Behavior-Controllable Stable Dynamics Models on Riemannian Configuration Manifolds

Abstract

Due to their stability and robustness, Stable Dynamical Systems (SDS) have received attention as means of representing motions in learning from demonstration tasks. Designing vector fields that fit complex trajectories while ensuring stability still remains a key challenge; although recent deep learning-based methods have shown progress, their tendency to overfit demonstration trajectories often leads to undesirable behaviors, particularly as tasks deviate from demonstrations. Fundamentally, the only reliable way to address this lack of generalization is to provide supervision in out-of-demonstration regions. Focusing on mimicking and contracting behaviors, we propose a Behavior-Controllable Stable Dynamics Model (BCSDM), a one-parameter family of SDS that allows users to adjust the system's overall behavior depending on user intent. We show how to extend BCSDM to accommodate demonstrations of multiple tasks, and propose a Deep Operator Vector Field (DeepOVec) for memory-efficient encoding of multiple dynamical systems. Experiments on tasks that involve mimicking or contracting behaviors demonstrate the advantages of BCSDMs over existing state-of-the-art methods.