Swarming control using parallel Gibbs sampling

In the prior work of the author and his coworkers, Gibbs sampling was proposed for coordination of autonomous swarms, where convergence results were only obtained for sequential sampling with additional requirement of modest global communication. In this paper the convergence behavior is investigated under parallel Gibbs sampling, where all mobile nodes update their locations simultaneously. It is established that, with a pairwise Gibbs potential, parallel Gibbs sampling and annealing minimizes a modified potential energy, where the extent of modification is determined by the maximum travel range of each node within one time step. This is the first convergence result for parallel sampling algorithms for Gibbs random fields with configuration-dependent neighborhood systems, and it provides justification for Gibbs sampling as a viable method for swarming control. The latter is further illustrated with simulation results.