Learning an Autonomous Dynamic System to Encode Complex Periodic Human Motion Skills

Autonomous dynamic systems (ADS)-based encoding of human motion skills has been widely demonstrated to exhibit high transfer efficiency in goal-directed tasks; however, significant gaps remain in the study of skill transfer for periodic motions, particularly complex periodic motions. In this letter, we propose a novel method for directly learning complex periodic movements using Lyapunov functions (LF), which is fundamentally different from all existing methods that learn periodic movements through limit cycle mapping. First, we introduce a polar coordinate transformation to decouple trajectory and angle modulation, enabling the radially increasing Lyapunov energy function to acquire non-radial expansion capabilities. Then, based on this, we learn a data-driven Lyapunov energy function by solving a dual objective optimization problem that combines geometric alignment and orbit parallelism constraints, aligning one of its horizontal surfaces with a periodic human demonstration trajectory. Finally, ADS is learned by sequentially solving LF-related constrained optimization problems. By designing appropriate constraint functions, we can ensure that the trajectories generated by ADS converge to an LF-level surface whose shape resembles that of periodic human demonstration trajectories. Both simulations and real robot experiments validate the effectiveness of the proposed method.