A multi-arm robot cooperative control method for double-arm series in-orbit operation task

Abstract

This invention discloses a cooperative control method for multi-armed robots performing in-orbit operations with dual-arm serial connections. The method includes steps S1, establishing a coupled dynamics model of the two arms; S2, constructing a hierarchical cooperative control architecture; S3, dynamically adjusting the master-slave cooperative strategy based on task priority; S4, implementing parameter-adaptive admittance-force hybrid control for the manipulator arm; and S5, implementing trajectory optimization and adaptive robust control for the auxiliary arm. This invention effectively solves the problems in existing cooperative control methods for dual-armed space robots, such as insufficient consideration of coupled dynamics effects, lack of task-stage adaptability in master-slave arm dynamic coordination, and insufficient accuracy of force-position hybrid control under unknown model parameters. It is applicable to space missions such as satellite maintenance, refueling, and module replacement.

Description

Technical Field

[0001] This invention relates to the field of space robot control technology, and in particular to a collaborative control method for multi-armed robots for dual-arm serial on-orbit operation tasks, applicable to scenarios such as satellite maintenance, refueling, module replacement and space debris removal in on-orbit service missions. Background Technology

[0002] As on-orbit servicing tasks (such as satellite repair, refueling, module replacement, and space debris removal) become increasingly sophisticated and complex, single-arm space robots are finding it increasingly difficult to meet the demands due to their limited payload capacity and insufficient operational flexibility. Multi-arm dexterous space robots, through collaborative operation with two arms, can significantly improve mission execution efficiency and adaptability, becoming an important development direction for on-orbit servicing equipment.

[0003] While traditional single-arm space robots have been successfully applied to tasks such as satellite capture and module transfer, they still have the following limitations: 1) Limited workspace: A single arm can achieve a wide range of motion through joint rotation, but the workspace of the end effector is limited by the arm length and joint angle, making it difficult to cover the entire surface of the target spacecraft; 2) Conflict between operational precision and load: Fine operations (such as tightening screws and connecting interfaces) require low speed and high torque control, while heavy load handling requires high rigidity and strong drive, which is difficult for a single arm to handle. 3) Insufficient fault tolerance: When a joint in a single arm fails, the task may fail completely, lacking redundancy.

[0004] Multi-arm space robots achieve a functional decomposition of "large-area positioning + precise operation" through the collaboration of two arms: the auxiliary arm is responsible for quickly moving the manipulator to the target area (expanding the workspace), while the manipulator is responsible for performing high-precision operations (such as docking and assembly). The two complement each other through collaborative control. The isomorphic arm design (with consistent structure and parameters) reduces system complexity and facilitates modular manufacturing and maintenance, while the end-mounted docking configuration (the manipulator is fixed to the end of the auxiliary arm) further enhances the compactness of motion control.

[0005] Despite the progress made in existing research, the following key issues remain unresolved regarding isomorphic dual-arm systems where the end of the manipulator docks with the auxiliary arm: 1) The system kinematics / dynamics modeling under the docking configuration does not consider the coupling effect between the two arms (such as the inertial load effect of the manipulator on the auxiliary arm); 2) In dual-arm collaborative control, there is a lack of real-time optimization methods for dynamically coordinating the precise operation requirements of the manipulator with the large-range movement of the auxiliary arm. 3) In the microgravity environment on orbit, force feedback control is easily disturbed, and breakthroughs are still needed to achieve high-precision force-position hybrid control. Summary of the Invention

[0006] To overcome the shortcomings of existing technologies, this invention provides a cooperative control method for multi-armed robots for dual-arm serial on-orbit operation tasks, which solves the problems of insufficient consideration of coupling dynamics effects, lack of task-stage adaptability in master-slave arm dynamic coordination, and insufficient accuracy of force-position hybrid control under unknown model parameters in existing dual-arm space robot cooperative control.

[0007] To achieve the aforementioned objectives of the invention, the technical solution adopted to solve its technical problems is as follows: A collaborative control method for a multi-arm robot performing on-orbit operations with two sequential arms, wherein the two arms include an auxiliary arm and a manipulator arm, the manipulator arm being docked and mounted at the end of the auxiliary arm, the method comprising the following steps: Step S1, establish the two-arm coupled dynamic model: The generalized coordinates of the auxiliary arm and the operating arm are used to form the overall generalized coordinates of the system. Based on the Lagrange equation, the overall dynamic equation of the two arms is constructed. This equation is characterized in block matrix form by the auxiliary arm inertia matrix, the auxiliary arm-operating arm coupling inertia matrix, the operating arm inertia matrix, and the corresponding Coriolis force and centrifugal force terms, and includes the external force terms at the ends of the two arms. Step S2, construct a hierarchical collaborative control architecture: The architecture is divided into a task planning layer, a coordination and control layer, and a bottom execution layer. The task planning layer generates the desired trajectory and force constraints of the two arm ends according to the task requirements. The coordination and control layer decomposes the task instructions into the joint control instructions of the two arms and compensates for the coupling effect through a master-slave collaborative control algorithm. The bottom execution layer is responsible for realizing the accurate tracking of joint torque. Step S3: Dynamically adjust the master-slave collaboration strategy based on task priority. Depending on the different stages of the on-orbit service mission, during the long-distance approach phase, the auxiliary arm takes the lead and the manipulator follows; during the capture / docking phase, the manipulator takes the lead and the auxiliary arm assists; and during the precision operation phase, the manipulator controls independently and the auxiliary arm maintains the position. Step S4: Implement admittance-force hybrid control based on parameter adaptation for the manipulator: The task space is decomposed into mutually orthogonal force control subspace and position control subspace. In the force control subspace, the deviation between the expected force and the actual contact force is converted into a displacement correction amount through the admittance model. In the position control subspace, the position control component of the original reference trajectory is tracked. The dynamics of the manipulator itself and the dynamics of the dual-arm coupling are unified and parameterized into the linear form of the total regression matrix and the total parameter vector. The self-load and coupling interference are simultaneously canceled through adaptive feedforward compensation. Step S5: Implement trajectory optimization and adaptive robust control on the auxiliary arm: In the task space, a command trajectory that satisfies the boundary conditions, kinematic continuity and global safety constraints is generated. This trajectory is then mapped to the joint space through differential kinematics. Finally, a composite control law for the auxiliary arm, which includes adaptive feedforward compensation and robust disturbance rejection terms, is designed.

[0008] Furthermore, in step S1, a coupled dynamic model of the two arms is established, including the following: Let the generalized coordinates of the auxiliary arm be... The generalized coordinates of the manipulator are The system's generalized coordinates 14 dimensions in total; total kinetic energy of the system To assist arm kinetic energy With the kinetic energy of the manipulator The sum of these, in a microgravity environment in orbit, represents the system's potential energy. The Lagrange equation for a two-arm series system is:

[0009] Substituting into the Lagrange equation:

[0010] Where t is a continuous time variable. For generalized speed It is a generalized force vector. , Given the joint driving torque vectors of the auxiliary arm and the operating arm, respectively, the coupled dynamic equations of the two arms can be obtained:

[0011] in, The inertia matrix of the auxiliary arm; Let be the coupling inertia matrix of the auxiliary arm and the manipulator arm, and In a microgravity environment, the potential energy term is approximately zero; The inertia matrix of the manipulator; These are the centrifugal force and Coriolis force terms, respectively. Given the geometric Jacobian matrix of the auxiliary arm, the joint velocities are mapped to the end effector Cartesian velocities. Let be the geometric Jacobian matrix of the manipulator; The term represents the virtual work mapping of the end-effector force to the joint space; The force is the external force at the ends of both arms.

[0012] Furthermore, in step S3, the master-slave collaboration strategy is dynamically adjusted based on task priority, including the following: The auxiliary arm, acting as the main arm, is responsible for carrying the manipulator and transporting it to the designated work point near the mission objective. This represents the actual pose of the end flange of the auxiliary arm in the current base coordinate system. The main control objective of the auxiliary arm is to minimize the position relative to the desired predetermined work point. Error between:

[0013] in, The Euclidean norm of a vector; The manipulator arm, acting as the slave arm, is responsible for performing high-precision trajectory tracking, force control, and compliant operation on the platform provided by the auxiliary arm. This indicates the actual position and orientation of the end flange of the manipulator in the current base coordinate system. To determine the final pose of the target object in the base coordinate system, the primary control objective of the manipulator is to minimize the end-effector pose error while satisfying force constraints:

[0014] in, Denotes the weighted quadratic norm; It is a symmetric positive definite weight matrix; For end contact force, The desired contact force / torque vector has a non-zero value in the force-controlled direction and a zero value in the position-controlled direction. The master and slave arms achieve collaboration through two-way information exchange. The master arm sends the end-effector pose and velocity to the slave arm controller, and the slave arm feeds back its own load status, end-effector pose, contact force and task progress to the master arm so that the master arm can make collaborative adjustments.

[0015] Furthermore, in step S4, implementing parameter-adaptive admittance-force hybrid control of the manipulator includes a task space decomposition step S41, which includes the following: The 6-dimensional Cartesian task space is orthogonally decomposed into a force control subspace and a position control subspace, providing a projection basis for subsequent admittance control and position control. Define the force control direction matrix and position control direction matrix ,in, To control the dimension of the subspace, To control the dimension of the subspace for position, satisfying ; It consists of a set of orthogonal unit vectors, and the subspace is controlled by Zhang Chengli; It consists of another set of orthogonal unit vectors, spanning a position-controlling subspace, and is related to... Orthogonal, satisfying ,and A set of orthogonal bases constituting a 6-dimensional space; For any 6-dimensional Cartesian quantity, projected onto the force control subspace and the position control subspace: Force control direction position: ; Position control direction: ; Force control direction force: ; Position control direction force: ; in, For position, For strength.

[0016] Furthermore, in step S4, implementing parameter-adaptive admittance-force hybrid control of the manipulator also includes admittance control law design step S42, which includes the following: Within the force control subspace obtained from step S41, the following second-order admittance model is established:

[0017] in, For the virtual mass matrix in the task space, For virtual damping matrix, The virtual stiffness matrix is ​​one of the three. Diagonal positive definite matrix; For the displacement, velocity, and acceleration corrections within the force control subspace; The actual contact force measured at the end of the manipulator arm; The desired 6-dimensional contact force has a value in the force-controlled direction and a value of 0 in the position-controlled direction; Explicitly solve for acceleration correction:

[0018] Implemented in discrete time, via forward Euler integration:

[0019]

[0020] in, To control the cycle; The force-controlled subspace target pose is:

[0021] Where k is the current time number; The reference pose trajectory of the slave arm end effector output by the task planning layer.

[0022] Furthermore, in step S4, implementing parameter-adaptive admittance-force hybrid control of the manipulator also includes a position control law design step S43, which includes the following: Within the position control subspace obtained in step S41, a proportional control law is used to track the reference trajectory. The target pose in the position control subspace is:

[0023] in, This is a preset reference trajectory; Using the proportional control law, we can obtain:

[0024]

[0025] in, This represents the actual pose of the end effector of manipulator B at time k. This is the scaling gain matrix for the position control subspace.

[0026] Furthermore, in step S4, implementing parameter-adaptive admittance-force hybrid control of the manipulator also includes trajectory synthesis and mapping step S44, which includes the following: The target poses obtained in the force control subspace and position control subspace in steps S42 and S43 are synthesized into the final reference trajectory and mapped to the joint space. The synthesis formula is as follows:

[0027] Mapped to joint space via Jacobi pseudo-inverse (damped least squares method):

[0028] in, , This is a damping factor used to suppress numerical oscillations in the ill-conditioned Jacobian matrix. for Time derivative, To correspond to the Cartesian space velocity command The expected velocity in the joint space; Alternatively, it can be solved using inverse kinematics:

[0029] in, This is the joint angle command for manipulator B at the next moment. The current joint angle of manipulator B. This is the actual position and orientation of the end effector of the manipulator calculated based on the current joint angle. Then, the desired joint velocity and acceleration are calculated using numerical difference:

[0030] .

[0031] Furthermore, in step S4, implementing parameter-adaptive admittance-force hybrid control of the manipulator also includes a dynamic parameterization step S45, which includes the following: The dynamics of the manipulator are uniformly parameterized to provide a basis for the design of adaptive control laws. The actual dynamic equations of the manipulator are as follows:

[0032] in, The inertia matrix of manipulator B itself. For the Coriolis force and centrifugal force of the manipulator B itself; Coupled interference torque Generated by the main arm:

[0033] in, and These are the joint angular velocity and joint angular acceleration of auxiliary arm A, respectively. The coupling inertia matrix of the manipulator-auxiliary arm. The coupling Coriolis force and centrifugal force terms of the auxiliary arm to the operating arm; The coupled inertial load is linearly parameterized as follows:

[0034] Linear parameterization of the coupled Coriolis / centrifugal load is as follows:

[0035] Among them, the regression matrix , , The dimension of the minimum parameter set of the coupled dynamics depends on the parameterization method; This is the corresponding unknown parameter vector; Substituting into the overall dynamic equation, we obtain the unified parameterized form:

[0036] in, The regression matrix is ​​the inertia of the manipulator itself. This is the unknown parameter vector corresponding to the inertia of the manipulator itself. The regression matrix of the manipulator's own Coriolis force / centrifugal force. This is the unknown parameter vector corresponding to the Coriolis force / centrifugal force of the manipulator itself.

[0037] Furthermore, in step S4, implementing parameter-adaptive admittance-force hybrid control of the manipulator also includes an adaptive control law design step S46, which includes the following: Based on the unified parameterization form of step S45, the following adaptive control law is designed:

[0038] in, , , , These correspond to the unknown dynamic parameters. , , , The real-time estimate is updated online by the adaptive law; Or equivalently written as:

[0039] in, Total regression matrix ; This is the total parameter estimation vector; For feedback gain matrix; sliding mode surface ,in , is the diagonal matrix of sliding mode surface gain.

[0040] Furthermore, in step S4, implementing parameter-adaptive admittance-force hybrid control of the manipulator also includes a parameter update law step S47, which includes the following: Based on the control law structure of step S46, a cooperative parameter update law with projection is designed to ensure the physical feasibility of the parameter estimates, and the total parameter vector and its estimated values ​​are defined:

[0041] Design a collaborative update law with projection:

[0042] in, For the parametric projection operator, the parameter estimation is constrained to a closed convex set. Inside, The first Physically feasible lower and upper bounds for each dynamic parameter It is a positive definite adaptive gain matrix. This is the sliding surface error signal. Total regression matrix Transpose of; The component-wise form of the projection function is:

[0043] in, For vectors The One component; Under the aforementioned control law and parameter update law, all signals of the manipulator closed-loop control system are consistent and eventually bounded UUB, and the joint trajectory tracking error eventually converges to a small neighborhood near the origin.

[0044] Furthermore, in step S5, the implementation of trajectory optimization-based and adaptive robust control of the auxiliary arm includes trajectory planning mode selection and the mandatory mapping sub-step S51, which includes the following: The main arm is a 7-DOF redundant robotic arm, whose core task is to quickly, smoothly, and robustly bring the end effector to the predetermined work point. ; First, the actual pose of the end effector of the main arm is obtained through forward kinematics:

[0045] in, This is the positive kinematic mapping of the main arm, with joint angles as input and the pose of the end effector in the base coordinate system as output. This is the actual pose of the end effector of the main arm in the base coordinate system; Then, the command trajectory of the main arm end effector is generated in the task space. The generation process can be performed in any of the following ways: Step S511, Trajectory planning without obstacle avoidance constraints: Generating the end-effector command trajectory using fifth-order polynomial interpolation:

[0046] Where t is the motion time. , , , , , The planning coefficient vector is uniquely determined by the preset trajectory start and end points, positions, velocities, and acceleration boundary conditions. The boundary conditions are:

[0047] in, The total duration for trajectory planning, This represents the initial actual pose of the auxiliary arm. The target endpoint pose of the auxiliary arm, i.e., the predetermined work point. and Let represent the velocity and acceleration of the desired trajectory of the auxiliary arm, respectively. The 0 on the right side of the equation represents the zero vector of the corresponding dimension. Solving for:

[0048] Taking its derivative yields the complete expressions for velocity and acceleration; Step S512, trajectory planning considering obstacle avoidance constraints: discretize the main arm along the link as follows: Key geometric points, among which The total number of discretized sampling points for the main arm link; Main arm Real-time position coordinates of preset geometric sampling points on each link; distributed within the workspace One obstacle ,in For the first Geometric representation of an obstacle; For the first The coordinates of representative points of each obstacle are required; at any given time... The minimum distance between any link point and any obstacle is greater than a safety threshold:

[0049] in, Minimum safe distance; Construct a nonlinear optimization problem:

[0050] in, These are the scalar weighting coefficients for smoothness and terminal tracking error, respectively. , , These correspond to the smoothing cost function, the tracking cost function, and the obstacle avoidance cost function, respectively. The obstacle avoidance weights are set as follows:

[0051] in, This is a global obstacle avoidance strength adjustment factor; This is the obstacle avoidance priority enhancement coefficient for the near-end link; The Euclidean distance between the link point and the representative point of the obstacle; To prevent the division of zero by a small constant; when When, it degenerates into fifth-order polynomial interpolation, i.e., step S511; when When the time comes, the numerical method of Sequential Quadratic Programming (SQP) is used to solve the problem; That is, steps S511 and S512 are mutually exclusive trajectory planning methods, and the choice is made based on whether there are obstacle threats in the task scenario; Finally, regardless of whether step S511 or step S512 is used, the following step S513 is executed. Step S513, mapping from task space to joint space: Solving using inverse kinematics:

[0052] in, The desired joint angle command for the auxiliary arm. This represents the inverse kinematic mapping of the assistive arm from its pose in Cartesian space to its joint space, ensuring that the end effector of the assistive arm can accurately track the desired pose. ; The redundant inverse kinematics are solved using the Jacobian pseudo-inverse, and a null space secondary optimization is introduced:

[0053] in, For undamped pseudo-inverse, For the auxiliary arm Jacobian matrix, For the desired Cartesian velocity of the auxiliary arm, The desired joint velocity command for the auxiliary arm; To optimize the velocity vector in null space, by The weighted summation of the weight coefficients of joint limits, singular avoidance, and obstacle avoidance in null space is as follows:

[0054] in, The velocity term for joint constraint avoidance is typically generated using the gradient projection method or the artificial potential field method. The velocity term is used to avoid singularities and maintain a good condition number for the Jacobian matrix. This is the obstacle avoidance speed term, used to drive the robot away from obstacles; The joint acceleration command is:

[0055] in, For the derivative of the auxiliary arm Jacobian matrix with respect to time, Let be the desired Cartesian acceleration of the auxiliary arm.

[0056] Furthermore, in step S5, implementing trajectory optimization-based and adaptive robust control of the auxiliary arm also includes step S52 of the main arm adaptive robust control law, which includes the following: Based on the joint space command trajectory generated in step S51 and the coupled dynamics model established in step S1, the following composite adaptive robust control law is designed: The main boom dynamic equation is:

[0057] in, and These are the inertia matrix and Coriolis / centrifugal force terms of the auxiliary arm itself. and These are the coupling inertia matrix of the manipulator to the auxiliary arm and the coupling Coriolis force / centrifugal force terms, respectively. The main arm's own dynamics and coupled dynamics are parameterized into regression matrix form respectively:

[0058]

[0059] in, and Represents the regression matrix. and Represents a vector of dynamic parameters; Design a composite adaptive robust control law:

[0060] in, For joint spatial position tracking error, - This indicates the joint space velocity tracking error; This refers to the spatial position error of the task. For mission space velocity error; These are the mission space position gain and velocity gain matrices, respectively; These are the joint spatial position gain and velocity gain matrices, respectively. and Unknown dynamic parameters and Real-time estimated value; The robust disturbance rejection term is designed as follows:

[0061] in, The auxiliary arm inertia matrix is ​​calculated based on the estimated parameters; For sliding surface, This is the diagonal matrix of the sliding surface gain, used to adjust the convergence rate of position and velocity tracking; For convergence gain; For robustness gain; Boundary layer thickness; For a saturation function, the component form is:

[0062] Used to smooth control signals within the boundary layer to suppress chattering; The parameter update law uses the projected gradient descent method:

[0063]

[0064] in, These are positive definite adaptive gain matrices, The dimension of the minimum parameter set of the main arm itself and the coupled dynamics; The gain is positive definite and the robust gain satisfies Under these conditions, the status of the main boom closed-loop control system UUB is ultimately bounded.

[0065] By employing the above technical solutions, this invention has the following advantages and positive effects compared with the prior art: 1. By establishing an overall dynamic model that includes the coupling effect of the two arms, the influence of the inertial load of the operating arm on the auxiliary arm is accurately described, laying the model foundation for high-precision collaborative control; 2. The hierarchical control architecture decouples task planning, coordination control, and underlying execution, improving the system's modularity and scalability; 3. The master-slave priority is dynamically adjusted based on the task stage, so that the auxiliary arm and the operating arm can give full play to their respective advantages in different task stages, taking into account both the efficiency of large-scale movement and the precision of fine operation. 4. The admittance-force hybrid control on the manipulator side, combined with unified parameter adaptive control, can actively learn and cancel the coupling interference caused by the main arm motion under the condition that its own dynamic parameters and coupled dynamic parameters are unknown, so as to achieve high-precision compliant force / position control. 5. The trajectory optimization of the auxiliary arm side makes full use of the redundant degrees of freedom characteristics to achieve obstacle avoidance, joint limit avoidance and singularity avoidance while satisfying end-effector tracking. 6. The adaptive robust control of the auxiliary arm processes the slow-changing parameter perturbations and the fast-changing unmodeled dynamics in a hierarchical manner, which improves the trajectory tracking accuracy while ensuring stability. 7. The entire method is applicable to microgravity on-orbit environments, providing an effective collaborative control solution for complex space operations such as satellite maintenance, refueling, and module replacement. Attached Figure Description

[0066] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In the drawings: Figure 1 This is a simplified flowchart illustrating a collaborative control method for multi-arm robots oriented towards dual-arm serial on-orbit operation tasks according to the present invention. Figure 2 This is a schematic diagram of the hierarchical collaborative control architecture of the present invention, illustrating the information flow and control flow between the task planning layer, the coordination and control layer, and the underlying execution layer. Figure 3 This is a schematic diagram of the admittance-force hybrid control system architecture based on parameter adaptation of the present invention, showing the signal flow of task space decomposition, admittance model, adaptive controller and parameter update law; Figure 4 The flowchart of the main arm mission space command trajectory generation algorithm of the present invention shows the solution process from fifth-order polynomial interpolation without obstacle avoidance constraints to nonlinear optimization problems with obstacle avoidance constraints. Figure 5 This is a schematic diagram of the main arm composite adaptive robust control system architecture of the present invention, showing the control structure of the upper parameter adaptation layer and the lower robust stabilization layer. Detailed Implementation

[0067] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0068] like Figure 1 As shown in the figure, this embodiment discloses a cooperative control method for a multi-arm robot for on-orbit operation tasks involving two-arm serial connections. The two arms include an auxiliary arm and a manipulator arm, with the manipulator arm docked to the end of the auxiliary arm. The method includes the following steps: Step S1, establish the two-arm coupled dynamic model: The generalized coordinates of the auxiliary arm and the operating arm are used to form the overall generalized coordinates of the system. Based on the Lagrange equation, the overall dynamic equation of the two arms is constructed. This equation is characterized in the form of a block matrix, including the auxiliary arm inertia matrix, the auxiliary arm-operating arm coupling inertia matrix, the operating arm inertia matrix, and the corresponding Coriolis force and centrifugal force terms, and also includes the external force terms at the ends of the two arms.

[0069] In this embodiment, the dual-arm system consists of an auxiliary arm (denoted as arm A) and an operating arm (denoted as arm B). It is assumed that both arms are 7-DOF isomorphic robotic arms (this also applies to heterogeneous robotic arms), with identical structural parameters. The operating arm is mounted to the end of the auxiliary arm via a dedicated flange, forming a "master-slave" serial configuration. Because the operating arm is docked to the end of the auxiliary arm, there is strong coupling in the dynamics of the two arms; that is, the motion of the operating arm will exert inertial forces and torques on the end of the auxiliary arm through the docking mechanism, and vice versa. Therefore, it is necessary to establish an overall dynamic model of the dual arms that considers the coupled dynamic effects.

[0070] Let the generalized coordinates of the auxiliary arm be... The generalized coordinates of the manipulator are The system's generalized coordinates 14 dimensions in total; total kinetic energy of the system To assist arm kinetic energy With the kinetic energy of the manipulator The sum of these, in a microgravity environment in orbit, represents the system's potential energy. The Lagrange equation for a two-arm series system is:

[0071] Substituting into the Lagrange equation:

[0072] Where t is a continuous time variable. For generalized speed It is a generalized force vector. , Given the joint driving torque vectors of the auxiliary arm and the operating arm, respectively, the coupled dynamic equations of the two arms can be obtained:

[0073] in, The inertia matrix of the auxiliary arm; Let be the coupling inertia matrix of the auxiliary arm and the manipulator arm, and In a microgravity environment, the potential energy term is approximately zero; The inertia matrix of the manipulator; These are the centrifugal force and Coriolis force terms, respectively. Given the geometric Jacobian matrix of the auxiliary arm, the joint velocities are mapped to the end effector Cartesian velocities. Let be the geometric Jacobian matrix of the manipulator; The term represents the virtual work mapping of the end-effector force to the joint space; The force is the external force at the ends of both arms.

[0074] Step S2, construct a hierarchical collaborative control architecture: like Figure 2 As shown, the present invention designs a "hierarchical" collaborative control architecture, which is divided into three layers: the architecture is divided into a task planning layer, a coordination control layer and a bottom execution layer; the task planning layer generates the expected trajectory and force constraints of the two arm ends according to the task requirements; the coordination control layer decomposes the task instructions into the joint control instructions of the two arms and compensates for the coupling effect through the master-slave collaborative control algorithm; and the bottom execution layer is responsible for realizing the accurate tracking of joint torque.

[0075] Based on the above hierarchical architecture, the implementation of the master-slave collaboration strategy is explained below in conjunction with specific task stages (corresponding to step S3).

[0076] Step S3: Dynamically adjust the master-slave collaboration strategy based on task priority. Considering that on-orbit servicing missions often include multiple sub-tasks (such as "approaching the target → capturing → docking → operation"), the priority of the master-slave collaborative control strategy is dynamically adjusted according to the mission phase: Long-distance approach phase: The auxiliary arm takes the lead, and the operating arm follows, with the priority being "minimizing the position tracking error of the auxiliary arm"; During the capture / docking phase: the manipulator takes the lead, with the auxiliary arm assisting, and the priority is "minimizing the force tracking error at the end of the manipulator + stabilizing the attitude of the auxiliary arm"; In the precision operation phase: the operating arm is controlled independently, while the auxiliary arm maintains its position, with the priority being "maximizing the precision of the operating arm force / position control".

[0077] Based on the aforementioned task phase priorities, the specific roles and functional positioning of the auxiliary arm and the operating arm are as follows: The auxiliary arm (arm A) acts as the main arm, responsible for carrying the manipulator and transporting it to the predetermined work point near the mission objective. This represents the actual pose (position and orientation) of the end flange of the auxiliary arm in the current base coordinate system. The main control objective of the auxiliary arm is to minimize the distance from the desired pre-defined work point. Error between (the pose of the predetermined work point given by the task planning layer in the base coordinate system) and (the error between these two points).

[0078] in, The Euclidean norm of a vector; The manipulator arm (arm B), acting as the slave arm, is responsible for performing high-precision trajectory tracking, force control, and compliant operation on the platform provided by the auxiliary arm. This indicates the actual position and orientation of the end flange of the manipulator in the current base coordinate system. For the final target's pose in the base coordinate system (such as the satellite docking interface pose), the main control objective of the manipulator is to minimize the end-effector pose error while satisfying force constraints:

[0079] in, Denotes the weighted quadratic norm; It is a symmetric positive definite weight matrix; For end contact force, The desired contact force / torque vector has a non-zero value in the force-controlled direction and a zero value in the position-controlled direction. The master and slave arms achieve collaboration through two-way information exchange. The master arm sends the end-effector pose and velocity to the slave arm controller, and the slave arm feeds back its own load status, end-effector pose, contact force and task progress to the master arm so that the master arm can make collaborative adjustments.

[0080] Step S4: Implement admittance-force hybrid control based on parameter adaptation for the manipulator: The task space is decomposed into mutually orthogonal force control subspace and position control subspace. In the force control subspace, the deviation between the expected force and the actual contact force is converted into a displacement correction amount through the admittance model. In the position control subspace, the position control component of the original reference trajectory is tracked. The dynamics of the manipulator itself and the dynamics of the dual-arm coupling are unified and parameterized into the linear form of the total regression matrix and the total parameter vector. The self-load and coupling interference are simultaneously offset through adaptive feedforward compensation.

[0081] The following steps, S41-S47, elaborate on the admittance-force hybrid control of the manipulator, sequentially covering task space decomposition, admittance control law design, position control law design, trajectory synthesis and mapping, dynamic parameterization, adaptive control law, and parameter update law, such as... Figure 3 As shown.

[0082] Step S41, Task space decomposition: The 6-dimensional Cartesian task space is orthogonally decomposed into a force control subspace and a position control subspace, providing a projection basis for subsequent admittance control and position control. Define the force control direction matrix and position control direction matrix ,in, To control the dimension of the subspace, To control the dimension of the subspace for position, satisfying ; It consists of a set of orthogonal unit vectors, and the subspace is controlled by Zhang Chengli; It consists of another set of orthogonal unit vectors, spanning a position-controlling subspace, and is related to... Orthogonal, satisfying ,and A set of orthogonal bases constituting a 6-dimensional space; For any 6-dimensional Cartesian quantity, projected onto the force control subspace and the position control subspace: Force control direction position: ; Position control direction: ; Force control direction force: ; Position control direction force: ; in, For position, For strength.

[0083] Step S42, Force Control Subspace – Admittance Control Law Design: Within the force control subspace obtained from step S41, the following second-order admittance model is established:

[0084] in, For the virtual mass matrix in the task space, For virtual damping matrix, The virtual stiffness matrix is ​​one of the three. Diagonal positive definite matrix; For the displacement, velocity, and acceleration corrections within the force control subspace; The actual contact force measured at the end of the manipulator arm; The desired 6-dimensional contact force has a value in the force-controlled direction and a value of 0 in the position-controlled direction; Explicitly solve for acceleration correction:

[0085] Implemented in discrete time, via forward Euler integration:

[0086]

[0087] in, To control the cycle; The force-controlled subspace target pose is:

[0088] Where k is the current time number; The reference pose trajectory of the slave arm end effector output by the task planning layer.

[0089] Step S43, Position Control Subspace -- Position Control Law Design: Within the position control subspace obtained in step S41, a proportional control law is used to track the reference trajectory. The target pose in the position control subspace is:

[0090] in, This is a preset reference trajectory; Using the proportional control law, we can obtain:

[0091]

[0092] in, This represents the actual pose of the end effector of manipulator B at time k. This is the scaling gain matrix for the position control subspace.

[0093] Step S44, Trajectory Synthesis and Mapping: The target poses obtained in the force control subspace and position control subspace in steps S42 and S43 are synthesized into the final reference trajectory and mapped to the joint space. The synthesis formula is as follows:

[0094] Mapped to joint space via Jacobi pseudo-inverse (damped least squares method):

[0095] in, , This is a damping factor used to suppress numerical oscillations in the ill-conditioned Jacobian matrix. for Time derivative, To correspond to the Cartesian space velocity command The expected velocity in the joint space; Alternatively, it can be solved using inverse kinematics:

[0096] in, This is the joint angle command for manipulator B at the next moment. The current joint angle of manipulator B. This is the actual position and orientation of the end effector of the manipulator calculated based on the current joint angle. Then, the desired joint velocity and acceleration are calculated using numerical difference:

[0097] .

[0098] Step S45, Dynamic parameterization: By uniformly parameterizing the manipulator dynamics, a foundation is provided for the design of adaptive control laws. The actual dynamic equations of the manipulator (including coupling) are as follows:

[0099] in, The inertia matrix of manipulator B itself. For the Coriolis force and centrifugal force of the manipulator B itself; Coupled interference torque Generated by the main arm:

[0100] in, and These are the joint angular velocity and joint angular acceleration of auxiliary arm A, respectively. The coupling inertia matrix of the manipulator-auxiliary arm. The coupling Coriolis force and centrifugal force terms of the auxiliary arm to the operating arm; The coupled inertial load is linearly parameterized as follows:

[0101] Linear parameterization of the coupled Coriolis / centrifugal load is as follows:

[0102] Among them, the regression matrix , , The dimension of the minimum parameter set of the coupled dynamics depends on the parameterization method; This is the corresponding unknown parameter vector; Substituting into the overall dynamic equation, we obtain the unified parameterized form:

[0103] in, The regression matrix is ​​the inertia of the manipulator itself. This is the unknown parameter vector corresponding to the inertia of the manipulator itself. The regression matrix of the manipulator's own Coriolis force / centrifugal force. This is the unknown parameter vector corresponding to the Coriolis force / centrifugal force of the manipulator itself.

[0104] Step S46, Adaptive control law design: Based on the unified parameterization form of step S45, the following adaptive control law is designed:

[0105] in, , , , These correspond to the unknown dynamic parameters. , , , The real-time estimate is updated online by the adaptive law; Or equivalently written as:

[0106] in, Total regression matrix ; This is the total parameter estimation vector; For feedback gain matrix; sliding mode surface ,in , is the diagonal matrix of sliding mode surface gain.

[0107] Step S47, Parameter Update Law: Based on the control law structure of step S46, a cooperative parameter update law with projection is designed to ensure the physical feasibility of the parameter estimates, and the total parameter vector and its estimated values ​​are defined:

[0108] Design a collaborative update law with projection:

[0109] in, For the parametric projection operator, the parameter estimation is constrained to a closed convex set. Inside, The first Physically feasible lower and upper bounds for a dynamic parameter (such as mass) Positive definite inertia, etc. It is a positive definite adaptive gain matrix. This is the sliding surface error signal. Total regression matrix Transpose of; The component-wise form of the projection function is:

[0110] in, For vectors The One component; Under the aforementioned control law and parameter update law, all signals of the manipulator closed-loop control system are uniformly and ultimately bounded (Uniformly Ultimately Bounded), and the joint trajectory tracking error eventually converges to a small neighborhood near the origin.

[0111] Step S5: Implement trajectory optimization and adaptive robust control on the auxiliary arm: In the task space, a command trajectory that satisfies the boundary conditions, kinematic continuity and global safety constraints is generated. This trajectory is then mapped to the joint space through differential kinematics. Finally, a composite control law for the auxiliary arm, which includes adaptive feedforward compensation and robust disturbance rejection terms, is designed.

[0112] The following steps S51~S52 elaborate on the trajectory optimization and adaptive robust control of the auxiliary arm, wherein step S51 includes trajectory planning and mapping, and step S52 is the design of composite control law.

[0113] Step S51, Trajectory Planning and Mapping Step S51 includes trajectory planning mode selection and mandatory mapping sub-steps, and the corresponding algorithm flow is as follows: Figure 4 As shown, the details are as follows: The main arm is a 7-DOF redundant robotic arm, whose core task is to quickly, smoothly, and robustly bring the end effector to the predetermined work point. ; First, the actual pose of the end effector of the main arm is obtained through forward kinematics:

[0114] in, This is the positive kinematic mapping of the main arm, with joint angles as input and the pose of the end effector in the base coordinate system as output. This is the actual pose of the end effector of the main arm in the base coordinate system; Then, the command trajectory of the main arm end effector is generated in the task space. The generation process can be performed in any of the following ways: Step S511, Trajectory planning without obstacle avoidance constraints: Generating the end-effector command trajectory using fifth-order polynomial interpolation:

[0115] Where t is the motion time. , , , , , The planning coefficient vector is uniquely determined by the preset trajectory start and end points, positions, velocities, and acceleration boundary conditions. The boundary conditions are:

[0116] in, The total duration for trajectory planning, This represents the initial actual pose of the auxiliary arm. The target endpoint pose of the auxiliary arm, i.e., the predetermined work point. and Let represent the velocity and acceleration of the desired trajectory of the auxiliary arm, respectively. The 0 on the right side of the equation represents the zero vector of the corresponding dimension. Solving for:

[0117] Taking its derivative yields the complete expressions for velocity and acceleration; Step S512, trajectory planning considering obstacle avoidance constraints: discretize the main arm along the link as follows: Key geometric points, among which The total number of discretized sampling points for the main arm links (3-5 points per link, 21-35 points for a 7-DOF arm); Main arm The real-time position coordinates of preset geometric sampling points on each link (calculated using forward kinematics to obtain their Cartesian coordinates); distributed within the workspace are... One obstacle ,in For the first The geometric representation of an obstacle (convex hull or sphere); For the first The coordinates of representative points of each obstacle (such as the centroid or a distance calculation reference point); at any given time... The minimum distance between any link point and any obstacle is greater than a safety threshold:

[0118] in, Minimum safe distance; Construct a nonlinear optimization problem:

[0119] in, These are the scalar weighting coefficients for smoothness and terminal tracking error, respectively. , , These correspond to the smoothing cost function, the tracking cost function, and the obstacle avoidance cost function, respectively. The obstacle avoidance weights are set as follows:

[0120] in, This is the global obstacle avoidance strength adjustment factor (dimensionless); This is the obstacle avoidance priority enhancement coefficient for the near-end link; The Euclidean distance between the link point and the representative point of the obstacle; To prevent the division of zero by a small constant; when When, it degenerates into a fifth-order polynomial interpolation, step S511; when At that time, numerical methods such as Sequential Quadratic Programming (SQP) are used to solve the problem; That is, steps S511 and S512 are mutually exclusive trajectory planning methods, and the choice is made based on whether there are obstacle threats in the task scenario; Finally, regardless of whether step S511 or step S512 is used, the following step S513 is executed. Step S513, Mapping from task space to joint space (this sub-step is mandatory): Solving using inverse kinematics:

[0121] in, The desired joint angle command for the auxiliary arm. This represents the inverse kinematic mapping of the assistive arm from its pose in Cartesian space to its joint space, ensuring that the end effector of the assistive arm can accurately track the desired pose. ; The redundant inverse kinematics are solved using the Jacobian pseudo-inverse, and a null space secondary optimization is introduced:

[0122] in, For undamped pseudo-inverse, For the auxiliary arm Jacobian matrix, For the desired Cartesian velocity of the auxiliary arm, The desired joint velocity command for the auxiliary arm; To optimize the velocity vector in null space, by The weighted summation of the weight coefficients of joint limits, singular avoidance, and obstacle avoidance in null space is as follows:

[0123] in, The velocity term for joint constraint avoidance is typically generated using the gradient projection method or the artificial potential field method. The velocity term is used to avoid singularities and maintain a good condition number for the Jacobian matrix. This is the obstacle avoidance speed term, used to drive the robot away from obstacles; The joint acceleration command is:

[0124] in, For the derivative of the auxiliary arm Jacobian matrix with respect to time, Let be the desired Cartesian acceleration of the auxiliary arm.

[0125] Step S52, Adaptive Robust Control Law for Main Arm: Based on the joint space command trajectory generated in step S51 and the coupled dynamics model established in step S1, the following composite adaptive robust control law is designed, and the corresponding control system architecture is as follows. Figure 5 As shown: The main boom dynamic equation is:

[0126] in, and These are the inertia matrix and Coriolis / centrifugal force terms of the auxiliary arm itself. and These are the coupling inertia matrix of the manipulator to the auxiliary arm and the coupling Coriolis force / centrifugal force terms, respectively. The main arm's own dynamics and coupled dynamics are parameterized into regression matrix form respectively:

[0127]

[0128] in, and Represents the regression matrix. and Represents a vector of dynamic parameters; Design a composite adaptive robust control law:

[0129] in, For joint spatial position tracking error, - This indicates the joint space velocity tracking error; This refers to the spatial position error of the task. For mission space velocity error (because) (For constant value operation pre-defined points); These are the mission space position gain and velocity gain matrices, respectively; These are the joint spatial position gain and velocity gain matrices, respectively. and Unknown dynamic parameters and Real-time estimated value; The robust disturbance rejection term is designed as follows:

[0130] in, The auxiliary arm inertia matrix is ​​calculated based on the estimated parameters; For sliding surface, This is the diagonal matrix of the sliding surface gain, used to adjust the convergence rate of position and velocity tracking; For convergence gain; For robustness gain; Boundary layer thickness; For a saturation function, the component form is:

[0131] Used to smooth control signals within the boundary layer to suppress chattering; The parameter update law uses the projected gradient descent method:

[0132]

[0133] in, These are positive definite adaptive gain matrices, The dimension of the minimum parameter set of the main arm itself and the coupled dynamics; The gain is positive definite and the robust gain satisfies ( Under the condition of unmodeled dynamic, nonlinear friction and known upper bound norm of parameter estimation transient error, the state of the main boom closed-loop control system. It is a consistent, ultimately bounded UUB.

[0134] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A multi-arm robot cooperative control method for dual-arm series in-orbit operation tasks, characterized in that, The dual arms include an auxiliary arm and an operating arm, with the operating arm docked to the end of the auxiliary arm. The method includes the following steps: Step S1, establish the two-arm coupled dynamic model: The generalized coordinates of the auxiliary arm and the operating arm are used to form the overall generalized coordinates of the system. Based on the Lagrange equation, the overall dynamic equation of the two arms is constructed. This equation is characterized in block matrix form by the auxiliary arm inertia matrix, the auxiliary arm-operating arm coupling inertia matrix, the operating arm inertia matrix, and the corresponding Coriolis force and centrifugal force terms, and includes the external force terms at the ends of the two arms. Step S2, construct a hierarchical collaborative control architecture: The architecture is divided into a task planning layer, a coordination and control layer, and a bottom execution layer. The task planning layer generates the desired trajectory and force constraints of the two arm ends according to the task requirements. The coordination and control layer decomposes the task instructions into the joint control instructions of the two arms and compensates for the coupling effect through a master-slave collaborative control algorithm. The bottom execution layer is responsible for realizing the accurate tracking of joint torque. Step S3: Dynamically adjust the master-slave collaboration strategy based on task priority. Depending on the different stages of the on-orbit service mission, during the long-distance approach phase, the auxiliary arm takes the lead and the manipulator follows; during the capture / docking phase, the manipulator takes the lead and the auxiliary arm assists; and during the precision operation phase, the manipulator controls independently and the auxiliary arm maintains the position. Step S4: Implement admittance-force hybrid control based on parameter adaptation for the manipulator: The task space is decomposed into mutually orthogonal force control subspace and position control subspace. In the force control subspace, the deviation between the expected force and the actual contact force is converted into a displacement correction amount through the admittance model. In the position control subspace, the position control component of the original reference trajectory is tracked. The dynamics of the manipulator itself and the dynamics of the dual-arm coupling are unified and parameterized into the linear form of the total regression matrix and the total parameter vector. The self-load and coupling interference are simultaneously canceled through adaptive feedforward compensation. Step S5: Implement trajectory optimization and adaptive robust control on the auxiliary arm: In the task space, a command trajectory that satisfies the boundary conditions, kinematic continuity and global safety constraints is generated. This trajectory is then mapped to the joint space through differential kinematics. Finally, a composite control law for the auxiliary arm, which includes adaptive feedforward compensation and robust disturbance rejection terms, is designed.

2. The multi-arm robot cooperative control method for dual-arm serial on-orbit operation tasks according to claim 1, characterized in that, In step S1, a two-arm coupled dynamic model is established, including the following: Let the generalized coordinates of the auxiliary arm be... The generalized coordinates of the manipulator are The system's generalized coordinates 14 dimensions in total; total kinetic energy of the system To assist arm kinetic energy With the kinetic energy of the manipulator The sum of these, in a microgravity environment in orbit, represents the system's potential energy. The Lagrange equation for a two-arm series system is: Substituting into the Lagrange equation: Where t is a continuous time variable. For generalized speed It is a generalized force vector. , Given the joint driving torque vectors of the auxiliary arm and the operating arm, respectively, the coupled dynamic equations of the two arms can be obtained: in, The inertia matrix of the auxiliary arm; Let be the coupling inertia matrix of the auxiliary arm and the manipulator arm, and In a microgravity environment, the potential energy term is approximately zero; The inertia matrix of the manipulator; These are the centrifugal force and Coriolis force terms, respectively. Given the geometric Jacobian matrix of the auxiliary arm, the joint velocities are mapped to the end effector Cartesian velocities. Let be the geometric Jacobian matrix of the manipulator; The term represents the virtual work mapping of the end-effector force to the joint space; The force is the external force at the ends of both arms.

3. The multi-arm robot cooperative control method for dual-arm serial on-orbit operation tasks according to claim 1, characterized in that, In step S3, the master-slave collaboration strategy is dynamically adjusted based on task priority, including the following: The auxiliary arm, acting as the main arm, is responsible for carrying the manipulator and transporting it to the designated work point near the mission objective. This represents the actual pose of the end flange of the auxiliary arm in the current base coordinate system. The main control objective of the auxiliary arm is to minimize the position relative to the desired predetermined work point. Error between: in, The Euclidean norm of a vector; The manipulator arm, acting as the slave arm, is responsible for performing high-precision trajectory tracking, force control, and compliant operation on the platform provided by the auxiliary arm. This indicates the actual position and orientation of the end flange of the manipulator in the current base coordinate system. To determine the final pose of the target object in the base coordinate system, the primary control objective of the manipulator is to minimize the end-effector pose error while satisfying force constraints: in, Denotes the weighted quadratic norm; It is a symmetric positive definite weight matrix; For end contact force, The desired contact force / torque vector has a non-zero value in the force-controlled direction and a zero value in the position-controlled direction. The master and slave arms achieve collaboration through two-way information exchange. The master arm sends the end-effector pose and velocity to the slave arm controller, and the slave arm feeds back its own load status, end-effector pose, contact force and task progress to the master arm so that the master arm can make collaborative adjustments.

4. The multi-arm robot cooperative control method for dual-arm serial on-orbit operation tasks according to claim 1, characterized in that, In step S4, implementing admittance-force hybrid control based on parameter adaptation for the manipulator includes the task space decomposition step S41, which includes the following: The 6-dimensional Cartesian task space is orthogonally decomposed into a force control subspace and a position control subspace, providing a projection basis for subsequent admittance control and position control. Define the force control direction matrix and position control direction matrix ,in, To control the dimension of the subspace, To control the dimension of the subspace at position, satisfying ; It consists of a set of orthogonal unit vectors, and the subspace is controlled by Zhang Chengli. It consists of another set of orthogonal unit vectors, spanning a position-controlling subspace, and is related to... Orthogonal, satisfying ,and A set of orthogonal bases constituting a 6-dimensional space; For any 6-dimensional Cartesian quantity, projected onto the force control subspace and the position control subspace: Force control direction position: ; Position control direction: ; Force control direction force: ; Position control direction force: ; in, For position, For strength.

5. A cooperative control method for a multi-arm robot oriented towards dual-arm serial on-orbit operation tasks, as described in claim 4, is characterized in that... In step S4, implementing parameter-adaptive admittance-force hybrid control of the manipulator also includes admittance control law design step S42, which includes the following: Within the force control subspace obtained from step S41, the following second-order admittance model is established: in, For the virtual mass matrix in the task space, For virtual damping matrix, The virtual stiffness matrix is ​​one of the three. Diagonal positive definite matrix; For the displacement, velocity, and acceleration corrections within the force control subspace; The actual contact force measured at the end of the manipulator arm; The desired 6-dimensional contact force has a value in the force-controlled direction and a value of 0 in the position-controlled direction; Explicitly solve for acceleration correction: Implemented in discrete time, via forward Euler integration: in, To control the cycle; The force-controlled subspace target pose is: Where k is the current time number; The reference pose trajectory of the slave arm end effector output by the task planning layer.

6. A cooperative control method for a multi-arm robot oriented towards a dual-arm serial on-orbit operation task, as described in claim 5, is characterized in that... In step S4, implementing admittance-force hybrid control based on parameter adaptation for the manipulator also includes step S43, which involves designing the position control law, including the following: Within the position control subspace obtained in step S41, a proportional control law is used to track the reference trajectory. The target pose in the position control subspace is: in, This is a preset reference trajectory; Using the proportional control law, we can obtain: in, This represents the actual pose of the end effector of manipulator B at time k. This is the scaling gain matrix for the position control subspace.

7. A cooperative control method for a multi-arm robot oriented towards dual-arm serial on-orbit operation tasks according to claim 6, characterized in that, In step S4, implementing admittance-force hybrid control based on parameter adaptation for the manipulator also includes trajectory synthesis and mapping step S44, which includes the following: The target poses obtained in the force control subspace and position control subspace in steps S42 and S43 are synthesized into the final reference trajectory and mapped to the joint space. The synthesis formula is as follows: Mapped to joint space via Jacobi pseudo-inverse (damped least squares method): in, , This is a damping factor used to suppress numerical oscillations in the ill-conditioned Jacobian matrix. for Time derivative, To correspond to the Cartesian space velocity command The expected velocity in the joint space; Alternatively, it can be solved using inverse kinematics: in, This is the joint angle command for manipulator B at the next moment. This represents the current joint angle of manipulator B. This is the actual position and orientation of the end effector of the manipulator calculated based on the current joint angle. Then, the desired joint velocity and acceleration are calculated using numerical difference: 。 8. A cooperative control method for a multi-arm robot oriented towards a dual-arm serial on-orbit operation task, as described in claim 7, is characterized in that... In step S4, implementing admittance-force hybrid control based on parameter adaptation for the manipulator also includes a dynamic parameterization step S45, which includes the following: The dynamics of the manipulator are uniformly parameterized to provide a basis for the design of adaptive control laws. The actual dynamic equations of the manipulator are as follows: in, The inertia matrix of manipulator B itself. For the Coriolis force and centrifugal force of the manipulator B itself; Coupled interference torque Generated by the main arm: in, and These are the joint angular velocity and joint angular acceleration of auxiliary arm A, respectively. The coupling inertia matrix of the manipulator-auxiliary arm. The coupling Coriolis force and centrifugal force terms of the auxiliary arm to the operating arm; The coupled inertial load is linearly parameterized as follows: Linear parameterization of the coupled Coriolis / centrifugal load is as follows: Among them, the regression matrix , , The dimension of the minimum parameter set of the coupled dynamics depends on the parameterization method; This is the corresponding unknown parameter vector; Substituting into the overall dynamic equation, we obtain the unified parameterized form: in, The regression matrix is ​​the inertia of the manipulator itself. This is the unknown parameter vector corresponding to the inertia of the manipulator itself. The regression matrix of the manipulator's own Coriolis force / centrifugal force. This is the unknown parameter vector corresponding to the Coriolis force / centrifugal force of the manipulator itself.

9. A cooperative control method for a multi-arm robot for dual-arm serial on-orbit operation tasks according to claim 8, characterized in that, In step S4, implementing parameter-adaptive admittance-force hybrid control of the manipulator also includes an adaptive control law design step S46, which includes the following: Based on the unified parameterization form of step S45, the following adaptive control law is designed: in, , , , These correspond to the unknown dynamic parameters. , , , The real-time estimate is updated online by the adaptive law; Or equivalently written as: in, Total regression matrix ; This is the total parameter estimation vector; For feedback gain matrix; sliding mode surface ,in , is the diagonal matrix of sliding mode surface gain.

10. A cooperative control method for a multi-arm robot for dual-arm serial on-orbit operation tasks according to claim 9, characterized in that, In step S4, implementing admittance-force hybrid control based on parameter adaptation for the manipulator also includes parameter update law step S47, which includes the following: Based on the control law structure of step S46, a cooperative parameter update law with projection is designed to ensure the physical feasibility of the parameter estimates, and the total parameter vector and its estimated values ​​are defined: Design a collaborative update law with projection: in, For the parametric projection operator, the parameter estimation is constrained to a closed convex set. Inside, The first Physically feasible lower and upper bounds for each dynamic parameter It is a positive definite adaptive gain matrix. This is the sliding surface error signal. Total regression matrix transpose; The component-wise form of the projection function is: in, For vectors The One component; Under the aforementioned control law and parameter update law, all signals of the manipulator closed-loop control system are consistent and eventually bounded by UUB, and the joint trajectory tracking error eventually converges to a small neighborhood near the origin.

11. A cooperative control method for a multi-arm robot for dual-arm serial on-orbit operation tasks according to claim 1, characterized in that, In step S5, the control of the auxiliary arm based on trajectory optimization and adaptive robustness includes trajectory planning mode selection and the mandatory mapping sub-step S51, which includes the following: The main arm is a 7-DOF redundant robotic arm, whose core task is to quickly, smoothly, and robustly bring the end effector to the predetermined work point. ; First, the actual pose of the end effector of the main arm is obtained through forward kinematics: in, This is the positive kinematic mapping of the main arm, with joint angles as input and the pose of the end effector in the base coordinate system as output. This is the actual pose of the end effector of the main arm in the base coordinate system; Then, the command trajectory of the main arm end effector is generated in the task space. The generation process can be performed in any of the following ways: Step S511, Trajectory planning without obstacle avoidance constraints: Generating the end-effector command trajectory using fifth-order polynomial interpolation: Where t is the motion time. , , , , , The planning coefficient vector is uniquely determined by the preset trajectory start and end points, positions, velocities, and acceleration boundary conditions. The boundary conditions are: in, The total duration for trajectory planning, This represents the initial actual pose of the auxiliary arm. The target endpoint pose of the auxiliary arm, i.e., the predetermined work point. and Let represent the velocity and acceleration of the desired trajectory of the auxiliary arm, respectively. The 0 on the right side of the equation represents the zero vector of the corresponding dimension. Solving for: Taking its derivative yields the complete expressions for velocity and acceleration; Step S512, trajectory planning considering obstacle avoidance constraints: discretize the main arm along the link as follows: Key geometric points, among which The total number of discretized sampling points for the main arm link; Main arm Real-time position coordinates of preset geometric sampling points on each link; distributed within the workspace One obstacle ,in For the first Geometric representation of an obstacle; For the first The coordinates of representative points of each obstacle are required; at any given time... The minimum distance between any link point and any obstacle is greater than a safety threshold: in, Minimum safe distance; Construct a nonlinear optimization problem: in, These are the scalar weighting coefficients for smoothness and terminal tracking error, respectively. , , These correspond to the smoothing cost function, the tracking cost function, and the obstacle avoidance cost function, respectively. The obstacle avoidance weights are set as follows: in, This is a global obstacle avoidance strength adjustment factor; This is the obstacle avoidance priority enhancement coefficient for the near-end link; The Euclidean distance between the link point and the representative point of the obstacle; To prevent the division of zero by a small constant; when When, it degenerates into fifth-order polynomial interpolation, i.e., step S511; when When the time comes, the numerical method of Sequential Quadratic Programming (SQP) is used to solve the problem; That is, steps S511 and S512 are mutually exclusive trajectory planning methods, and the choice is made based on whether there are obstacle threats in the task scenario; Finally, regardless of whether step S511 or step S512 is used, the following step S513 is executed. Step S513, mapping from task space to joint space: Solving using inverse kinematics: in, The desired joint angle command for the auxiliary arm. This represents the inverse kinematic mapping of the assistive arm from its pose in Cartesian space to its joint space, ensuring that the end effector of the assistive arm can accurately track the desired pose. ; The redundant inverse kinematics are solved using the Jacobian pseudo-inverse, and a null space secondary optimization is introduced: in, For undamped pseudo-inverse, For the auxiliary arm Jacobian matrix, For the desired Cartesian velocity of the auxiliary arm, The desired joint velocity command for the auxiliary arm; To optimize the velocity vector in null space, by The weighted summation of the weight coefficients of joint limits, singular avoidance, and obstacle avoidance in null space is as follows: in, The velocity term for joint constraint avoidance is typically generated using the gradient projection method or the artificial potential field method. The velocity term is used to avoid singularities and maintain a good condition number for the Jacobian matrix. This is the obstacle avoidance speed term, used to drive the robot away from obstacles; The joint acceleration command is: in, For the derivative of the auxiliary arm Jacobian matrix with respect to time, Let be the desired Cartesian acceleration of the auxiliary arm.

12. A multi-arm robot cooperative control method for dual-arm serial on-orbit operation tasks according to claim 11, characterized in that, In step S5, implementing trajectory optimization-based and adaptive robust control of the auxiliary arm also includes step S52 of the adaptive robust control law for the main arm, which includes the following: Based on the joint space command trajectory generated in step S51 and the coupled dynamics model established in step S1, the following composite adaptive robust control law is designed: The main boom dynamic equation is: in, and These are the inertia matrix and Coriolis / centrifugal force terms of the auxiliary arm itself. and These are the coupling inertia matrix of the manipulator to the auxiliary arm and the coupling Coriolis force / centrifugal force terms, respectively. The main arm's own dynamics and coupled dynamics are parameterized into regression matrix form respectively: in, and Represents the regression matrix. and Represents a vector of dynamic parameters; Design a composite adaptive robust control law: in, For joint spatial position tracking error, - This indicates the joint space velocity tracking error; This refers to the spatial positioning error of the task. For mission space velocity error; These are the mission space position gain and velocity gain matrices, respectively; These are the joint spatial position gain and velocity gain matrices, respectively. and Unknown dynamic parameters and Real-time estimated value; The robust disturbance rejection term is designed as follows: in, The auxiliary arm inertia matrix is ​​calculated based on the estimated parameters; For sliding surface, This is the diagonal matrix of the sliding surface gain, used to adjust the convergence rate of position and velocity tracking; For convergence gain; For robustness gain; Boundary layer thickness; For a saturation function, the component form is: Used to smooth control signals within the boundary layer to suppress chattering; The parameter update law uses the projected gradient descent method: in, These are positive definite adaptive gain matrices, The dimension of the minimum parameter set of the main arm itself and the coupled dynamics; The gain is positive definite and the robust gain satisfies Under these conditions, the status of the main boom closed-loop control system It is a consistent, ultimately bounded UUB.

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