Parametrised collision-free optimal motion planning algorithms in 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.

arXiv comment16 pages. Final version. To appear in Morfismos