Wavelet Movement Primitives: A Unified Framework for Learning Discrete and Rhythmic Movements

Real-world tasks often require combinations of both discrete and rhythmic movements. However, most of current methods can only address one of them. This letter proposes a unified framework, Wavelet Movement Primitives (WMPs), which are built on Probabilistic Movement Primitives (ProMPs) integrated with Discrete Wavelet Transform (DWT), to model and learn both discrete and rhythmic trajectories from demonstrations. The key advantage of WMPs lies in its ability to naturally identify and facilitate a smooth transition between discrete and rhythmic motions using wavelet transforms. Additionally, we propose local frame WMPs (LF-WMPs) for discrete tasks, enabling the learned movements to generalize to new environments. For rhythmic tasks, a phase-adaptive weight adjustment algorithm is proposed, allowing the system to capture time-frequency features of the demonstrations and safely guide the trajectory back to the desired region. Finally, the method is validated through several simulations and a real-world robotic stirring task, demonstrating its good extrapolation capabilities.