“Brownian motion” by macroscopic group robots
We apply microscopic Brownian motion to macroscopic transportation systems by group of robots with energy dissipation. We extend continuum mechanical picture of group robots so far developed by the author. We treat systems where frictional force proportional to velocity acts on each robot. Taking Hamiltonian with specified exponential function of time allows us to deal with motion of robots by canonical equation. We give methods how to explicitly calculate force between robots and the object that is to be transported. For this we set up an ordinary time-differential equation for temperature parameter. That parameter characterizes distribution function of robots in approximate
equilibrium. We make use of the formula of the force in simulation studies. We obtain physically adequate results that the small/large frictional coefficient values lead to good/bad transportation characteristics. Comparison of our results based on continuum picture of robots with those by Newtonian mechanics for robots and objects leads to good agreement.
CYBERNETICS AND PHYSICS, Vol. 1, No. 4, 2012 , 258–265.