A multi-branch spacecraft layered passive whole-body compliance control method

Abstract

The application provides a multi-branch spacecraft layered passive whole-body compliant control method, which 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 method has the advantages that multi-stage compatible control of end effector compliant contact and whole-body configuration maintenance can be realized, an adaptive variable impedance control strategy is introduced in the end compliant control layer, the safe compliant contact with a target is solved, and a system passivity compensation controller based on an energy tank is embedded in each control layer, so that the safety and stability of the system during operation can be ensured.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of on-orbit service, spacecraft control and whole-body control, and particularly relates to a multi-branch spacecraft hierarchical passive whole-body compliant control method. BACKGROUND

[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 attracted widespread attention. In order to meet the needs of autonomous construction and maintenance, various types of manipulator spacecraft and space robots have been developed. Compared with traditional fixed-base manipulators and single-arm or double-arm spacecraft, multi-branch spacecraft systems can independently complete various space manipulations with single arms or cooperatively complete various space manipulations with multiple arms, and can move flexibly on the surface of large space facilities, and are the main tools and carriers for the construction and maintenance of large space facilities in the future. During the operation of the multi-branch spacecraft on the surface of the large facility, not only the force / position control of the manipulator end effector is needed, but also the overall configuration maintenance control of the spacecraft is needed, and the challenge of multi-level coordinated control is faced, and the traditional control method only focusing on the end position is difficult to realize the whole-body coordinated compliant control of the multi-branch spacecraft. Therefore, the application proposes a multi-branch spacecraft hierarchical passive whole-body compliant control method which can realize multi-arm cooperation and is compatible with end compliant manipulation and overall configuration maintenance.

[0003] For end compliant control, the traditional fixed-parameter impedance control method is difficult to cope with the uncertainty of target position and stiffness, and the impedance control method based on reinforcement learning has good performance, but the calculation amount is large and a large amount of related training data is needed. Considering the actual demand of on-orbit manipulation, the self-adaptive variable impedance compliant control strategy with small calculation amount and easy to be embedded into the hierarchical control framework is a method with good application prospect.

[0004] In addition, the stiffness variation and the zero-space projection operator of hierarchical control may produce active behavior, resulting in unstable system, and in view of this problem, the application introduces a system passivity recovery method based on energy tank, which guarantees the safe and stable operation of the multi-branch spacecraft during on-orbit manipulation. SUMMARY

[0005] The application aims to solve the problems in the prior art and proposes a multi-branch spacecraft layered passive whole-body compliant control method. A layered passive whole-body compliant control method is designed for the surface operation of a multi-branch spacecraft in a space station. The method is a spacecraft whole-body control method combining the cooperative control theory, layered control theory, passive control theory and impedance control theory. The advantages are that it can realize multi-level compatible control of end effector compliant contact and whole-body configuration maintenance, and an adaptive variable impedance control strategy is introduced in the end compliant control layer to solve the problem of safe compliant contact with the target. At the same time, an energy tank-based system passivity compensation controller is embedded in each control level to ensure the safety and stability of the system during operation.

[0006] The application is realized by the following technical scheme. The application proposes a multi-branch spacecraft layered passive whole-body compliant control method, which comprises the following steps:

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

[0008] Step 2: Use a master-slave multi-arm cooperative strategy to generate the desired position and attitude of the master operating arm according to the target position and attitude, and then obtain the desired position and attitude of the slave arm according to the relative position and attitude relationship between the master and slave arms;

[0009] Step 3: According to the priority of multiple control purposes, set the end 6-DOF compliant control as the main control target and the joint compliant configuration maintenance control as the secondary control target, design a layered coordinated control framework based on the zero space projection method, and perform system inertia weighted processing on the zero space matrix to ensure the minimization of transient kinetic energy during the operation of the manipulator. Use a classic impedance control form similar to PD to design the control law of each level to obtain the basic layered control system;

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

[0011] Step 5: Modify the fixed stiffness gain of the master 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;

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

[0013] Step seven: the task space control command generated by each level control subsystem is mapped to joint space through inertia weighted pseudo-inverse of corresponding Jacobian matrix of each level, and joint torque control command is generated.

[0014] Further, in step one, for the multi-branch spacecraft single-arm anchoring in the space station with 4 seven-joint manipulators, the cooperative manipulation task of three arms grabbing the target, first, the coupled dynamics model of the multi-branch spacecraft and the space station is established:

[0015]

[0016] Wherein, represents the coupled inertia matrix of 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 position and attitude of the space station centroid; θ q represents the joint angle.

[0017] Further, the relative position and attitude derivation process of the two slave manipulators and the master manipulator in step two is as follows:

[0018] First step: the geometric relationship when the three manipulators cooperatively grab the target can be obtained, and the kinematic closed-chain constraint of the three end effectors is expressed as:

[0019]

[0020] Wherein i=[1,2,3] represents the label of the three manipulators; is the rotation matrix of the i-th end coordinate system relative to the target centroid coordinate system; is the attitude 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 centroid; is the position and attitude of the target; is the position and attitude of the i-th end in the spacecraft base coordinate system;

[0021] Second step: the end position and attitude of the master manipulator are expressed in the space station body coordinate system, and the desired position and attitude of the master arm are obtained as:

[0022]

[0023] Third step: the relative position and attitude of the two slave arms are derived by subtracting the end position and attitude of the master arm from the end position and attitude of the two slave arms:

[0024]

[0025] where, is the relative position and pose between the i-th slave arm and the tip of the master arm.

[0026] Further, the hierarchical control framework design procedure based on null-space projection in step three is:

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

[0028]

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

[0030] Step 2: The task space dynamics is established from the joint space dynamics of the multi-branch spacecraft as:

[0031]

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

[0033] Step 3: The inertia-weighted null-space projection operator is designed as:

[0034]

[0035] where, U i-1 represents the null-space matrix of the Jacobian matrix J i-1 of the upper level control task, obtained by singular value decomposition of the matrix; H m is the inertia matrix of the multi-branch spacecraft;

[0036] Step 4: The control law of each level is designed as:

[0037]

[0038] where, represents the error between the actual value and the desired value of the i-th level task space state; K i = K c_i + K v_i (t) represents the stiffness gain, composed of two parts: fixed gain and 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 The coupled block matrix representing the nonlinear terms at two levels;

[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] where, ψ t is the system state of the energy tank; γ t_i and δ t_i represent the input and output of the energy tank respectively, and the specific forms are as follows:

[0055]

[0056] λ i represents the energy supplement coefficient of the energy tank system, when the energy in the energy tank is greater than or equal to a predetermined upper limit, the coefficient is set to 0; otherwise, it is set to a fixed value in the range of 0 to 1, and the value determines the speed of energy charging; x i represents the redefined state of the i-th hierarchical control task; x i represents the redefined state of the i-th hierarchical control task, which can be represented as:

[0057]

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

[0059] The second step is to design an energy tank compensation subsystem as follows:

[0060]

[0061] where, α i is the control switch between the energy tank and each hierarchical controller, when the energy in the energy tank is greater than a predetermined lower limit and the system also produces active behavior, α i = 1 is set, representing that the energy tank compensates the system; otherwise, α i = 0 is set, representing that the energy tank is disconnected from each hierarchical controller;

[0062] The third step is to obtain the control instruction of the compensated task space system:

[0063]

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

[0065]

[0066] The present application has the beneficial effects that:

[0067] The application can be compatible with the multi-level control task of the on-orbit operation process of the multi-branched spacecraft, can realize coordinated control of the end compliant contact and overall configuration maintenance, effectively improves the compliance of the contact target process of the end effector of the operating arm, and guarantees the stability of the multi-branched spacecraft during operation. Compared with the traditional method which only focuses on the end compliant control, the application can realize the compliant control of the end effector while maintaining the overall configuration of the spacecraft, to a certain extent, can avoid the collision of the arm and the environment / target, and will play an important role in the on-orbit service field such as space station extravehicular inspection and maintenance, and on-orbit construction of large space facilities. BRIEF DESCRIPTION OF DRAWINGS

[0068] Figure 1 Figure 1 is a schematic diagram of the single-arm anchoring three-arm cooperative operation of the multi-branched spacecraft according to the application.

[0069] Figure 2 Figure 2 is a schematic diagram of the on-orbit operation equivalent model of the multi-branched spacecraft according to the application.

[0070] Figure 3 Figure 3 is a block diagram of the layered passive whole-body compliant control system of the multi-branched spacecraft according to the application.

[0071] Figure 4 Figure 4 is a schematic diagram of the configuration change during the cooperative capture of the space target by the multi-branched spacecraft, wherein a) is the configuration of the multi-branched spacecraft at t=0s, b) is the configuration of the multi-branched spacecraft at t=10s, c) is the configuration of the multi-branched spacecraft at t=20s, and d) is the configuration of the multi-branched spacecraft at t=300s.

[0072] Figure 5 Figure 5 is a schematic diagram of the end motion trajectory during the cooperative capture of the space target by the multi-branched spacecraft. DETAILED DESCRIPTION

[0073] The technical solutions in the embodiments of the application will be clearly and completely described below with reference to the drawings in the embodiments of the application. Obviously, the described embodiments are only part of the embodiments of the application, not all. Based on the embodiments in the application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the application.

[0074] Referring to Figures 1-5 The application provides a layered passive whole-body compliant control method for a multi-branched spacecraft, which comprises the following steps:

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

[0076] Step two: According to the target position and attitude, the desired position and attitude of the master manipulator are generated by using the master-slave multi-arm cooperative strategy, and then the desired position and attitude of the slave manipulator are obtained according to the relative position and attitude relationship between the master and slave arms.

[0077] Step three: According to the priority of multiple control purposes, the end 6-DOF compliant control is set as the main control target, the joint compliant configuration maintenance control is set as the secondary control target, a hierarchical coordination control framework based on zero space projection method is designed, and the zero space matrix is processed by system inertia weighting to minimize the transient kinetic energy in the process of manipulator control; The classic impedance control form of PD (proportional-differential) is used to design the control law of each level to obtain the basic hierarchical control system.

[0078] Step four: Combining the coupling relationship of nonlinear terms at each level, the coupling part is eliminated by using the passivity feedback control strategy to avoid the mutual influence of each level control.

[0079] Step five: Modify the fixed stiffness gain of the master 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 six: Design a system passivity compensation subsystem based on 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 instruction.

[0081] Step seven: The task space control instruction generated by each level control subsystem is mapped to the joint space through the inertia weighted pseudo-inverse of the corresponding Jacobian matrix at each level to generate the joint torque control instruction.

[0082] In step one, for the multi-branch spacecraft single-arm anchored in the space station with a 4-7 joint manipulator, the three-arm cooperative grasping target control task, first, the coupled dynamics model of the multi-branch spacecraft and the space station is established:

[0083]

[0084] Wherein, represents the coupled inertia matrix of 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 position and attitude of the space station centroid; θ q represents the joint angle.

[0085] The relative position and attitude derivation process of the two slave manipulators and the master manipulator in step two is:

[0086] First step: the geometric relationship of the three arms when grabbing the target can get the closed-chain constraint of the motion of the three arms end as:

[0087]

[0088] Where i=[1,2,3] represents the label of the three mechanical arms; is the rotation matrix of the i-th end coordinate system relative to the target mass center coordinate system; is the pose transformation matrix of the target relative to the i-th end effector; p i is the equivalent virtual rod from the end effector to the target mass center; is the position and pose of the target; is the position and pose of the i-th end in the spacecraft base coordinate system;

[0089] Second step: the position and pose of the main operating arm end are expressed in the space station body coordinate system, and the desired position and pose of the main arm are obtained as:

[0090]

[0091] Third step: the relative position and pose of the two slave arms and the main arm are derived by subtracting the position and pose of the main arm end from the position and pose of the two slave arms as:

[0092]

[0093] Where, is the relative position and pose between the i-th slave arm and the main arm end.

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

[0095] First step: for a hierarchical control task with h levels, h=2 in this invention, the forward kinematics is expressed as:

[0096]

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

[0098] Second step: the task space dynamics is established from the joint space dynamics of the multi-branch spacecraft as:

[0099]

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

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

[0102]

[0103] where U i-1 denotes the null-space matrix of the Jacobian matrix J i-1 of the upper-level control task, which is obtained by singular value decomposition; H m is the inertia matrix of the multi-branch spacecraft;

[0104] Step 4: Design the control law of each level as:

[0105]

[0106] where, denotes the error between the actual value and the desired value of the state of the i-th level task space; 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 is the control command of each level task space. The time-varying part is designed in the primary control level of the end compliant contact to realize adaptive variable impedance control, and the time-varying part is set to zero in the secondary control level of the configuration maintenance.

[0107] The derivation process of the passivity-based feedback control law described in Step 4 for coupling elimination is described as follows:

[0108] Step 1: Expand the nonlinear term C e in formula (6) into:

[0109]

[0110] where c 11 and c 22 represent the diagonal block matrices of the primary level control task and the secondary control task, respectively; c 21 = -c 12 represents the coupling block matrix of the two level nonlinear terms;

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

[0112]

[0113] where τ dc is the joint torque control command with the coupling term eliminated by feedback.

[0114] The adaptive variable impedance control law described in Step Five is designed as:

[0115]

[0116] where ε(t) is an adaptive adjustment coefficient with 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 respectively represent the desired contact force and the actual contact force of the end effector; and according to the Routh stability criterion, η is in the range of to ensure that the actual contact force converges to the desired value.

[0117] The design process of the energy tank-based system passivity compensation subsystem described in Step Six is as follows:

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

[0119]

[0120] Define an energy tank system as follows:

[0121]

[0122] where 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, and the specific form is:

[0123]

[0124] λ i represents the energy supplement coefficient of the energy tank system, which is set to 0 when the energy in the energy tank is greater than or equal to the specified upper limit; otherwise, it is set to a fixed value within the range of 0 to 1, and the value determines the speed of energy charging; x i represents the redefined state of the i-th hierarchical control task; x i represents the redefined state of the i-th hierarchical control task, which can be represented as:

[0125]

[0126] And, represents the tracking error of the i-th hierarchical control task; define the energy stored in the energy tank as

[0127] Second step: design the energy tank compensation subsystem as follows:

[0128]

[0129] Wherein, alpha i is a 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, alpha i = 1 is set, representing that the energy tank compensates for the system; otherwise, alpha i = 0 is set, representing that the energy tank is disconnected from each level controller.

[0130] Third step: obtain the compensated task space system control instruction:

[0131]

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

[0133]

[0134] Embodiment

[0135] The present application proposes a multi-branch spacecraft layered passive whole-body compliance control method, as shown in Figure 3 The method comprises the following steps:

[0136] Step one: according to the linkage relationship between the multi-branch spacecraft and the space station, the coupled dynamics model of the whole is derived:

[0137]

[0138] Step two: a master-slave multi-arm cooperation strategy is adopted, the desired position and attitude of the master operating arm are generated according to the target position and attitude, and then the desired position and attitude of the slave arm are obtained according to the relative position and attitude relationship between the master-slave arms:

[0139]

[0140] Step three: according to the priority of multiple control purposes, the end 6-DOF (degree of freedom) compliance control is set as the main control target, the joint compliance configuration maintenance control is set as the secondary control target, a layered coordination control framework based on zero space projection method is designed, and the zero space matrix is processed by system inertia weighting to ensure that the transient kinetic energy is minimized during the manipulation of the robot arm. A classic impedance control form similar to PD (proportional-derivative) is used to design each level control law to obtain the basic layered control system.

[0141] Step four: by a passive feedback control strategy, the coupling part is eliminated, and the mutual influence of each level control is avoided, and the obtained coupling part elimination passive feedback control instruction is:

[0142]

[0143] Step five: the fixed stiffness gain of the main control level is modified, and an adaptive variable impedance adjustment strategy is introduced, the stiffness gain is adjusted in real time according to the position tracking error and the force tracking error, and the gain adjustment strategy is obtained:

[0144]

[0145] Step six: the system passivity compensation subsystem based on the energy tank is designed in each control level, the active behavior caused by the null space projection operator and the stiffness change is compensated, and the passivity of the system is restored, and the compensated task space system control instruction is obtained:

[0146]

[0147] Step seven: the task space control instruction generated by each level control subsystem is mapped to the joint space through the inertia weighted pseudo-inverse of the corresponding Jacobian matrix of each level, and the joint torque control instruction is generated:

[0148]

[0149] The layered passive whole body compliant control method is designed for the space station surface control task demand of the multi-branch spacecraft. In view of the problem that the existing control method focuses on the end compliant control system design and ignores the self configuration maintenance control demand, the layered passive impedance control architecture based on the null space projection is developed, and the adaptive variable impedance control strategy is introduced in the end compliant control layer, the safe compliant contact problem with the target is solved, and the energy tank based system passivity compensation controller is embedded in each control level, so that the safety and stability of the system during operation can be guaranteed.

[0150] Although the present application has been disclosed as above with preferred embodiments, it is not intended to limit the present application, and any person skilled in the art can make various modifications and modifications without departing from the spirit and scope of the present application, therefore the protection scope of the present application should be limited by the claims.

Claims

1. A multi-branched spacecraft hierarchical passive whole-body compliance control method, characterized in that, The method comprises the following steps: Step one: establish the coupling dynamics model of the multi-branch spacecraft and the space station as a whole; Step two: adopt the master-slave multi-arm cooperative strategy, generate the desired position and attitude of the master operating arm according to the target position and attitude, and then obtain the desired position and attitude of the slave arm according to the relative position and attitude relationship between the master-slave arms; Step three: according to the priority of multiple control purposes, set the end 6-DOF compliant control as the main control target, the joint compliant configuration maintenance control as the secondary control target, design a hierarchical coordination control framework based on the zero space projection method, and perform system inertia weighted processing on the zero space matrix to ensure that the transient kinetic energy is minimized during the mechanical arm operation; adopt the classic impedance control form of the PD type to design the control law of each level to obtain the basic hierarchical control system; Step four: combine the coupling relationship of the nonlinear terms at each level, eliminate the coupling part through the passivity feedback control strategy, and avoid the mutual influence of each level control; Step five: modify the fixed stiffness gain of the master 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 six: 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 the stiffness change, restore the passivity of the system, and obtain the compensated task space control instruction; Step seven: map the task space control instruction generated by each level control subsystem to the joint space through the inertia weighted pseudo-inverse of the corresponding Jacobian matrix at each level to generate the joint torque control instruction.

2. The method of claim 1, wherein: In step one, for the multi-branch spacecraft with four 7-joint manipulators, the single-arm of the spacecraft is anchored in the space station, and the three-arms cooperatively grasp the target, first, the coupling dynamics model of the multi-branch spacecraft and the space station is established: where, represents the coupling inertia matrix of the multi-branched spacecraft and the space station; C = [C b C m ] represents the nonlinear term matrix; T is the space station control force and moment; τ is the manipulator joint control moment; F ext represents the external disturbance force and moment; x b denotes the space station center of mass position and attitude; θ q represents the joint angle.

3. The method of claim 2, wherein: The relative position and attitude derivation process of the two slave operating arms and the master operating arm in step two is as follows: First step: the geometric relationship when the three operating arms cooperatively grasp the target can be obtained as the kinematic closed-chain constraint of the three-arm end is expressed as: where i = [1, 2, 3] denotes the index of the three robotic arms; is the rotation matrix of the ith end-effector coordinate frame with respect to the target center of mass coordinate frame; is the pose transformation matrix of the target with respect to the ith end-effector; i is the equivalent virtual link from the end-effector to the target center of mass; is the position and pose of the target; is the position and pose of the ith end-effector in the spacecraft base coordinate frame; Second step: the end position and attitude of the master operating arm are expressed in the space station body coordinate system, and the desired position and attitude of the master arm are obtained as: Third step: the relative position and attitude of the two slave arms are derived by subtracting the end position and attitude of the master arm as:

4. The method of claim 3, wherein: The hierarchical control framework design process based on zero space projection in step three is as follows: First step: for a hierarchical control task with h levels, the forward kinematics is expressed as: where J i represents the Jacobian matrix of the ith level; is the joint angular velocity i∈[1,2]; Second step: the task space dynamics is established from the joint space dynamics of the multi-branch spacecraft as: wherein represents joint torques caused by external forces and torques acting on the end effector; A e represents a layered task inertia matrix; C e is a nonlinear term for the layered task; is the velocity in the layered task space; represents the extended Jacobian matrix, where P1= J1, Third step: the inertia-weighted zero space projection operator is designed as: where U i-1 represents the null space matrix of the Jacobian matrix J i-1 of the upper-level control task, obtained by matrix singular value decomposition; H m is the inertia matrix of the multi-branch spacecraft; Fourth step: the control law of each level is designed as: wherein, represents the error between the actual value and the desired value of the i-th level task space state; K i = K c_i + K v_i (t) represents the stiffness gain, which consists of two parts: a fixed gain and a time-varying gain; D i represents the damping gain; F i is the control command of each level task space.

5. The method of claim 4, wherein: The derivation process of the passivity feedback control law described in step four for coupling elimination is described as follows: First step: expand the non-linear term C in equation (6) into: e C = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + where c 11 and c 22 represent the diagonal block matrices of the primary and secondary control tasks, respectively; c 21 = -c 12 represents the coupling block matrix of the two-level nonlinear terms. Second step: the passivity feedback control law of the nonlinear term coupling part is designed as: where τ dc is the joint torque control command for the coupling term cancellation feedback.

6. The method of claim 5, wherein: The adaptive variable impedance control law described in step five is designed as: where ε(t) is an adaptive adjustment coefficient with initial value set to 0; represent redesigned variable stiffness gains; η is the update rate; T is the sampling period of the controller; f d_i and f et_i represent the desired and actual contact forces of the end effector, respectively; and according to the Routh stability criterion, η is in the range of to ensure that the actual contact force converges to the desired value.

7. The method of claim 6, wherein: The design process of the system passivity compensation subsystem based on an energy tank in step six is as follows: First step: rewriting formula (5) can obtain: An energy tank system is defined as follows: where ψ t is the system state of the energy tank; γ t_i and δ t_i represent the input and output of the energy tank, respectively, and are given by λ i represents the energy replenishment coefficient of the energy tank system, which is set to 0 when the energy in the energy tank is greater than or equal to a specified upper limit; otherwise, it is set to a fixed value in the range of 0 to 1, and the value determines the speed of energy charging;x i represents the state of the i-th hierarchical control task redefinition;x i represents the state of the i-th hierarchical control task redefinition, which can be represented as: And, represents the tracking error of the level i control task; defines the energy stored in the energy tank as Second step: design the energy tank compensation subsystem as follows: wherein, α i 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 represents that the energy tank compensates for the system; otherwise, set α i = 0, which represents that the energy tank is disconnected from each level controller. Third step: get the compensated task space system control command:

8. The method of claim 7, wherein: The joint torque control law described in step seven is designed as follows:

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