Topological complexity of collision free motion planning algorithms in the presence of multiple moving obstacles

TL;DR

This paper analyzes the topological complexity of collision-free motion planning algorithms involving multiple moving objects and obstacles, providing insights that could improve automated traffic control systems.

Contribution

It introduces a topological framework for understanding the complexity of motion planning with moving obstacles, using cohomology algebra of configuration spaces.

Findings

Computed topological complexity for multi-object motion planning

Applied cohomology algebra to configuration spaces

Results applicable to automatic traffic control systems

Abstract

We study motion planning algorithms for collision free control of multiple objects in the presence of moving obstacles. We compute the topological complexity of algorithms solving this problem. We apply topological tools and use information about cohomology algebras of configuration spaces. The results of the paper may potentially be used in systems of automatic traffic control.