# Multitasking collision-free motion planning algorithms in Euclidean spaces

## TL;DR

This paper introduces optimal multitasking collision-free motion planning algorithms in Euclidean spaces, minimizing local planners and improving efficiency for systems with many moving objects.

## Contribution

The paper develops new optimal algorithms for multitasking motion planning in Euclidean spaces, extending previous work and aiming for better efficiency in complex multi-object systems.

## Key findings

- Algorithms are optimal with minimal local planners.
- Expected to outperform previous algorithms in large multi-object systems.
- Based on and extending prior work by Mas-Ku, Torres-Giese, and Farber.

## Abstract

We present optimal motion planning algorithms which can be used in designing practical systems controlling objects moving in Euclidean space without collisions. Our algorithms are optimal in a very concrete sense, namely, they have the minimal possible number of local planners. Our algorithms are motivated by those presented by Mas-Ku and Torres-Giese (as streamlined by Farber), and are developed within the more general context of the multitasking (a.k.a.~higher) motion planning problem. In addition, an eventual implementation of our algorithms is expected to work more efficiently than previous ones when applied to systems with a large number of moving objects.