Three dimensional deployment of robot swarms

This paper addresses the deployment problem for a swarm of autonomous mobile robots initially randomly distributed in 3 dimensional space. A fully decentralized geometric self-configuration approach is proposed to deploy individual robots at a given spatial density. Specifically, each robot interacts with three neighboring robots in a selective and dynamic fashion without using any explicit communication so that four robots eventually form a regular tetrahedron. Using such local interactions, the proposed algorithms enable a swarm of robots to span a network of regular tetrahedrons in a designated space. The convergence of the algorithms is theoretically proved using Lyapunov theory. Through extensive simulations, we validate the effectiveness and scalability of the proposed algorithms.