicates the energy replenishment coefficient of the energy tank system. When the energy in the energy tank is greater than or equal to the specified upper limit, the coefficient is set to 0; otherwise, it is set to a fixed value in the range of 0 to 1, and its value determines the speed of charging; x i represents the state of redefinition of the i-th level control task; x i It indicates the state of redefinition of the i-th level control task, which can be expressed as:

[0057]

[0058] and, represents the tracking error of the level i control task; the energy stored in the energy tank is defined as

[0059] Step 2: Design the following energy tank compensation subsystem:

[0060]

[0061] Among them, α i It is the control switch between the energy tank and each level controller. When the energy in the energy tank is greater than the preset lower limit and the system also generates active behavior, set α i =1, which means the energy tank compensates the system; otherwise, set α i =0, indicating that the energy tank is disconnected from all levels of controllers;

[0062] Step 3: Get the compensated mission space system control instructions:

[0063]

[0064] Furthermore, the joint torque control law described in step 7 is designed as follows:

[0065]

[0066] The present invention has the following beneficial effects:

[0067] The present invention is compatible with the multi-level control tasks of the on-orbit control process of multi-branch spacecraft, and can realize the coordinated control of the end-effector compliant contact and the overall configuration maintenance, effectively improving the compliance of the end-effector of the operating arm in the process of contacting the target, and ensuring the stability of the multi-branch spacecraft during operation. Compared with the traditional method that only focuses on the compliant control of the end contact, the present invention can achieve the compliant control of the end-effector while maintaining the overall configuration of the spacecraft, and can avoid the collision of the arm with the environment / target to a certain extent, and will play an important role in on-orbit service fields such as extravehicular inspection and maintenance of space stations and on-orbit construction of large space facilities. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 It is a schematic diagram of the coordinated operation of three arms anchoring a single arm of the multi-branch spacecraft according to the present invention.

[0069] Figure 2 It is a schematic diagram of an equivalent model of on-orbit control of a multi-branch spacecraft according to the present invention.

[0070] Figure 3 It is a block diagram of the multi-branch spacecraft layered passive whole-body compliant control system described in the present invention.

[0071] Figure 4 Schematic diagram of the configuration changes of multi-branch spacecraft during the collaborative capture of space targets, including: a) the configuration of the multi-branch spacecraft at t = 0s, b) the configuration of the multi-branch spacecraft at t = 10s, c) the configuration of the multi-branch spacecraft at t = 20s, and d) the configuration of the multi-branch spacecraft at t = 300s.

[0072] Figure 5 It is a schematic diagram of the terminal motion trajectory during the collaborative capture of space targets by multiple-branch spacecraft. DETAILED DESCRIPTION

[0073] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0074] See also Figure 1-Figure 5 The present invention proposes a multi-branch spacecraft layered passive whole-body compliance control method, the method comprising the following steps:

[0075] Step 1: Establish the coupled dynamics model of the multi-branch spacecraft and the space station as a whole;

[0076] Step 2: Using the master-slave multi-arm collaborative strategy, the expected position and posture of the master operating arm are generated according to the target position and posture, and then the expected position and posture of the slave arm are obtained according to the relative position and posture relationship between the master and slave arms;

[0077] Step 3: According to the priority of multiple control objectives, the terminal 6-DOF compliant control is set as the main control target, and the joint compliant configuration maintenance control is set as the secondary control target. A hierarchical coordination control framework based on the null space projection method is designed, and the null space matrix is ​​weighted by the system inertia to ensure that the transient kinetic energy is minimized during the robot manipulation process; the control laws of each level are designed using the PD (proportional-differential)-like classical impedance control form to obtain a basic hierarchical control system;

[0078] Step 4: Combine the coupling relationship of each level in the nonlinear term and eliminate the coupling part through the passive feedback control strategy to avoid the mutual influence of each level control;

[0079] Step 5: Modify the fixed stiffness gain of the main control level, introduce an adaptive variable impedance adjustment strategy, and adjust the stiffness gain in real time according to the position tracking error and force tracking error;

[0080] Step 6: Design a system passivity compensation subsystem based on an energy tank at each control level to compensate for the active behavior caused by the zero space projection operator and stiffness change, restore the passivity of the system, and obtain the compensated task space control instructions;

[0081] Step 7: Map the task space control instructions generated by each level of control subsystem into the joint space through the inertia weighted pseudo-inverse of the Jacobian matrix corresponding to each level to generate joint torque control instructions.

[0082] In step 1, for the multi-branch spacecraft with four 7-joint robotic arms, one arm is anchored on the space station, and the three arms cooperate to grasp the target. First, the coupling dynamics model of the multi-branch spacecraft and the space station is established:

[0083]

[0084] in, represents the coupling inertia matrix between the multi-branch spacecraft and the space station; C = [C b C m ] represents the nonlinear term matrix; T is the space station control force and torque; τ is the manipulator joint control torque; F ext represents the external disturbance force and torque; x b represents the center of mass position and attitude of the space station; θ q Represents the joint angle.

[0085] The relative position and posture derivation process of the two slave operating arms and the master operating arm in step 2 is:

[0086] Step 1: The geometric relationship when the three manipulators work together to grasp the target can be obtained by expressing the motion closed chain constraint of the three arms as follows:

[0087]

[0088] Where i = [1, 2, 3] represents the labels of the three robotic arms; is the rotation matrix of the i-th terminal coordinate system relative to the target center of mass coordinate system; is the posture transformation matrix of the target relative to the i-th end effector; ρ i is the equivalent virtual rod from the end effector to the target center of mass; It is the position and posture of the target; is the position and attitude of the ith terminal in the spacecraft base coordinate system;

[0089] Step 2: Express the end position and attitude of the main manipulator arm in the space station body coordinate system, and obtain the expected position and attitude of the main arm:

[0090]

[0091] Step 3: Difference between the end positions and postures of the two slave arms and the master arm is used to derive their relative positions and postures:

[0092]

[0093] in, is the relative position and posture between the end of the i-th slave arm and the master arm.

[0094] The design process of the hierarchical control framework based on null space projection in step 3 is:

[0095] Step 1: For a hierarchical control task with h levels, h=2 in the present invention, the forward kinematics is expressed as:

[0096]

[0097] Among them, J i represents the Jacobian matrix of the i-th level; is the joint angular velocity i∈[1,2];

[0098] Step 2: Establish the mission space dynamics from the joint space dynamics of the multi-branch spacecraft:

[0099]

[0100] in A represents the joint torque caused by the external force and moment acting on the end effector; erepresents the hierarchical task inertia matrix; C e is the nonlinear term of the hierarchical task; is the speed of the hierarchical task space; represents the extended Jacobian matrix, where

[0101] Step 3: Design the inertia-weighted null space projection operator as:

[0102]

[0103] Among them, U i-1 Represents the Jacobian matrix J of the previous control task i-1 The null space matrix of H is obtained by matrix singular value decomposition; m is the inertia matrix of the multi-branch spacecraft;

[0104] Step 4: Design the control laws for each level as follows:

[0105]

[0106] in, represents the error between the actual value and the expected value of the task space state at the i-th level; K i =K c_i +K v_i (t) represents the stiffness gain, which consists of a fixed gain and a time-varying gain; D i represents the damping gain; F i It is the control instruction of the task space at each level. The time-varying part is designed at the main control level of the terminal compliant contact to realize adaptive variable impedance control, and the time-varying part is set to zero at the secondary control level of configuration maintenance.

[0107] The derivation process of the passive feedback control law for coupling elimination described in step 4 is described as follows:

[0108] Step 1: Substitute the nonlinear term C in formula (6) e Expands to:

[0109]

[0110] Among them, c 11 and c 22 The diagonal block matrices representing the primary control task and the secondary control task, respectively; c 21 =-c 12 A coupled block matrix representing two levels of nonlinear terms;

[0111] Step 2: Design the passive feedback control law of the nonlinear coupling part as follows:

[0112]

[0113] Among them, τ dc is the joint torque control instruction with the coupling term eliminating feedback.

[0114] The adaptive variable impedance control law described in step 5 is designed as:

[0115]

[0116] Among them, ε(t) is the adaptive adjustment coefficient with the initial value set to 0; represents the redesigned variable stiffness gain; η is the update rate; T is the sampling period of the controller; f d_i and f et_i They represent the expected contact force and actual contact force of the end effector respectively; and according to the Routh stability criterion, the value range of η is Only when the actual contact force converges to the expected value can it be guaranteed.

[0117] The design process of the passive compensation subsystem for the energy tank-based system described in step 6 is as follows:

[0118] Step 1: Rewrite formula (5) to get:

[0119]

[0120] Define an energy tank system as follows:

[0121]

[0122] Among them, ψ t is the system state of the energy tank; γ t_i and δ t_i Respectively represent the input and output of the energy tank, the specific form is:

[0123]

[0124] λ i Indicates the energy replenishment coefficient of the energy tank system. When the energy in the energy tank is greater than or equal to the specified upper limit, the coefficient is set to 0; otherwise, it is set to a fixed value in the range of 0 to 1, and its value determines the speed of charging; x i represents the state of redefinition of the i-th level control task; x i It indicates the state of redefinition of the i-th level control task, which can be expressed as:

[0125]

[0126] and, represents the tracking error of the level i control task; the energy stored in the energy tank is defined as

[0127] Step 2: Design the following energy tank compensation subsystem:

[0128]

[0129] Among them, α i It is the control switch between the energy tank and each level controller. When the energy in the energy tank is greater than the preset lower limit and the system also generates active behavior, set α i =1, which means the energy tank compensates the system; otherwise, set α i =0, indicating that the energy tank is disconnected from all levels of controllers;

[0130] Step 3: Get the compensated mission space system control instructions:

[0131]

[0132] The joint torque control law described in step 7 is designed as follows:

[0133]

[0134] Example

[0135] The present invention proposes a multi-branch spacecraft layered passive full-body compliant control method, such as Figure 3 As shown, the method comprises the following steps:

[0136] Step 1: Derive the overall coupling dynamics model of the multi-branch spacecraft and the space station based on their connection relationship:

[0137]

[0138] Step 2: Using the master-slave multi-arm collaborative strategy, the expected position and posture of the master operating arm are generated according to the target position and posture, and then the expected position and posture of the slave arm are obtained according to the relative position and posture relationship between the master and slave arms:

[0139]

[0140] Step 3: According to the priority of multiple control objectives, the terminal 6-DOF compliant control is set as the main control target, and the joint compliant configuration maintenance control is set as the secondary control target. A hierarchical coordination control framework based on the null space projection method is designed, and the null space matrix is ​​weighted by the system inertia to ensure that the transient kinetic energy is minimized during the robot manipulation process. The control laws of each level are designed using the PD (proportional-differential)-like classical impedance control form to obtain a basic hierarchical control system;

[0141] Step 4: Combined with the coupling relationship of each level in the nonlinear term, a passive feedback control strategy is used to eliminate the coupling part to avoid mutual influence of each level control. The obtained coupling term elimination passive feedback control instruction is:

[0142]

[0143] Step 5: Modify the fixed stiffness gain of the main control level and introduce an adaptive variable impedance adjustment strategy to adjust the stiffness gain in real time according to the position tracking error and force tracking error. The gain adjustment strategy is:

[0144]

[0145] Step 6: Design a system passivity compensation subsystem based on the energy tank at each control level to compensate for the active behavior caused by the zero space projection operator and stiffness change, restore the passivity of the system, and obtain the compensated task space system control instructions:

[0146]

[0147] Step 7: Map the task space control instructions generated by each level of control subsystem to the joint space through the inertia weighted pseudo-inverse of the Jacobian matrix corresponding to each level to generate joint torque control instructions:

[0148]

[0149] Aiming at the requirements of multi-branch spacecraft maneuvering tasks on the surface of the space station, the present invention designs a hierarchical passive whole-body compliance control method. In view of the problem that the existing control methods focus on the design of the terminal compliance control system and ignore the need to maintain the control of its own configuration, a hierarchical passive impedance control architecture based on zero space projection is developed, and an adaptive variable impedance control strategy is introduced in the terminal compliance control layer to solve the problem of safe and compliant contact with the target. At the same time, a system passive compensation controller based on an energy tank is embedded in each control level to ensure the safety and stability of the system operation process.

[0150] Although the present invention has been disclosed as above in the preferred embodiment, it is not intended to limit the present invention. Anyone familiar with this technology can make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, the scope of protection of the present invention should be based on the definition of the claims.

Claims

1. A multi-branch spacecraft layered passive whole-body compliant control method, characterized in that: The method comprises the following steps: Step 1: Establish the coupled dynamics model of the multi-branch spacecraft and the space station as a whole; Step 2: Using the master-slave multi-arm collaborative strategy, the expected position and posture of the master operating arm are generated according to the target position and posture, and then the expected position and posture of the slave arm are obtained according to the relative position and posture relationship between the master and slave arms; Step 3: According to the priority of multiple control objectives, the terminal 6-DOF compliant control is set as the main control target, and the joint compliant configuration maintenance control is set as the secondary control target. A hierarchical coordination control framework based on the null space projection method is designed, and the null space matrix is ​​weighted by the system inertia to ensure that the transient kinetic energy is minimized during the robot manipulation process; the control laws of each level are designed using the PD-like classic impedance control form to obtain a basic hierarchical control system; Step 4: Combine the coupling relationship of each level in the nonlinear term and eliminate the coupling part through the passive feedback control strategy to avoid the mutual influence of each level control; Step 5: Modify the fixed stiffness gain of the main control level, introduce an adaptive variable impedance adjustment strategy, and adjust the stiffness gain in real time according to the position tracking error and force tracking error; Step 6: Design a system passivity compensation subsystem based on an energy tank at each control level to compensate for the active behavior caused by the zero space projection operator and stiffness change, restore the passivity of the system, and obtain the compensated task space control instructions; Step 7: Map the task space control instructions generated by each level of control subsystem into the joint space through the inertia weighted pseudo-inverse of the Jacobian matrix corresponding to each level to generate joint torque control instructions.

2. The method according to claim 1, characterized in that: In step 1, for the multi-branch spacecraft with four 7-joint robotic arms, one arm is anchored on the space station, and the three arms cooperate to grasp the target. First, the coupling dynamics model of the multi-branch spacecraft and the space station is established: in, represents the coupling inertia matrix between the multi-branch spacecraft and the space station; C = [C b C m ] represents the nonlinear term matrix; T is the space station control force and torque; τ is the manipulator joint control torque; F ext represents the external disturbance force and torque; x b represents the center of mass position and attitude of the space station; θ q Represents the joint angle.

3. The method according to claim 2, characterized in that: The relative position and posture derivation process of the two slave operating arms and the master operating arm in step 2 is: Step 1: The geometric relationship when the three manipulators work together to grasp the target can be obtained by expressing the motion closed chain constraint of the three arms as follows: Where i = [1, 2, 3] represents the labels of the three robotic arms; is the rotation matrix of the i-th terminal coordinate system relative to the target center of mass coordinate system; is the posture transformation matrix of the target relative to the i-th end effector; ρ i is the equivalent virtual rod from the end effector to the target center of mass; It is the position and posture of the target; is the position and attitude of the ith terminal in the spacecraft base coordinate system; Step 2: Express the end position and attitude of the main manipulator arm in the space station body coordinate system, and obtain the expected position and attitude of the main arm: Step 3: Difference between the end positions and postures of the two slave arms and the master arm is used to derive their relative positions and postures:

4. The method according to claim 3, characterized in that: The design process of the hierarchical control framework based on null space projection in step 3 is: Step 1: For a hierarchical control task with h levels, the forward kinematics is expressed as: Among them, J i represents the Jacobian matrix of the i-th level; is the joint angular velocity i∈[1,2]; Step 2: Establish the mission space dynamics from the joint space dynamics of the multi-branch spacecraft: in A represents the joint torque caused by the external force and moment acting on the end effector; e represents the hierarchical task inertia matrix; C e is the nonlinear term of the hierarchical task; is the speed of the hierarchical task space; represents the extended Jacobian matrix, where P1 = J1, Step 3: Design the inertia-weighted null space projection operator as: Among them, U i-1 Represents the Jacobian matrix J of the previous control task i-1 The null space matrix of H is obtained by matrix singular value decomposition; m is the inertia matrix of the multi-branch spacecraft; Step 4: Design the control laws for each level as follows: in, represents the error between the actual value and the expected value of the task space state at the i-th level; K i =K c_i +K v_i (t) represents the stiffness gain, which consists of a fixed gain and a time-varying gain; D i represents the damping gain; F i It is the control instruction of task space at each level.

5. The method according to claim 4, characterized in that: The derivation process of the passive feedback control law for coupling elimination described in step 4 is described as follows: The first step: Substitute the nonlinear term C in formula (6) e Expands to: Among them, c 11 and c 22 The diagonal block matrices representing the primary control task and the secondary control task, respectively; c 21 =-c 12 A coupled block matrix representing two levels of nonlinear terms; Step 2: Design the passive feedback control law of the nonlinear coupling part as follows: Among them, τ dc is the joint torque control instruction with the coupling term eliminating feedback.

6. The method according to claim 5, characterized in that: The adaptive variable impedance control law described in step 5 is designed as: Among them, ε(t) is the adaptive adjustment coefficient with the initial value set to 0; represents the redesigned variable stiffness gain; η is the update rate; T is the sampling period of the controller; f d_i and f et_i They represent the expected contact force and actual contact force of the end effector respectively; and according to the Routh stability criterion, the value range of η is Only when the actual contact force converges to the expected value can it be guaranteed.

7. The method according to claim 6, characterized in that: The design process of the passive compensation subsystem for the energy tank-based system described in step 6 is as follows: Step 1: Rewrite formula (5) to get: Define an energy tank system as follows: Among them, ψ t is the system state of the energy tank; γ t_i and δ t_i Respectively represent the input and output of the energy tank, the specific form is: λ i Indicates the energy replenishment coefficient of the energy tank system. When the energy in the energy tank is greater than or equal to the specified upper limit, the coefficient is set to 0; otherwise, it is set to a fixed value in the range of 0 to 1, and its value determines the speed of charging; x i represents the state of redefinition of the i-th level control task; x i It indicates the state of redefinition of the i-th level control task, which can be expressed as: and, represents the tracking error of the level i control task; the energy stored in the energy tank is defined as Step 2: Design the following energy tank compensation subsystem: Among them, α i It is the control switch between the energy tank and each level controller. When the energy in the energy tank is greater than the preset lower limit and the system also generates active behavior, set α i =1, which means the energy tank compensates the system; otherwise, set α i =0, indicating that the energy tank is disconnected from all levels of controllers; Step 3: Get the compensated mission space system control instructions:

8. The method according to claim 7, characterized in that: The joint torque control law described in step 7 is designed as follows:

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