Behavior-Controllable Stable Dynamics Models on Riemannian Configuration Manifolds
Byeongho Lee, Yonghyeon Lee, Junsu Ha, Frank Park
AI summary
Problem
Deep learning-based stable dynamical systems for learning from demonstration often overfit to training trajectories, producing erratic or undesirable motions in out-of-demonstration regions due to a lack of intuitive behavioral supervision.
Approach
The authors introduce BCSDM, which blends contracting and mimicking velocity components via a single control parameter, and extends this framework to curved Riemannian manifolds using geodesics and parallel transport. They also propose a Deep Operator Vector Field to efficiently encode multiple task-specific dynamics.
Key results
- One-parameter BCSDM enabling smooth interpolation between contracting and mimicking behaviors
- Coordinate-free geometric formulation for orthogonal velocity directions on Riemannian manifolds
- Memory-efficient DeepOVec model for simultaneous encoding of multiple task dynamics
- Superior fitting accuracy and task success rates on S² and SE(3) manifolds compared to state-of-the-art methods
Why it matters
Provides roboticists and AI researchers with a robust, geometrically sound framework for generating predictable motions in complex, curved configuration spaces where traditional methods fail.
Abstract
Due to their stability and robustness properties, stable dynamical systems (SDSs) have received considerable attention as a 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 sub- stantial progress in this direction, their tendency to overfit to demonstration trajectories often leads to undesirable behaviors, particularly as tasks deviate from demonstrations. At a fun- damental level, the only reliable way to address this lack of generalization is to provide supervision in out-of-demonstration regions. Focusing on two types of general behaviors, mimick- ing and contracting, 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 the BCSDM to accommodate demonstrations of multiple tasks, and also propose a deep operator vector field for memory-efficient encoding of multiple dynamical systems. Extensive experiments on tasks that involve mimicking or contracting behaviors demonstrate the advantages of BCSDMs over existing state-of-the-art SDS learning methods.