Reproduce “A Riemannian Take on Distance Fields and Geodesic Flows in Robotics” on OpenResearch

About this paper

Yiming Li, Jiacheng Qiu, Sylvain Calinon

This research introduces the Neural Riemannian Eikonal Solver (NES), a physics-informed neural network framework designed to learn geodesic distance fields on Riemannian manifolds. It enables the generation of dynamics-aware and energy-efficient motion plans for high-dimensional robots, demonstrating improved energy efficiency and scalability over traditional methods.

Key insights

• Physics-informed neural networks can effectively learn globally consistent, continuous, and differentiable geodesic distance fields on high-dimensional Riemannian manifolds by directly incorporating the governing PDE.
• Leveraging Riemannian metrics (e.g., kinetic energy, Jacobi) allows NES to inherently generate dynamics-aware and energy-efficient robot trajectories that minimize relevant physical costs.
• Conditioning the neural network on task-space boundaries or varying metric parameters (C-NES) provides a flexible framework for adapting motion generation to diverse robotic tasks and changing geometric contexts.

Summary by alphaXiv.