# Quotient-Space Motion Planning

arXiv: https://arxiv.org/abs/1807.09468 · HTML: https://mlsanity.com/paper/1807.09468/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jul 2018.

## Built on by (most cited first, 1 of 1)

- [RecBundle: A Next-Generation Geometric Paradigm for Explainable Recommender Systems](https://mlsanity.com/paper/2603.16088/) (2026)

## Abstract (arXiv)

A motion planning algorithm computes the motion of a robot by computing a path through its configuration space. To improve the runtime of motion planning algorithms, we propose to nest robots in each other, creating a nested quotient-space decomposition of the configuration space. Based on this decomposition we define a new roadmap-based motion planning algorithm called the Quotient-space roadMap Planner (QMP). The algorithm starts growing a graph on the lowest dimensional quotient space, switches to the next quotient space once a valid path has been found, and keeps updating the graphs on each quotient space simultaneously until a valid path in the configuration space has been found. We show that this algorithm is probabilistically complete and outperforms a set of state-of-the-art algorithms implemented in the open motion planning library (OMPL).