Robot Arm Motion Planning Based on Geodesics

Abstract

Naturally, finding joint trajectories for robotic manipulators involves competing optimization goals. On the one hand, the end-effector should move along a predictable and short path while on the other hand joint movement and acceleration should be kept to a minimum. Obstacles in the workspace or joint limits complicate the situation even further. Constructing a metric that makes undesired configurations more expensive to travel through, we equip the joint space with a notion of cost. The motion planning task then reduces to the problem of finding cheapest paths connecting two configurations – so-called geodesics. We show how to construct suitable metrics for a variety of typical scenarios and present an efficient algorithm for the computation of the corresponding geodesics. Our approach makes it very easy to balance different optimization goals and produces natural and smooth manipulator movement.