Adapting to contacts: Energy tanks and task energy for passivity-based dynamic movement primitives

In this paper, we develop a framework to encode demonstrated trajectories as periodic dynamic motion primitives (DMP) for an impedance-controlled robot and their modification to fulfil the task objective, i. e. to adapt based on the force feedback and encoded desired wrench profile via an admittance controller. This behavior by itself can violate stability. Therefore, a passivity analysis for the whole system is presented, and based on input power ports and the demonstrated reference power, a passivity observer (PO) is designed. Subsequently, a DMP phase altering law is introduced according to the passivity criterion in order to adjust the phase based on the passivity criterion. However, since this does not necessarily guarantee passivity, a suitable virtual energy tank is used. Experimental results on a Kuka LWR-4 robot polishing an unknown surface underline the real world applicability the suggested controller.