Joint solutions of many degrees-of-freedom systems using dextrous workspaces

Several studies have focussed on robotic systems with many degrees-of-freedom. Such robots often have stringent joint limits. For motion planning, a key question is to find feasible joint solutions of the system of a given position and orientation of the end-effector. In the presence of join limits, the solutions are found by searching the joint space using heuristics. In this paper, we propose a simple algorithm to construct the joint solutions for a robot chain with many degrees-of-freedom and joint limits, using dextrous workspaces. The algorithm provides a set of sufficient conditions to guarantee feasible joint solutions in the presence of limits. The procedures are illustrated by theory and experiments on PolyBot, a modular robot developed at Xerox PARC.