Probabilistic Swarm Guidance using Inhomogeneous Markov Chains

Abstract

Probabilistic swarm guidance involves designing a Markov chain so that each autonomous agent or robot determines its own trajectory in a statistically independent manner. The swarm converges to the desired formation and the agents repair the formation even if it is externally damaged. In this paper, we present an inhomogeneous Markov chain approach to probabilistic swarm guidance algorithms for minimizing the number of transitions required for achieving the desired formation and then maintaining it. With the help of communication with neighboring agents, each agent estimates the current swarm distribution and computes the tuning parameter which is the Hellinger distance between the current swarm distribution and the desired formation. We design a family of Markov transition matrices for a desired stationary distribution, where the tuning parameter dictates the number of transitions. We discuss methods for handling motion constraints and prove the convergence and the stability guarantees of the proposed algorithms. Finally, we apply these proposed algorithms for guidance and motion planning of swarms of spacecraft in Earth orbit.