Decentralized coordination of autonomous swarms using parallel Gibbs sampling

Xiaobo Tana, Wei Xi, John S. Baras

Automatica 46 (2010) 2068–2076

Abstract:

In this paper we present analysis of a discrete-time, decentralized, stochastic coordination algorithm for a
group of mobile nodes, called an autonomous swarm, on a finite spatial lattice. All nodes take their moves
by sampling in parallel their locally perceived Gibbs distributions corresponding to a pairwise, nearestneighbor
potential. The algorithm has no explicit requirements on the connectedness of the underlying
information graph, which varies with the swarm configuration. It is established that, with an appropriate
annealing schedule, the algorithm results in swarm configurations converging to the (global) minimizers
of a modified potential energy function. The extent of discrepancy between the modified and original
potential energy functions is determined by the maximum node travel between time steps, and when
such distance is small, the ultimate swarm configurations are close to the global minimizers of the original
potential energy. Simulation results are further presented to illustrate the capability of the sampling
algorithm in approximate global optimization for swarms.