Decentralized State-Dependent Markov Chain Synthesis for Swarm Guidance

This paper introduces a decentralized state-dependent Markov chain synthesis method for probabilistic swarm guidance of a large number of autonomous agents to a desired steady-state distribution. The probabilistic swarm guidance approach is based on using a Markov chain that determines the transition probabilities of agents to transition from one state to another while satisfying prescribed transition constraints and converging to a desired steady-state distribution. Our main contribution is to develop a decentralized approach to the Markov chain synthesis that updates the underlying column stochastic Markov matrix as a function of the state, i.e., the current swarm probability distribution. Having a decentralized synthesis method eliminates the need to have complex communication architecture. Furthermore, the proposed method aims to cause a minimal number of state transitions to minimize resource usage while guaranteeing convergence to the desired distribution. It is also shown that the convergence rate is faster when compared with previously proposed methodologies.