WaveSync: Constrained Wavefront Optimization for Synchronized Co-Speech Gestures in Humanoid Robots

Expressive co-speech gestures are crucial for natural human--robot interaction, yet generating them on physical humanoid robots remains challenging because, unlike virtual avatars, robots must synchronize gestures with speech under strict kinematic and actuator constraints. We present WaveSync, a hybrid framework in which a Large Language Model decomposes dialogue responses into structured semantic schemas and assigns per-word importance weights, forming a continuous Semantic Importance Wave. Gesture trajectories are shaped through Dynamic Movement Primitives to ensure kinematic feasibility while enhancing expressiveness. A Wavefront Optimization stage aligns gesture stroke peaks with speech emphasis peaks and resolves residual temporal conflicts through gesture-duration compression and forward propagation. Experimental evaluation across five dialogue scenarios demonstrates effective gesture--speech alignment and favorable performance in both objective and subjective evaluations. The results further show that the key components of WaveSync contribute to producing gestures that are expressive, semantically grounded, and kinematically feasible. The code, resources, and videos are available at https://github.com/pairs-lab/WaveSync{WaveSync}.