Abstract
Communication is of key importance for the control of unmanned aerial vehicle (UAV) networks. From the viewpoint of statistical mechanics, it plays the role of bond and correlation in the ensemble of particles. A statistical mechanics model is set for UAV networks with limited communication ranges, including potentials and stochastic evolutions. Based on the framework, an equation describing the behavior of UAV network, in terms of canonical thermodynamics metrics, is derived using the technique of cluster expansion. The critical temperature, characterizing the phase transition (between unstable and stable), is derived in explicit expression. Numerical simulation shows that the statistical mechanics analysis provides an operable estimation on the stability condition of UAV networks, in terms of communication range. In particular, it is shown that the critical temperature (the power of random perturbation) follows a power law in terms of the communication range, given the model adopted in this paper.
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