Analysis of a Stochastic Model of Adaptive Task Allocation in Robots

Adaptation is an essential requirement for self-organizing multi-agent systems functioning in unknown dynamic environments. Adaptation allows agents to change their actions in response to environmental changes or actions of other agents in order to improve overall system performance, and remain robust even while a sizeable fraction of agents fails. In this paper we present and study a simple model of adaptation for task allocation problem in a multi-robot system. In our model robots have to choose between two types of task, and the goal is to achieve desired task division without any explicit communication between robots. Robots estimate the state of the environment from repeated local observations and decide what task to choose based on these observations. We model robots and observations as stochastic processes and study the dynamics of individual robots and the collective behavior. We validate our analysis with numerical simulations.