Labor division for swarm robotic systems with arbitrary finite number of task types

In this paper we address the problem of modelling labor division when the number of task types is arbitrary finite integer for homogeneous robot swarms in the foraging scenario. The aim of labor division is to let the proportion of various tasks foraged by robotic swarm equal to the density of various tasks in the environment. The improved observation model is proposed to estimate transition rates in Markov process. Specifically instead of using a first-order differential equation which is only applicable for case study, we present a matrix differential equation to characterize the dynamics of generalised labor division. We use eigenvalue theory and matrix diagonalization method to derive the analytic solution of the proposed equation. And through analysing the steady state of individual dynamics the averaged global labor division of the swarm is deduced theoretically. The experiments verify that the new mathematical model shows excellent agreement with simulation results.