Sample-Based Motion Planning for Robot Manipulators with Closed Kinematic Chains

Random sampling-based methods for motion planning of constrained robot manipulators have been widely studied in recent years. The main problem to deal with is the lack of an explicit parametrization of the non linear submanifold in the Configuration Space (CS) imposed by the constraints in the system. Most of the proposed planning methods use projections to generate valid configurations of the system slowing the planning process. Recently, new robot mechanism includes compliance either in the structure or in the controllers. In this kind of robot most of the times the planned trajectories are not executed exactly due to uncertainties and interactions with the environment. Indeed, controller references are generated such that the constraint is violated to indirectly generate forces during interactions. With the purpose of avoiding projections, in this paper we take advantage of the compliance of systems to relax the geometric constraints imposed by closed kinematic chains. The relaxed constraint is then used in a state-of-the-art suboptimal random sampling based technique to generate paths for constrained robot manipulators. As a consequence of relaxation, arising contact forces acting on the constraint change from configuration to configuration during the planned path. Those forces can be regulated using a proper controller that takes advantage of the geometric decoupling of the subspaces describing constrained rigid-body motions of the mechanism and the controllable forces.