Physics-informed Temporal Difference Metric Learning for Robot Motion Planning

TL;DR

This paper introduces a novel self-supervised temporal difference metric learning method that improves robot motion planning by better solving the Eikonal equation, especially in complex and unseen environments.

Contribution

It proposes a new approach combining temporal difference learning with metric learning to accurately solve the Eikonal equation for robot motion planning.

Findings

Outperforms existing methods in complex environments

Generalizes well to unseen environments

Handles robot configurations from 2 to 12 DOF

Abstract

The motion planning problem involves finding a collision-free path from a robot's starting to its target configuration. Recently, self-supervised learning methods have emerged to tackle motion planning problems without requiring expensive expert demonstrations. They solve the Eikonal equation for training neural networks and lead to efficient solutions. However, these methods struggle in complex environments because they fail to maintain key properties of the Eikonal equation, such as optimal value functions and geodesic distances. To overcome these limitations, we propose a novel self-supervised temporal difference metric learning approach that solves the Eikonal equation more accurately and enhances performance in solving complex and unseen planning tasks. Our method enforces Bellman's principle of optimality over finite regions, using temporal difference learning to avoid spurious local minima while incorporating metric learning to preserve the Eikonal equation's essential geodesic properties. We demonstrate that our approach significantly outperforms existing self-supervised learning methods in handling complex environments and generalizing to unseen environments, with robot configurations ranging from 2 to 12 degrees of freedom (DOF).