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Cooperative behavior of mobile robots as a macro-scale analogous of the quantum harmonic oscillator

This paper studies a model of cooperative behavior in a multi-robot system that consists of N mobile robots. It is assumed that the robots correspond to diffusing particles, and interact to each other as the theory of Brownian motion predicts. Brownian motion is the analogous of the quantum harmonic oscillator (Q.H.O.), i.e. of Schrodinger's equation under harmonic (parabolic) potential. It is shown that the motion of the robots can be described by Langevin's equation which is a stochastic linear differential equation. It is proved that Langevin's equation is a generalization of conventional gradient algorithms. Therefore the kinematic models of mobile robots which follow conventional gradient algorithms can be considered as a subcase of the kinematic models which are derived from the diffusion analogous of the Q.H.O model.