On geometric control models of a robotic snake

Abstract

We present three possible ways of controlling a robotic system called a 3-link snake robot. First, we recall the classical approach by constructing the controlling vector fields and their Lie brackets. Next we modify the coordinate system in order to obtain a nilpotent approximation of the controlling distribution. This is based on the notions of sub-Riemannian geometry. The third model is based on serpenoid curve and maintains the global control task.