Optimal enveloping trajectory tracking control method for space non-cooperative target under multi-objective constraints

Abstract

The application discloses a kind of optimal envelope trajectory tracking control methods of space non-cooperative target under multi-target constraint, mainly include the following steps: design the full-drive multi-finger space capture configuration with adaptive configuration adjustment and anti-escape capability, generate effective multi-finger envelope configuration using bidirectional Hausdorff distance based on finger feature and target edge point feature, and construct multi-finger dynamic capture domain according to target motion characteristics and joint feature length;Desired trajectory parameterization is carried out using continuous high-order Bezier curve, and smooth envelope trajectory is planned under minimum base disturbance based on multi-target constraint and multi-modal particle collaborative learning mechanism;Through the nonlinear coupling characteristics of inverse dynamics compensation system of multi-finger, design multi-finger collaborative hierarchical tubular model predictive control strategy based on disturbance observer to realize envelope trajectory tracking control.The method can effectively overcome the interference caused by target shape complexity, motion uncertainty, nonlinear dynamic coupling, realize the accurate tracking control of space non-cooperative target trajectory.

Description

Technical Field

[0001] This invention relates to the field of space target acquisition and control, and more particularly to a method for optimal envelope trajectory tracking and control of non-cooperative space targets under multi-target constraints. Background Technology

[0002] With the ever-increasing demands of space exploration and activities, the number of satellites successfully launched globally has been climbing year by year. Due to the lack of effective means of recovering failed satellites, the number of non-cooperative targets in Earth orbit has increased significantly. Furthermore, these targets typically lack their own propulsion control and communication capabilities, making effective interaction with the ground impossible. Their on-orbit disintegration and collisions further exacerbate the complexity of the space environment, posing a serious threat to the safety of spacecraft, space stations, and astronauts in orbit.

[0003] Compared to non-cooperative target capture methods such as docking-based recovery, net capture, grappling hook traction, and laser propulsion, rigid capture methods based on robotic arms and end effectors offer advantages such as high connection stiffness, reusability, and precise force control, leading to widespread research and application in the industry. However, in actual on-orbit capture of non-cooperative targets, external disturbances such as Earth's gravity, air resistance, and solar radiation pressure cause targets to exhibit large size ranges, diverse shapes, and uncertain motion, often accompanied by tumbling, spinning, or nutation. Furthermore, multi-finger systems face constraints during trajectory tracking, including bounded actuator outputs, target motion boundaries, and joint velocity limitations. The complex spatial kinematics and nonlinear dynamics also lead to dynamic coupling phenomena, resulting in poor trajectory tracking control performance of existing methods in the capture of non-cooperative targets in space.

[0004] To address the aforementioned problems, this invention focuses on the design of an all-drive multi-finger capture configuration, dynamic capture domain positioning under escape constraints, minimum base disturbance envelope trajectory planning, and disturbance compensation multi-finger coordinated control strategy design, and discloses an optimal envelope trajectory tracking control method for non-cooperative targets in space under multi-objective constraints. Summary of the Invention

[0005] This invention addresses the problems and challenges of trajectory tracking control for non-cooperative targets in space, and provides a method for optimal envelope trajectory tracking control of non-cooperative targets in space under multi-objective constraints. The technical solution and steps of this invention are as follows:

[0006] Step 1: Taking into account the target's external dimensions, mass inertia, and motion characteristics, construct an all-drive multi-finger spatial capture configuration with adaptive configuration adjustment and anti-escape capabilities, and establish a multi-finger envelope capture coupling dynamics model based on the Lagrange method and the hypothetical mode method.

[0007] Step 2: Generate candidate multi-finger configurations based on the target's shape characteristics and joint thresholds. Use bidirectional Hausdorff distance to select effective multi-finger envelope configurations similar to the target contour. Construct a multi-finger dynamic capture domain based on the target's motion characteristics and joint feature lengths, as detailed below:

[0008] (1) Determine the near joint angle of the multi-finger mechanism based on the shape characteristics of the rolling target, and generate a series of candidate configurations of the finger joints using the joint threshold and sampling step size;

[0009] (2) The position coordinates of the finger joints, fingertips and the center point of the connecting rod are used as the feature point sequence, and the bidirectional Hausdorff distance is calculated based on the finger feature set and the target edge feature point set;

[0010] (3) Based on the projection relationship between the multi-finger end effector and the bottom plane of the palm, establish the constraint conditions for the escape between the rolling target fingers, and select the configuration with the smallest sum of the range of motion of the finger joints as the optimal configuration of the multi-finger mechanism.

[0011] Step 3: Determine continuous high-order Bézier curves through time interval mapping, establish the optimal trajectory optimization cost function by integrating multi-objective constraints, and use a particle cooperative learning mechanism to solve for the multi-finger smooth envelope trajectory that minimizes base perturbation, as detailed below:

[0012] (1) By normalizing, the trajectory planning time interval is mapped to the standard interval, and the fifth-order Bézier curve of the expected trajectory in joint space is established based on the starting point, ending point and shape control point;

[0013] (2) Based on the minimum distance between links to avoid collision during the envelope process, construct the repulsive potential field function, and combine the motion restrictions of multi-finger joints, the perturbation of palm posture and the constraints of self-collision avoidance of multi-finger links to construct the optimal joint trajectory multi-objective optimization cost function;

[0014] (3) Design a dynamic collaborative learning mechanism based on fitness, search progress and particle distance, and integrate multimodal characteristics to adjust the speed update strategy of different regions to establish an update mechanism for the enhanced particle swarm optimization algorithm.

[0015] Step 4: Based on the distributed dynamic equations of the multi-finger system and the coupling relationship between fingers, separate the dynamic equations of a single finger. Using inverse dynamics, decouple the nonlinear tracking error system into a linear subsystem. Design a multi-finger cooperative hierarchical tubular model predictive control strategy to achieve accurate tracking control of the multi-finger envelope trajectory, as detailed below:

[0016] (1) Linearized feedforward torque is used to represent the inertial coupling and velocity coupling between fingers, and the dynamic equation of a single finger is separated based on the distributed dynamic equation of the multi-finger system and the coupling relationship between fingers;

[0017] (2) Based on the nonlinearity and coupling effect of the coupling torque and inverse dynamics control compensation system, the nonlinear tracking error system with multiple inputs and multiple outputs is reduced to a linear system with a single input and single output;

[0018] (3) Design a disturbance observation controller to estimate the uncertainty in the system and actively compensate for external disturbances based on the disturbance observations;

[0019] (4) Based on the nominal model’s energy, state tracking error, terminal state constraint and single finger inertial force change in the prediction time domain, establish a multi-finger collaborative optimization cost function, and design a tube model predictive controller based on the deviation feedback between the optimal control input trajectory and the actual state trajectory to suppress residual interference.

[0020] The advantages of this invention are:

[0021] 1. This invention designs a dynamic capture domain localization method that integrates escape constraints and bidirectional Hausdorff distance, which can adaptively determine the optimal multi-finger envelope configuration.

[0022] 2. This invention designs a trajectory planning method based on continuous high-order Bézier curves and particle collaborative learning, which can reasonably plan multi-finger envelope trajectories with minimal base perturbation.

[0023] 3. This invention proposes a multi-finger cooperative hierarchical tubular model predictive control method with perturbation observer compensation, which can realize multi-degree-of-freedom finger cooperative envelope task under nonlinear dynamic coupling. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of the overall process in a specific implementation of the present invention;

[0025] Figure 2 This is a flowchart of the dynamic capture domain positioning method in a specific implementation of the present invention;

[0026] Figure 3 This is a flowchart of the trajectory planning method in a specific implementation of the present invention;

[0027] Figure 4 This is a flowchart of the multi-finger coordination control method in a specific implementation of the present invention;

[0028] Figure 5 The accompanying drawings are for the abstract of this invention. Implementation

[0029] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in detail below with reference to the accompanying drawings. The following embodiments are for illustrative purposes only and should not be used to limit the scope of the invention.

[0030] Optimal envelope trajectory tracking control method for non-cooperative targets in space under multi-objective constraints, such as Figure 1 As shown, the specific steps are as follows:

[0031] S1. Based on human hand gesture analysis, a fully driven 16-DOF spatial capture mechanism with adaptive configuration adjustment and anti-escape capability is designed. The mechanism adopts a four-finger configuration, with each finger having independent motion capability. Each finger has four degrees of freedom and two degrees of freedom near the joint. The four fingers are symmetrically distributed in a cross shape to simulate a hugging grasping gesture. When grasping irregular objects, multi-point contact can be achieved through kinematic adjustment, which can ensure the stability of the grasp and adaptability to the shape of the target. This solves the problems of small tolerance range, poor shape adaptability and excessive contact collision force in end effectors during operation.

[0032] By combining the Lagrange method and the assumed modal method, a multi-finger envelope proximity coupling dynamic equation is established:

[0033]

[0034] in, and The matrix representing the inertia of the palm and fingers. This represents the coupling matrix between the palm and fingers. and The Jacobian matrix representing the palm and fingers, and This represents the nonlinear term related to the speed of the palm and fingers. This represents the coupling matrix related to the speed of the palm and fingers. This represents the force and torque acting on the palm. Indicates the joint angle. Indicates the speed of the palm. This represents the torque vector of the finger joints. This represents the unknown disturbance force and disturbance torque.

[0035] S2. Generate candidate multi-finger configurations based on the target's shape characteristics and joint thresholds. Use bidirectional Hausdorff distance to select effective multi-finger envelope configurations similar to the target contour. Construct a multi-finger dynamic capture domain based on the target's motion characteristics and joint feature lengths. (Refer to...) Figure 2 The details are as follows:

[0036] (1) Determine the near joint angle of the multi-finger mechanism based on the shape characteristics of the rolling target, and generate a series of candidate configurations of the finger joints using the joint threshold and sampling step size;

[0037] (2) Using the position coordinates of the finger joints, fingertips, and the center point of the connecting rod as the feature point sequence, the bidirectional Hausdorff distance is calculated based on the finger feature set and the target edge feature point set:

[0038]

[0039] in, This represents the feature set of the k-th finger. Represents the set of feature points on the target edge, function This indicates taking the maximum value. and Both represent one-way Hausdorff distances:

[0040]

[0041] in, Represents a set The point in the middle, Represents a set The point in the middle, Point and The Euclidean distance between them;

[0042] (3) Based on the projection relationship between the multi-finger end effector and the bottom plane of the palm, establish the constraints for the escape between the fingers of the rolling target:

[0043]

[0044] in, This represents the finger near-joint angle that satisfies the constraints. Indicates the initial multi-finger configuration projection and perpendicular to The angle between them Indicates joint and The distance between them Indicates joint and The optimal configuration for multi-finger mechanisms is determined by the distance between the finger joints, which minimizes the sum of their range of motion.

[0045]

[0046] in, This indicates optimal registration. This indicates multiple candidate configurations. This represents the range of motion of the i-th joint.

[0047] S3. A continuous high-order Bézier curve is established using time interval mapping. An optimal trajectory optimization cost function is then established, incorporating joint motion constraints, hand posture perturbations, and link self-collision avoidance constraints. Based on a particle cooperative learning mechanism under multimodal characteristics, a multi-finger smooth envelope trajectory minimizing base perturbations is solved. (See reference...) Figure 3 The details are as follows:

[0048] (1) By normalizing the trajectory planning time interval to a standard interval, a fifth-order Bézier curve for the desired trajectory in joint space is established based on the start point, end point, and shape control points:

[0049]

[0050] in, Indicates the joint angle. Indicates the control points of the construction curve. Indicates the current time. and Indicates the start and end points of the time interval for trajectory planning;

[0051] (2) Represent the positional relationship of any two fingers during the envelope process as a spatial geometric vector, and construct the repulsive potential field function based on the minimum collision avoidance distance between the links:

[0052]

[0053] in, Represents virtual repulsion. Indicates the repulsion coefficient. Indicates the effective range of the repulsive force. This indicates the minimum distance between the links. It is a constant;

[0054] Considering the motion constraints of multiple finger joints, perturbations of hand posture, and constraints on self-collision avoidance of multiple finger links, a multi-objective optimization cost function for optimal joint trajectory is constructed:

[0055]

[0056] in, Indicates the joint angle. This represents the weight matrix at the end of the finger. The penalty factor represents the perturbation of hand posture. Indicates the position of the distal end of the finger. This indicates the drifting and perturbation of the hand's posture. Denotes the Euclidean norm;

[0057] (3) Based on fitness, search progress and particle distance, design a dynamic collaborative learning mechanism, integrate multimodal characteristics to adjust the speed update strategy of different regions, and design an update mechanism to enhance the particle swarm optimization algorithm:

[0058]

[0059] in, Indicates non-negative inertia weight. and Let their positions and velocities be the position and velocity of particle k in the s-th iteration, respectively. Let represent the optimal position of particle k. This represents the optimal position for collaborative learning of particle k. This indicates that the particle's velocity is adjusted based on multimodal recognition. Represents dynamic collaborative weights:

[0060]

[0061] in, and Let represent the fitness of particle k and the global optimal solution. Indicates the maximum number of iterations. Represents the distance factor. This represents the distance between particle k and the globally optimal particle.

[0062] S4. Based on the distributed dynamic equations of the multi-finger system and the coupling relationship between fingers, the dynamic equations of individual fingers are separated. Using inverse dynamics, the nonlinear tracking error system is decoupled into a linear subsystem. A multi-finger cooperative hierarchical tubular model predictive control strategy based on disturbance observer compensation is designed to achieve multi-finger envelope trajectory tracking control. (See reference...) Figure 4 The details are as follows:

[0063] (1) Linearized feedforward torque is used to represent the inertial coupling and velocity coupling between fingers. Based on the distributed dynamic equation of the multi-finger system and the coupling relationship between fingers, the dynamic equation of a single finger is separated:

[0064]

[0065] in, The inertia matrix of the finger. Indicates and and Related nonlinear terms, Indicates external disturbance. This indicates the control torque of the fingers. This indicates the coupling between fingers. This indicates joint friction.

[0066] (2) Linearize the coupling torque based on the symmetrical distribution of crossed fingers and the coupling relationship between adjacent fingers:

[0067]

[0068] in, The parameter matrix representing stiffness, The parameter matrix representing damping, based on the nonlinearity and coupling effect of the inverse dynamics control compensation system, reduces the multi-input multi-output nonlinear tracking error system to a single-input single-output linear system;

[0069] (3) Design a disturbance observation controller to estimate the uncertainty in the system and actively compensate for external disturbances based on the disturbance observations:

[0070]

[0071] in, Represents auxiliary variables. The derivative of the auxiliary variable. Indicates the observer parameters, This represents the disturbance observations of the system. Represents the actual trajectory. Represents the state matrix of the system. Represents the system's input matrix;

[0072] (4) The degree of cooperation of the multi-finger system is indirectly measured by the change in inertial force of a single finger. The multi-finger cooperative optimization cost function is established based on the energy, state tracking error and terminal state constraints of the nominal model in the prediction time domain:

[0073]

[0074] in, Indicators representing the synergy of multiple factors This represents the cost function for energy, state tracking error, and terminal state constraints. Indicates the nominal model predictive controller. Indicates time Control input, Indicates the nominal state trajectory. Indicates time In the predicted state, and This represents the set of constraints corresponding to the nominal variable. A set of constraints representing the terminal state;

[0075] Based on the optimal control input trajectory and the feedback of the deviation between the actual state trajectory and the nominal state trajectory, a tube model predictive controller is designed to suppress residual disturbances.

[0076]

[0077] in, This represents the control input of the tube model controller. This represents the optimal control input trajectory. This indicates the feedback gain.

Claims

1. A method for tracking and controlling the optimal envelope trajectory of a non-cooperative spatial target under multi-objective constraints, characterized in that, The method includes the following steps: S1. Design an all-drive multi-finger spatial capture configuration with adaptive configuration adjustment and escape prevention capabilities, and establish a multi-finger envelope capture coupling dynamics model by comprehensively utilizing the Lagrange method and the hypothetical modal method; S2. Generate multi-finger candidate configurations based on the target's shape characteristics and joint thresholds, select effective multi-finger envelope configurations similar to the target contours using bidirectional Hausdorff distance, and construct a multi-finger dynamic capture domain based on the target's motion characteristics and joint feature lengths. S3. Establish continuous high-order Bézier curves using time interval mapping, design the optimal trajectory optimization cost function that integrates joint motion constraints, hand posture perturbation and link self-collision avoidance constraints, and solve the multi-finger smooth envelope trajectory that minimizes base perturbation based on the particle cooperative learning mechanism with multimodal characteristics. S4. Based on the distributed dynamic equation of the multi-finger system and the coupling relationship between fingers, separate the dynamic equation of a single finger. Based on inverse dynamics, decouple the nonlinear tracking error system into a linear subsystem. Design a multi-finger cooperative hierarchical tubular model predictive control strategy based on disturbance observer compensation to realize multi-finger envelope trajectory tracking control.

2. The optimal envelope trajectory tracking and control method for non-cooperative spatial targets under multi-objective constraints according to claim 1, characterized in that, Step S2 includes: S201. Determine the near-joint angle of the multi-finger mechanism based on the shape characteristics of the tumbling target, and generate a series of candidate configurations for the multi-finger joints using joint thresholds and sampling step size; S202. Using the position coordinates of the finger joints, fingertips, and the center point of the connecting rod as a sequence of feature points, calculate the bidirectional Hausdorff distance based on the finger feature set and the target edge feature point set: in, This represents the feature set of the k-th finger. Represents the set of feature points on the target edge, function This indicates taking the maximum value. and Both represent one-way Hausdorff distances; S203. Based on the projection relationship between the multi-finger end effector and the bottom plane of the palm, establish the constraints for the escape between the fingers of the rolling target: in, This represents the finger near-joint angle that satisfies the constraints. Indicates the initial multi-finger configuration projection and perpendicular to The angle between them Indicates joint and The distance between them Indicates joint and The optimal configuration for multi-finger mechanisms is determined by the distance between the finger joints, which minimizes the sum of their range of motion. in, This indicates optimal registration. This indicates multiple candidate configurations. Let N represent the range of motion of the i-th joint, and N represent the number of finger joints.

3. The optimal envelope trajectory tracking and control method for non-cooperative spatial targets under multi-objective constraints according to claim 1, characterized in that, Step S3 includes: S301. By normalizing, the trajectory planning time interval is mapped to a standard interval, and a fifth-order Bézier curve of the desired trajectory in joint space is established based on the start point, end point and shape control point; S302. Represent the positional relationship between any two fingers during the envelope process as a spatial geometric vector, and construct the repulsive potential field function based on the minimum collision avoidance distance between the links: in, Represents virtual repulsion. Indicates the repulsion coefficient. Indicates the effective range of the repulsive force. This indicates the minimum distance between the links. It is a constant; Considering the motion constraints of multiple finger joints, perturbations of hand posture, and constraints on self-collision avoidance of multiple finger links, a multi-objective optimization cost function for optimal joint trajectory is constructed: in, Indicates the joint angle. This represents the weight matrix at the end of the finger. The penalty factor represents the perturbation of hand posture. Indicates the position of the distal end of the finger. This indicates the drifting and perturbation of the hand's posture. Denotes the Euclidean norm; S303. Based on fitness, search progress, and particle distance, a dynamic collaborative learning mechanism is designed, which integrates multimodal characteristics to adjust the speed update strategy in different regions, and an update mechanism to enhance the particle swarm optimization algorithm is designed: in, Indicates non-negative inertia weight. and Let their positions and velocities be the position and velocity of particle k in the s-th iteration, respectively. Let represent the optimal position of particle k. This represents the optimal position for collaborative learning of particle k. This indicates that the particle's velocity is adjusted based on multimodal recognition. This represents the dynamic collaborative weight.

4. The optimal envelope trajectory tracking and control method for non-cooperative spatial targets under multi-objective constraints according to claim 1, characterized in that, Step S4 includes: S401. Linearized feedforward torque is used to represent the inertial and velocity coupling between fingers. Based on the distributed dynamic equations of the multi-finger system and the coupling relationship between fingers, the dynamic equations of a single finger are separated: in, The inertia matrix of the finger. Indicates and and Related nonlinear terms, Indicates external disturbance. This indicates the control torque of the fingers. This indicates the coupling between fingers. This indicates joint friction. S402. Based on the symmetrical distribution of intersecting fingers and the coupling relationship between adjacent fingers, the coupling torque is linearized. Based on the nonlinearity and coupling effect of the inverse dynamics control compensation system, the nonlinear tracking error system with multiple inputs and multiple outputs is reduced to a linear system with a single input and single output. S403. Design a disturbance observation controller to estimate uncertainties in the system and actively compensate for external disturbances based on disturbance observations: in, Represents auxiliary variables. The derivative of the auxiliary variable. Indicates the observer parameters, This represents the disturbance observations of the system. Represents the actual trajectory. Represents the state matrix of the system. Represents the system's input matrix; S404. The degree of coordination in a multi-finger system is indirectly measured by the change in inertial force of a single finger. A multi-finger coordination optimization cost function is established based on the nominal model's energy, state tracking error, and terminal state constraints in the prediction time domain. A tube model predictive controller is designed to suppress residual disturbances based on the optimal control input trajectory and the feedback between the actual state trajectory and the nominal state trajectory. in, This represents the control input of the tube model controller. This represents the optimal control input trajectory. Indicates feedback gain. This indicates the nominal state trajectory.

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