Rapid Synchronization and Accurate Phase-locking of Rhythmic Motor Primitives Dimitris Pongas, Aude Billard Autonomous System Laboratory Swiss Federal Institute of Technology Lausanne (EPFL) http://asl.epfl.ch {dimitris.pongas, aude.billard}@epfl.ch Stefan Schaal Computer Science & Neuroscience University of Southern California, Los Angeles, CA 90089 ATR Computational Neuroscience Laboratory, Kyoto 619-02, Japan sschaal@usc.edu, http://www-clmc.usc.edu Abstract— Rhythmic movement is ubiquitous in human and animal behavior, e.g., as in locomotion, dancing, swimming, chewing, scratching, music playing, etc. A particular feature of rhythmic movement in biology is the rapid synchronization and phase locking with other periodic events in the environment, for instance music or visual stimuli as in ball juggling. In traditional oscillator theories to rhythmic movement generation, synchronization with another signal is relatively slow, and it is not easy to achieve accurate phase locking with a particular feature of the driving stimulus. Using a recently developed framework of dynamic motor primitives, we demonstrate a novel algorithm for very rapid synchronization of a rhythmic movement pattern, which can phase lock any feature of the movement to any particular event in the driving stimulus. As an example application, we demonstrate how an anthropomorphic robot can use imitation learning to acquire a complex drumming pattern and keep it synchronized with an external rhythm generator that changes its frequency over time. Index Terms— Motor primitives, Synchronization and Phase locking, learning from demonstration, Periodic movement I. I NTRODUCTION Humans have the ability to perform and learn a large vari- ety of rhythmic movements, where movement patterns can be as simple as a sinusoidal oscillation, or rather complex as in dancing or drumming the Bolero of Ravel. A key feature of rhythmic movement is the synchronization and phase locking with external events. For instance, in dancing, we learn the steps synchronized with the beat of the music, in music playing in a band, we need to follow the lead musician’s tempo, or in walking with a friend, we synchronize our locomotory pattern to the frequency of the friend’s walking pattern in order to move at the same speed. The benefit of such synchronization lies often in advanced abilities to perform group behavior, to achieve complex coordination tasks, or to accomplish energy efficiency as in resonance tuning [6]. Traditional methods of trajectory planning and execution, however, are not always well suited for such sensorimotor coordination of rhythmic movement. Movement planning in robotics is mostly performed offline by using optimization approaches or other complex planning techniques. In a stochastic environment with quick dynamic changes, such planning approaches cannot adapt fast enough to changes in the environment, and often it would also be unclear what planning criteria to use for complex movement skills as described above [2]. In contrast, a framework for movement planning that facilitates sensorimotor coupling can be adopted from work on biological pattern generators [1]. From a formal point of view, pattern generators are nonlinear dynamical system with attractor dynamics that encode a robust accom- plishing of a task goal. Synchronization and phase locking can naturally be coded in such dynamic system in the spirit of coupled oscillators. However, controlling synchronization and accurate phase locking in nonlinear dynamic system is often not trivial, as the nonlinear differential equations of such systems are typically rather sensitive to parameter changes. A recently suggested framework of Dynamic Movement Primitives (DMP) [5] has changed the way of how nonlinear pattern generators can be manipulated. The authors of this work developed a novel formulation of nonlinear differential Fig. 1. A photo of our Sarcos Master Arm, a 10 degree-of-freedom hydraulic robot, with a drum stick attached to the thumb of the endeffector.