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A novel approach for analysing collective dynamics of large-scale multi-robot system in task allocation

In this paper we propose a generalized macroscopic mathematical model to analyse multi-robot system (MRS) engaged in task allocation. Our novel model outperforms other existing ones because of the number of task types is arbitrary limited number rather than a fixed number. We find the statistic law of macroscopic variable which reflects the collective dynamics, and from its property we can predict both positive and negative effects of emergent task allocation. A two-dimensional Markov process is employed to model the state transitions of the whole MRS directly. Our proposed analysis model has closed-form expressions, such that we find relationship between collective performance and the model parameter which makes an impact on the system performance. We conduct simulations with dozens and hundred number of robots. The experiments verify the mathematical model and illustrate that the model shows excellent agreement with simulation results.