求一般6-SPS并联机器人机构的全部位置正解的混沌迭代方法

Finding all solutions to forward displacement analysis problem of 6-SPS parallel robot mechanism with chaos-iteration method

采用简单的牛顿迭代法迭代,并将非线性方程视为非线性的动力学系统,利用使系统产生混沌的Julia集的点求解方程的全部实数解,而Julia集的点在Jocobi矩阵行列式的值为零的解集的邻域内,给定矩阵的行列式的值的表达式的一些变量为已知,仅有一个变量未知,把它转化为一元非线性方程,进而求出一元非线性方程全部解.再在给定变量的邻域内取定给定变量,根据一元非线性方程的全部解以确定该变量的搜索范围,运用粗、精迭代法求解全部位置解.运用该算法编写了MATLAB程序,对一般机器人6-SPS机构的全部位置正解问题进行了研究,得出了Jocobi矩阵的通用表达式,从而得到了其全部位置正解,为实际的6-SPS机构的位置正解问题提供了全新的方法.

A numerical method was found, taking the iteration of Newton method as a nonlinear dynamitic system in which Julia sets leads to chaos. Those points of Julia set was in the neighborhood of those points where belong to the determinant of satisfies Jacobian matrix was equal to zero. Jacobian matrix equation was changed in a non\|linear equation with one variable by giving the other variable's value and the variable scope of the non\|given variable was confirmed, then all solutions of the equation with one variable were found. All values were given in the neighborhood of those points to given variables and the scope for the non\|given variable by the solution was confirmed, then all solutions of wanting problems were determined by rude and fine iteration method. The finding all solutions to forward displacement analysis problem of 6\|SPS parallel robot mechanism was solved by this method, general expression of Jacobian with Newton iteration was obtained, and thus all solutions for this problem were determined. This provides a simple and new realization method for robot mechanics design.