Parametrised collision-free optimal motion planning algorithms in Euclidean spaces

TL;DR

This paper introduces parametrised motion planning algorithms for collision-free movement of point objects in even-dimensional Euclidean spaces with up to three unknown obstacles, optimizing local planner size.

Contribution

It presents the first optimal parametrised motion planning algorithms for systems with unknown obstacle positions in Euclidean spaces.

Findings

Algorithms are optimal with minimal local planner size.

Applicable to systems with up to three unknown obstacles.

Effective in even-dimensional Euclidean spaces.

Abstract

We describe parametrised motion planning algorithms for systems controlling objects represented by points that move without collisions in an even dimensional Euclidean space and in the presence of up to three obstacles with \emph{a priori} unknown positions. Our algorithms are optimal in the sense that the parametrised local planners have minimal posible size.