Globally optimal passive compliance control for tasks having multiple homotopy classes

Abstract

Redundant serial manipulators with variable stiffness actuators (VSAs) are capable of passive compliance control, in which the elastic behavior of the end-effector is controlled for robust interaction with a stiff environment. This paper addresses the problem of finding the globally optimal joint manipulation path (sequence of joint positions and compliances) that yields a desired task manipulation path (sequence of end-effector positions and compliances) when there is one degree of redundancy. The space of admissible joint paths can be very complex, with multiple bifurcations resulting in multiple homotopy classes of joint paths. Bifurcations due to singularities in the combined kinematic and compliance joint space are quickly identified using geometric conditions and root-finding. Bifurcations due to joint limits are identified using a novel path planner that traces the solution space boundary edges. With the bifurcations located, joint paths in all homotopy class are generated and deformed into locally optimal paths. The best of these is very likely the globally optimal joint path. Concepts are illustrated in a case study for particle-planar passive compliance control with a 3R-VSA manipulator.