Feedback-Based Inhomogeneous Markov Chain Approach To Probabilistic Swarm Guidance

Abstract

This paper presents a novel and generic distributed swarm guidance algorithm using inhomogeneous Markov chains that guarantees superior performance over existing homogeneous Markov chain based algorithms, when the feedback of the current swarm distribution is available. The probabilistic swarm guidance using inhomogeneous Markov chain (PSG–IMC) algorithm guarantees sharper and faster convergence to the desired formation or unknown target distribution, minimizes the number of transitions for achieving and maintaining the formation even if the swarm is damaged or agents are added/removed from the swarm, and ensures that the agents settle down after the swarm’s objective is achieved. This PSG–IMC algorithm relies on a novel technique for constructing Markov matrices for a given stationary distribution. This technique incorporates the feedback of the current swarm distribution, minimizes the coefficient of ergodicity and the resulting Markov matrix satisfies motion constraints. This approach is validated using Monte Carlo simulations of the PSG–IMC algorithm for pattern formation and goal searching applications