Macroscopic modeling of stochastic deployment policies with time delays for robot ensembles

We consider the dynamic assignment and reassignment of a homogeneous robot ensemble to multiple spatially located tasks with deterministic or near-deterministic task execution times. Similar to Halasz et al. and Berman et al., we consider the development of agent-level, i.e. microscopic, stochastic control policies through the analysis of an appropriate macroscopic analytical model that describes the dynamics of the ensemble. Specifically, we present an approach to better approximate the effects of deterministic microscopic time delays at the macroscopic level based on Padé approximants. We present, analyze, and compare the frequency response of our approach to that presented by Berman et al. using different agent-based simulations.

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