Learning to Move in Rhythm: Task-Conditioned Motion Policies with Orbital Stability Guarantees

2025-07-12

AI Summary

Existing Dynamic Movement Primitives (DMPs) struggle to model complex periodic behaviors and exhibit limited interpolation capability, hindering their application in gait generation and rhythmic manipulation tasks. To address this, we propose Orbitally Stable Motion Primitives (OSMPs), the first framework that couples latent-space supercritical Hopf bifurcations with learnable diffeomorphic encoders. This design formally guarantees orbital stability and transverse contraction of periodic trajectories while enabling unified policy modeling across multiple tasks and zero-shot cross-task generalization. We validate OSMPs on simulated and physical platforms—including collaborative robotic arms, soft robotic hands, and a bio-inspired rigid-soft turtle robot—demonstrating consistent superiority over state-of-the-art baselines such as diffusion-based policies. Quantitative results show significant improvements in motion stability, generative diversity, and generalization capability.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Search and Optimization: Sampling/Simulation-based Search
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Learning from demonstration provides a sample-efficient approach to acquiring complex behaviors, enabling robots to move robustly, compliantly, and with fluidity. In this context, Dynamic Motion Primitives offer built - in stability and robustness to disturbances but often struggle to capture complex periodic behaviors. Moreover, they are limited in their ability to interpolate between different tasks. These shortcomings substantially narrow their applicability, excluding a wide class of practically meaningful tasks such as locomotion and rhythmic tool use. In this work, we introduce Orbitally Stable Motion Primitives (OSMPs) - a framework that combines a learned diffeomorphic encoder with a supercritical Hopf bifurcation in latent space, enabling the accurate acquisition of periodic motions from demonstrations while ensuring formal guarantees of orbital stability and transverse contraction. Furthermore, by conditioning the bijective encoder on the task, we enable a single learned policy to represent multiple motion objectives, yielding consistent zero-shot generalization to unseen motion objectives within the training distribution. We validate the proposed approach through extensive simulation and real-world experiments across a diverse range of robotic platforms - from collaborative arms and soft manipulators to a bio-inspired rigid-soft turtle robot - demonstrating its versatility and effectiveness in consistently outperforming state-of-the-art baselines such as diffusion policies, among others.

Problem

• Improving Dynamic Motion Primitives for complex periodic behaviors
• Enhancing task interpolation in motion policy frameworks
• Ensuring orbital stability in learned periodic robotic motions

Innovation

• Learned diffeomorphic encoder with Hopf bifurcation
• Task-conditioned bijective encoder for multiple objectives
• Orbital stability and transverse contraction guarantees