差分粒子群算法在PUMA机器人逆运动学求解中的应用

Application of Particle Swarm Optimization with Differential Evolution Algorithm in Solving Inverse Kinematics of PUMA Robot

传统逆运动学求解主要从逆运动学方程出发,基于一定的数学理论推导,不能完全实现计算机程序化,且精度与计算效率较低;为改善这一缺陷,基于机器人正向运动学方程,借助MATLAB工具,使用蒙特卡洛法仿真分析出PUMA560机器人的工作空间,任取一点末端执行器位姿作为逆运动学求解的已知位姿矩阵T,结合差分粒子群仿生智能算法作为逆运动学求解的主要理论算法。将计算出的旋转关节变量θ_1~θ_6代入正运动学方程,得出末端位姿矩阵■;通过计算分析T与■相关角度误差,两矩阵所对应的位置向量与姿态向量误差精度为0.001数量级,完全满足目前机器人定位要求。基于差分粒子群理论的机器人逆运动学求解方法计算收敛速度更快,能高度实现计算机程序化,误差精度高,提高计算效率。

The solution of traditional inverse kinematics is mainly based on the inverse kinematics equation with certain mathematical theory derivation,but it can’t fully realize computer programming,and the accuracy and computational efficiency is low.In order to improve these defects,the paper based on the direct kinematics equation of the robot,and Monte Carlo method is used to simulate and analyze the working space of PUMA560 robot by using the MATLAB tool.Any end-effector pose can be taken as the known pose matrix T of inverse kinematics solution,combining with differential particle swarm bionic intelligent algorithm as the main theoretical algorithm for inverse kinematics solution,the calculated rotational joint variable is substituted into the direct kinematics equation to obtain the end pose matrix.By calculating and analyzing the T and ■ the correlation angle error,the error accuracy of the two matrices of corresponding position vector and the pose vector is 0.001 orders of magnitude,which can fully meet the current robot positioning requirements.The inverse kinematics solution based on differential evolution particle swarm theory can calculate the convergence faster,achieving high computer programming,high error precision,and improve computational efficiency.