Distributed Task Allocation in Homogeneous Swarms Using Language Measure Theory

TL;DR

This paper introduces algorithms for controlling homogeneous robot swarms to efficiently distribute over multiple tasks using language measure theory and Markov chain ergodicity, with proven correctness and demonstrated performance.

Contribution

It presents novel algorithms combining global and local feedback controllers based on language measure theory for task allocation in homogeneous swarms.

Findings

Algorithms are proven correct through analysis.

Numerical experiments demonstrate effective task distribution.

Controllers leverage ergodicity of Markov chains for global control.

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.