Distributed Task Allocation in Homogeneous Swarms Using Language Measure Theory

Abstract: In this paper, we present algorithms for synthesizing controllers to distribute a group (possibly swarms) of homogeneous robots (agents) over heterogeneous tasks which are operated in parallel. We present algorithms as well as analysis for global and local-feedback-based controller for the swarms. Using ergodicity property of irreducible Markov chains, we design a controller for global swarm control. Furthermore, to provide some degree of autonomy to the agents, we augment this global controller by a local feedback-based controller using Language measure theory. We provide analysis of the proposed algorithms to show their correctness. Numerical experiments are shown to illustrate the performance of the proposed algorithms.