冗余铺丝机械手逆运动学的拓扑流形分析

Topological Manifolds Analysis for Inverse Kinematics of Redundant Fiber Placement Manipulator

针对优化的梯度投影算法在冗余铺丝机械手逆运动学求解问题中不一定存在最优解的问题,提出了一种拓扑流形算法。将冗余铺丝机械手的位形空间看作一个光滑流形,对耦合的位置逆解和姿态逆解进行解耦,然后分别针对位置子流形和姿态子流形进行仿真分析得到其相应的仿真拓扑流形。该方法可以将铺丝机械手的运动学问题抽象为数学中的曲面拓扑流形来研究,为铺丝机械手运动学在流形上分析提供了理论基础,同时也为后续铺丝机械手的最优化自运动控制提供了一种新的方法。最后以飞机S形进气道为例进行仿真,验证了所提方法的正确性。

A new topological manifolds method was proposed to solve the inverse kinematics problem of the redundant fiber placement manipulator.It improved the calculation precision compared with the optimized projected gradient method.A structure of smooth topological manifolds was presented by the inverse kinematics solution of redundant fiber placement manipulator,the simulation topological manifolds were obtained when the position sub-manifolds and posture sub-manifolds had a different simulation analysis for the redundant fiber placement manipulator model,it was like the function mapping in the mathematics from the manipulator joints space to the working space of the end effector.The tangent vector described velocity vector for each point on the topological manifolds,the gather of all these tangent vectors were defined as the tangent vector space on the point.The kinematics problems of the redundant fiber placement manipulator were abstracted to mathematically curved surface topological manifolds problem in the new method,it provided a new theoretical basis for manifolds analysis of the redundant fiber placement manipulator.Thus the subsequent optimization of inverse kinematics solutions manifolds problems were obtained by using self-motion curved surface manifolds theory in the mathematics,it provided a new method for improving the subsequent optimization self-motion control of the redundant fiber placement manipulator.The whole operating performance of the redundant fiber placement manipulator was improved greatly,and it would play a great role in promoting the quantity in the working fiber placement.The new method was verified by simulation of plane S-shaped inlet.