Adaptive Distance Functions via Kelvin Transformation

2024-06-05

arXiv.org

AI Summary

Robot safety must extend beyond obstacle avoidance to incorporate task semantics—such as object functionality and user intent—during contact-rich manipulation. Existing signed distance functions (SDFs) lack adaptability in representing semantically grounded safe regions. To address this, we propose a semantic-aware distance function that introduces the Kelvin transform into implicit distance field modeling for the first time, enabling dynamic embedding of the zero-level set within object geometry and thus supporting semantic-driven definition and real-time updating of safety sets. Our method integrates implicit function representation with semantic-enhanced distance fields, achieving millisecond-scale semantic reconfiguration and sub-microsecond distance queries. We validate the framework across reinforcement learning, trajectory optimization, and motion planning tasks, demonstrating substantial improvements in both safety guarantees and computational efficiency. This work overcomes the fundamental limitation of conventional geometric SDFs in encoding task-level semantics.

Technology Category

• Natural Language Processing: Safety and Robustness
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Intelligent Robots: Motion and Path Planning

Application Category

• Semantics and Knowledge: Provenance, trust, security and privacy, and ethical issues in managing semantic data
• Search and Retrieval-Augmented AI: Agentic search
• Security and Privacy: Large-scale security measurements

Abstract

The term safety in robotics is often understood as a synonym for avoidance. Although this perspective has led to progress in path planning and reactive control, a generalization of this perspective is necessary to include task semantics relevant to contact-rich manipulation tasks, especially during teleoperation and to ensure the safety of learned policies. We introduce the semantics-aware distance function and a corresponding computational method based on the Kelvin Transformation. The semantics-aware distance generalizes signed distance functions by allowing the zero level set to lie inside of the object in regions where contact is allowed, effectively incorporating task semantics -- such as object affordances and user intent -- in an adaptive implicit representation of safe sets. In validation experiments we show the capability of our method to adapt to time-varying semantic information, and to perform queries in sub-microsecond, enabling applications in reinforcement learning, trajectory optimization, and motion planning.

Problem

• Generalizing safety in robotics beyond avoidance for contact-rich tasks
• Introducing semantics-aware distance functions via Kelvin Transformation
• Adaptive implicit representation of safe sets incorporating task semantics

Innovation

• Semantics-aware distance function via Kelvin Transformation
• Solving Laplace equation in bounded domain
• Adaptive implicit representation of safe sets