# Safe Bubble Cover for Motion Planning on Distance Fields

arXiv: https://arxiv.org/abs/2408.13377 · HTML: https://mlsanity.com/paper/2408.13377/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Aug 2024.

## Built on by (most cited first, 4 of 4)

- [SplatSDF: Boosting SDF-NeRF via Architecture-Level Fusion with Gaussian Splats](https://mlsanity.com/paper/2411.15468/) (2024)
- [Neural Configuration-Space Barriers for Manipulation Planning and Control](https://mlsanity.com/paper/2503.04929/) (2025)
- [From Distances to Trajectories: Real-Time Signed Distance Function Mapping and Distance-Accelerated Motion Planning for UAVs](https://mlsanity.com/paper/2607.19306/) (2026)
- [Learning Scene-Level Signed Directional Distance Function with Ellipsoidal Priors and Neural Residuals](https://mlsanity.com/paper/2503.20066/) (2025)

## Abstract (arXiv)

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.