Diffeomorphic Obstacle Avoidance for Contractive Dynamical Systems via Implicit Representations

2025-04-26

AI Summary

Dynamic robotic skill execution in complex environments faces dual challenges of obstacle avoidance and stability assurance. Method: This paper proposes the first whole-body obstacle avoidance framework grounded in contraction dynamics. It innovatively integrates signed distance fields (SDFs) with flow-based differential diffeomorphisms to enable real-time, contraction-preserving avoidance under implicit geometric representations. Contribution/Results: Theoretically, it establishes the first guarantee of both local adaptivity and global Lyapunov stability for neural contraction systems. Experimentally, the framework outperforms state-of-the-art methods in both synthetic benchmarks and real-world kitchen tasks—achieving lower path curvature, reduced dynamic tracking error, and superior safety, robustness, and computational efficiency.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Natural Language Processing: Safety and Robustness
• Multiagent Systems: Adversarial Agents

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Ensuring safety and robustness of robot skills is becoming crucial as robots are required to perform increasingly complex and dynamic tasks. The former is essential when performing tasks in cluttered environments, while the latter is relevant to overcome unseen task situations. This paper addresses the challenge of ensuring both safety and robustness in dynamic robot skills learned from demonstrations. Specifically, we build on neural contractive dynamical systems to provide robust extrapolation of the learned skills, while designing a full-body obstacle avoidance strategy that preserves contraction stability via diffeomorphic transforms. This is particularly crucial in complex environments where implicit scene representations, such as Signed Distance Fields (SDFs), are necessary. To this end, our framework called Signed Distance Field Diffeomorphic Transform, leverages SDFs and flow-based diffeomorphisms to achieve contraction-preserving obstacle avoidance. We thoroughly evaluate our framework on synthetic datasets and several real-world robotic tasks in a kitchen environment. Our results show that our approach locally adapts the learned contractive vector field while staying close to the learned dynamics and without introducing highly-curved motion paths, thus outperforming several state-of-the-art methods.

Problem

• Ensuring safety and robustness in dynamic robot skills
• Achieving contraction-preserving obstacle avoidance in cluttered environments
• Leveraging SDFs and diffeomorphisms for stable robot motion planning

Innovation

• Uses neural contractive dynamical systems for robustness
• Leverages SDFs for implicit scene representations
• Applies diffeomorphic transforms for obstacle avoidance