Geometric aspects of robot navigation: From individual Robots to massive particle swarms

Abstract

We describe a spectrum of challenges and results related to geometric aspects of robot navigation, advancing from centralized methods for difficult offline problems (such as the Art Gallery Problem), to online tasks for many Robots (as in online exploration by a swarm of Robots), locally managing the connectivity and shape of a large swarm (i.e., cohesive control), all the way to controlling massive swarms of particles by global forces.