Cooperative behavior of nano-robots as an analogous of the quantum harmonic oscillator. (English) Zbl 1186.68473
Summary: A multi-robot system that consists of N nano-robots is studied. 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 Schrödinger’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.
MSC:
| 68T40 | Artificial intelligence for robotics |
| 60G07 | General theory of stochastic processes |
| 70B05 | Kinematics of a particle |
| 70F45 | The dynamics of infinite particle systems |
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 82C22 | Interacting particle systems in time-dependent statistical mechanics |
| 82C31 | Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics |
| 93E03 | Stochastic systems in control theory (general) |
| 93A14 | Decentralized systems |
| 93A30 | Mathematical modelling of systems (MSC2010) |
Keywords:
multi-robot systemReferences:
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