Decentralized coordination of autonomous swarms using parallel Gibbs sampling

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, nearest-neighbor 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.