| Space-robot system has always been one of the most important options of on-orbit servicing technologies.With increasing kinds of servicing objects and higher requirements of reliability for space missions,single-arm,even multi-arm,space robots will face some incompetent tasks.With the application of small satellites and the maturity of formation technology,collaborative services by multiple space robots will be possible.This paper focuses on the on-orbit servicing system composed of multiple space robots in formation.Lie group,Lie algebra and Screw theory are used as the fundamental tools.On the basis of modelling kinematic and dynamic models of the servicing system,motion planning and tracking control are mainly studied.The main results are as follows:1.The kinematic model of the servicing system is systematically established.(1)Based on the Product of Exponentials formula and the rigid body transformation rule,forward kinematic equations at position-level of the multi-arm space robot is built,with selecting the system centroid as the origin of inertial coordinate system;(2)Under the conditions that only partial pose of the base is known,equations of state variables are established by using unit quaternion method,and solved by Newton iteration method;(3)Based on the kinematic equations of single space robot,kinematic equations at positionlevel of the servicing system are established in terms of global coordinate system,both before and after capturing the target;4)The generalized Jacobian matrix of the base and the end-effector is derived,both before and after capturing the target.And a method to solve the attitude of the base by using improved Euler method is proposed.2.Workspace issues of the servicing system are discussed and analysed.(1)The modified virtual manipulator(MVM)modeling method is proposed for dualarm space robots,which can avoid multiple independent passive-spherical-joints are introduced into the virtual model;(2)Workspace of dual-arm space robots is classified with clear mathematical descriptions.Then,the Sim Mechanics model of the virtual manipulator is built,and the Monte Carlo method is used to obtain the workspace cloud maps of the dual-arm system for different types.It can be seen that the shape of every type is ring,and the workspace of left and right arms are symmetrical;(3)Based on kinematic equations of the dual-arm system,the workspace cloud maps,with the attitude of the base is constrained,is calculated by using the Monte Carlo method;4)Based on the general collaborative workspace,the concept of generalized collaborative workspace is proposed for cooperative capture,and detail procedures are given.In the simulation example,these two types of workspace were solved separately and compared.3.The joint trajectory planning with considering the optimal berth position is studied.(1)By the coordinate transformation,the berth position is expressed in the centroidfixed coordinate system of the space-robot system,and its constraints are also given;(2)The sine function combined with the fifth-order polynomial is used to parameterize the joint trajectory.The range of the parameters to be determined is calculated;(3)The objective functions are established for two conditions,minimization of disturbance and adjustment of the attitude of the base to the desired position,respectively;(4)The Genetic Algorithm with improved Gaussian mutation operator is given,and steps of the algorithm are detailed;(5)The feasibility of the planning strategy is verified by simulation example.4.The problem of multi-objective coordinated trajectory planning of multiple space robots in Cartesian space is studied.(1)A drive transform method combined with trapezoidal velocity interpolation is proposed,which can obtain the linear pose trajectory of EE with acceleration and deceleration stages;(2)A multi-objective optimization problem with coordination constraints is built,whose optimization objects are the optimal motion time and the minimum disturbance to the attitude of the base;(3)A dual-population multi-object fruit fly optimization algorithm is proposed,combined with non-dominated sorting,which has better global optimization ability and searching efficiency;(4)The servicing system composed of two planar three-links space robots is used as the simulation object,and a Pareto frontier curve with fine shape is obtained.Then the typical solutions are analyzed in detail.5.The pose tracking control based on SE(3)is studied.(1)According to the Lagrangian principle,the dynamic model of the servicing system before capturing the target is established.Then,the dynamic equations in the workspace are derived based on GJM;(2)The error feedback of state variables is constructed based on the logarithm mapping of SE(3)and spatial velocity,then the closed-loop continuous tracking control strategy with PD control law is designed based on the kinematic equations and GJM derived above,it is proved to have relatively high control accuracy;(3)Considering that the accuracy of PD control law will be reduced when the system state changes dramatically,a robust sliding mode control law is further designed,which can overcome the shortcoming of PD control law;(4)Considering the parametrical uncertainty of the model and unexpected disturbance,a fuzzy sliding mode control law is designed,the closed-loop continuous tracking control strategy with this control law has high control accuracy and robustness,and can eliminate chatter. |
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