Fast Interval Bisection Method for Finding All Solutions of Nonlinear Equations And Its Application to Inverse Kinematics for General Manipulators

Abstract

A method based on the interval analysis is given for finding every solution of the inverse kinematics problem of general manipulators. The method is an interval version of binary search and rather simple in principle; however, it has been slow for practical applications. Therefore, a main contribution of this paper is to speed up the primitive version of the method by introducing some skillful techniques. In an improved version named the Fast Interval Bisection (FIB) method, not only the number of operations but also the storage space of variables are reduced successfully according to the topological analysis of computational graph. Furthermore, in order to generate a complete program of the FIB from an arbitrary kinematics equation automatically, a kind of compiler system is also developed. The experimental evaluation of the FIB is performed on the inverse kinematics problem for a six-revolute-joint manipulator with 16 solutions.