Continuum Mechanical Analysis of Collective Motion of Robots

Abstract

Group of robots that works mainly in macroscopic systems is considered as a continuum. We need not mount specific sensors for mutual information among these robots. Increasing number of the robots makes it difficult to predict collective motion of the robots. To give a well organized strategy of designing the task, we describe these robots as that like fluid in continuum mechanics, where number density $f_1 (\vec{x},\vec{p}; t)$ of the robots located at around $\vec{x}$ with momentum around $\vec{p}$ at time $t$ is a main variable. Also we propose methods to move these robots by external potential energy $V(\vec{x};t)$. To specify a concept, we take a transportation system by group of robots. The objects located at $\vec{X}(t)$ that do not feel a potential $V(\vec{X}(t);t)$ can be transported by a collision with the robots moving aimlessly under the potential force $-\frac{\partial V(\vec{x};t)}{\partial \vec{x}}$. The new scheme of a design based on continuum mechanics is validated by direct method of dynamical development of the system in time.