一种水下电动机械臂运动学与奇异性分析

Kinematics and Singularity Analysis of an Underwater Electric Manipulator

水下电动机械臂是水下机器人重要的作业工具。水下电动机械臂的控制需要运动学模型,但是不同结构的水下电动机械臂其运动学模型不同。另外,水下电动机械臂存在一些奇异位置,当机械臂位于奇异位置时,机械臂末端微小变化可能引起关节位置巨大变化,从而容易损坏机械臂,因此控制中需要规避水下电动机械臂的奇异位置。文章针对一种水下电动机械臂,基于改进D-H参数法推导出机械臂的正、逆运动学方程,建立机械臂运动学模型,求得了机械臂雅克比矩阵,并分析了机械臂奇异位置,同时采用条件数判断机械臂当前关节状态的可操作性。仿真实验结果表明,文章建立的运动学模型可以根据机械臂关节位置精确计算机械臂末端位姿,也可以根据机械臂末端位姿反解机械臂关节位置;当机械臂靠近奇异位置时,条件数呈指数级增长,这说明可以采用条件数规避水下电动机械臂的奇异位置。

An underwater electric manipulator is a key operational tool for unmanned underwater vehicles.The control of this manipulator demands kinematic models,but for arms of different structures,these models differ.Furthermore,underwater electric manipulators encounter certain singular positions;at these positions,minor changes at the manipulator's endpoint may yield substantial alterations in joint positions,potentially causing damage to the manipulator.Therefore,avoiding these singular positions in control is crucial.This paper focuses on an underwater electric manipulator and utilizes an enhanced Denavit-Hartenberg parameter method to derive forward and inverse kinematic equations,establishing its kinematic model.The Jacobian matrix of the manipulator was calculated,followed by an analysis of the manipulator's singular positions,using the condition number to gauge the current operational status of the manipulator's joints.Simulation experiment results demonstrate that the kinematics model developed in this study accurately calculates endpoint poses based on joint positions and inversely determines joint positions based on endpoint poses.As the manipulator nears singular positions,the condition number exponentially increases,indicating its effectiveness as a tool in avoiding these singular positions of the underwater electric manipulator.