Multi-homotopy class optimal path planning for manipulation with one degree of redundancy

Abstract

Redundant manipulators have an infinitely large set of joint paths that yield a desired end-effector path in the task space. A unique joint path can be obtained by minimizing a global cost function. Prior optimal control methods minimize a global cost function to find a local minimum within a homotopy class. Many possible locally optimal joint paths are in different homotopy classes. This paper presents an algorithm that effectively searches the solution space and finds many locally optimal paths in all relevant homotopy classes. The path with the lowest cost is very likely the globally optimal path. The algorithm is demonstrated in a case study for which the globally optimal path would be impossible to find using traditional methods.