基于唯一域方法的机器人逆向运动学求解

Solution of Inverse Kinematics of Robots Based on Unique Domain Method

针对机器人的逆运动学多解问题,提出一种基于唯一域求解的新方法。利用机器人的雅可比矩阵行列式等于0确定的边界,将机器人的关节空间划分为与逆运动学多解数目一致的唯一域;各唯一域的边界作为约束条件,将唯一域内的逆运动学求解转换为CMA-ES算法的有约束寻优;利用佳点集均匀分布性的特点,优化唯一域中CMA-ES算法求解的初始均值点。通过求6R工业机器人的逆运动学多解,阐述了该方法的应用,并以机械臂逆解数值法为参照,在钱江一号6R工业机器人和KUKA仿人机械臂上进行了2个仿真实验对比。仿真结果表明,本文所提方法在满足精度要求的前提下,平均求解时间更短。实验1中,CMA-ES算法求解一组逆解的平均速度约为5.1 ms/次,数值法求解的平均速度约为7.5 ms/次;实验2中,一组逆解的求解平均速度约为18.9 ms/次,数值法求解的平均速度约为54.8 ms/次;CMA-ES算法对两款机器人的位置跟踪精度均稳定在10-6mm数量级。

The inverse robot kinematics problem has been extensively studied by many workers, but still some problems related to the complexity and strong nonlinear of the inverse kinematics process need suitable heuristic and adhoc techniques and simplifications. A novel method based on uniqueness domains notion was proposed. With using the boundary confirmed by robot’s Jacobian matrix determinant equal to zero, the joint space of the robot was divided into uniqueness domains with the same number of solutions as the inverse kinematics, and the boundary of each uniqueness domain was used as a constraint condition. Then the inverse kinematics solution in the uniqueness domain was transformed into the constrained optimization of the CMA ES algorithm, the initial mean points of the CMA ES algorithm in the uniqueness domain were optimized by using the characteristics of the uniform distribution of the good point set. The application of the presented method was described in detail by solving the inverse kinematics multiple solution of the 6R industrial robot, and comparing with the numerical method on Qianjiang No.1 industrial robot and the KUKA humanoid manipulator. The simulation results showed that under the precondition of accuracy requirement, the proposed method had a faster solution speed. For the industrial 6R robot, the average solution time of CMA ES algorithm was about 5.1 ms/time, and that of numerical method was about 7.5 ms/time, and KUKA humanoid manipulator, the average solution time of inverse solutions was about 18.9 ms/time, and the average solution time of numerical method was about 54.8 ms/time. The presented CMA ES algorithm stabilized the position tracking accuracy of both robots at 10 -6 mm level.