Phase-Synchronized Learning of Periodic Compliant Movement Primitives (P-CMPs)

Autonomous trajectory and torque profile synthesis through modulation and generalization require a database of motion with accompanying dynamics, which is typically difficult and time-consuming to obtain. Inspired by adaptive control strategies, this paper presents a novel method for learning and synthesizing Periodic Compliant Movement Primitives (P-CMPs). P-CMPs combine periodic trajectories encoded as Periodic Dynamic Movement Primitives (P-DMPs) with accompanying task-specific Periodic Torque Primitives (P-TPs). The state-of-the-art approach requires to learn TPs for each variation of the task, e.g., modulation of frequency. Comparatively, in this paper, we propose a novel P-TPs framework, which is both frequency and phase-dependent. Thereby, the executed P-CMPs can be easily modulated, and consequently, the learning rate can be improved. Moreover, both the kinematic and the dynamic profiles are parameterized, thus enabling the representation of skills using corresponding parameters. The proposed framework was evaluated on two robot systems, i.e., Kuka LWR-4 and Franka Emika Panda. The evaluation of the proposed approach on a Kuka LWR-4 robot performing a swinging motion and on Franka Emika Panda performing an exercise for elbow rehabilitation shows fast P-CTPs acquisition and accurate and compliant motion in real-world scenarios.