# Characterizing minimum-length coordinated motions for two discs

arXiv: https://arxiv.org/abs/1607.04005 · HTML: https://mlsanity.com/paper/1607.04005/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jul 2016.

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

- [Reconfiguring Shortest Paths in Graphs](https://mlsanity.com/paper/2112.07499/) (2021)

## Abstract (arXiv)

We study the problem of determining optimal coordinated motions for two disc robots in an otherwise obstacle-free plane. Using the total path length traced by the two disc centres as a measure of distance, we give an exact characterization of a shortest collision-avoiding motion for all initial and final configurations of the robots. The individual paths are composed of at most six (straight or circular-arc) segments, and their total length can be expressed as a simple integral with a closed form solution depending only on the initial and final configuration of the robots. Furthermore, the paths can be parametrized in such a way that (i) only one robot is moving at any given time (decoupled motion), or (ii) the angle between the two robots' centres changes monotonically.