Collision-free path planning for a three-degree-of-freedom robot

Abstract

A safe trajectory for a point robot is determined by producing a sequence of edges which are alternately traversed ( slides) and then linked by line segment paths ( jumps), referred to herein as slide-jump trajectories. A slide-jump trajectory exists if any safe trajectory exists. Hence, if no slide-jump trajectories exist, then there is no solution. An σ ( n 2) algorithm (in path safety checks) is developed herein, where n is the number of edges in the environment. Heuristic algorithms are presented which relax the slide-jump trajectory towards a locally optimal, but not necessarily safe, trajectory. The relaxation process constantly maintains the safety of the trajectories as the sum of their path lengths squared is decreased. A 3 degree-of-freedom 3 DOF robot manipulator trajectory is handled through the use of pseudo-obstacles which converts the 3 DOF manipulator problem to a 3 DOF point robot problem.