表面改性冗余机器人关节动能的流形分析

Manifold analysis of joint kinetic energy of a surface modified redundant robot

针对冗余机器人关节流形上算法研究较少的现状,提出一种利用克里斯托佛尔矩阵函数及其测地线在流形上分析表面改性,冗余机器人关节运动动能稳定性的新算法。利用一阶变分方程分别得到特殊欧式群上的克里斯托佛尔矩阵函数及其测地线方程,然后利用初始条件计算黎曼度量后得到相应的黎曼梯度,黎曼梯度与克里斯托佛尔矩阵函数的结合可以定义特殊欧式群上的收缩映射,从而可以在流形上来分析冗余机器人关节运动动能的稳定性。计算冗余机器人一组关节数据的黎曼平均来研究关节动能在表面改性工作过程中是否有剧烈变化,当代价函数收敛时,通过冗余机器人各关节动能仿真可知其变化范围均局限于某一区间,没有出现大范围剧烈波动情况,证明了文中所提新算法的正确性。

According to the present situation on redundant robot joint manifold ＇algorithm research,a Chris Tuofoer matrix func- tion and geodesic analysis algorithm has been proposed for surface modification of redundant robot kinetic stability in manifold. By using the first-order variational equation, Chris Tuofoer matrix function group and special Euclidean geodesic equations has been ob- tained, and then we calculated the Riemann metric obtained after Riemann gradient using the initial conditions. With Riemann and Chris Tuofoer gradient matrix function, the special Euclidean group on the contraction, stability in manifold analysis joint the motion of redundant robots kinetic energy can be defined,The Riemann average of a set of joint data of a redundant robot is calculated to study whether the joint kinetic energy has a dramatic change during the surface rnodifieation.When the contemporary valence func- tion converges ,the range of change is limited to a certain range through the kinetic energy simulation of the joints of a redundant ro- bot.The correctness of the new algorithm proposed in this paper is correct.