Safe Bubble Cover for Motion Planning on Distance Fields

TL;DR

This paper introduces a novel approach for motion planning using safe bubbles derived from distance fields, significantly reducing computational costs and improving efficiency in collision-free trajectory planning.

Contribution

The paper proposes three new algorithms for constructing safe bubble covers and a hierarchical planning method that combines sampling with convex optimization.

Findings

Up to 10 times cost reduction compared to baselines

Orders of magnitude reduction in computational effort

Effective safe bubble coverage for collision-free planning

Abstract

We consider the problem of planning collision-free trajectories on distance fields. Our key observation is that querying a distance field at one configuration reveals a region of safe space whose radius is given by the distance value, obviating the need for additional collision checking within the safe region. We refer to such regions as safe bubbles, and show that safe bubbles can be obtained from any Lipschitz-continuous safety constraint. Inspired by sampling-based planning algorithms, we present three algorithms for constructing a safe bubble cover of free space, named bubble roadmap (BRM), rapidly exploring bubble graph (RBG), and expansive bubble graph (EBG). The bubble sampling algorithms are combined with a hierarchical planning method that first computes a discrete path of bubbles, followed by a continuous path within the bubbles computed via convex optimization. Experimental results show that the bubble-based methods yield up to 5- 10 times cost reduction relative to conventional baselines while simultaneously reducing computational efforts by orders of magnitude.