Encoding of periodic and their transient motions by a single dynamic movement primitive

Present formulations of periodic dynamic movement primitives (DMPs) do not encode the transient behavior required to start the rhythmic motion, although these transient movements are an important part of the rhythmic movements (i.e. when walking, there is always a first step that is very different from the subsequent ones). An ad-hoc procedure is then necessary to get the robot into the periodic motion. In this contribution we present a novel representation for rhythmic Dynamic Movement Primitives (DMPs) that encodes both the rhythmic motion and its transient behaviors. As with previously proposed DMPs, we use a dynamical system approach where an asymptotically stable limit cycle represents the periodic pattern. Transients are then represented as trajectories converging towards the limit cycle, different trajectories representing varying transients from different initial conditions. Our approach thus constitutes a generalization of previously proposed rhythmic DMPs. Experiments conducted on the humanoid robot ARMAR-III demonstrate the applicability of the approach for movement generation.