多节双八面体变几何桁架臂逆运动学解析算法

Analytical inverse kinematics algorithm for double-octahedral variable geometry truss manipulators

针对多节双八面体变几何桁架臂(VGT)的逆运动学快速准确求解问题,提出逆运动学解析算法.根据双八面体VGT对称结构和镜像变换矩阵,引入不依赖于欧拉角和Denavit-Hartenberg(D-H)参数的旋转矩阵.通过建立2个辅助坐标系,将整体逆运动学问题分解为求解辅助坐标系旋转矩阵子问题和求解辅助坐标系内位置矢量子问题,给出两节双八面体VGT的逆运动学解析算法.通过分析两节VGT逆运动学的解析解,给出可以将多节臂等效为一节臂的简化运动学构型,将N节VGT臂等效为两节双八面体VGT臂.利用两节双八面体VGT臂的逆运动学算法和简化构型,可得N节臂逆运动学解.仿真验证表明,逆运动学解析算法的计算速度和精度优于雅可比矩阵法.在实际双八面体VGT机构上的测试验证了逆运动学算法的有效性.

An analytical inverse kinematics（IK）algorithm was proposed in order to obtain fast and accurate IK solution for multi-section double-octahedral variable geometry truss（VGT）manipulator.A rotation matrix was introduced without using Euler angle and Denavit-Hartenberg（D-H）parameters based on VGT manipulator symmetric structure property and mirror transformation matrix.The full IK problem was reduced into sub-problems involving finding the rotation matrices of auxiliary coordinate systems and determining position vector in the auxiliary coordinate system by establishing two auxiliary coordinate systems.A two-section VGT manipulator IK algorithm was given.A simplified kinematic configuration capable of converting multi-section VGT manipulator into a single-section manipulator was given by analyzing two-section VGT manipulator IK solution.The N-section VGT manipulator was equivalent to two-section VGT manipulator.The N-section VGT manipulator IK solution was obtained by using twosection VGT manipulator IK algorithm and the simplified kinematic configuration.Simulation results indicate that the proposed IK algorithm has improved computation speed and accuracy than solutions from Jacobian matrix method.The effectiveness of the algorithm was verified on a VGT manipulator test device.