Local controllability of trident snake robot based on sub-Riemannian extremals

Abstract

To solve trident snake robot local controllability by differential geometry tools, we construct a privileged system of coordinates with respect to the distribution given by Pffaf system based on local nonholonomic conditions and, furthermore, we construct a nilpotent approximation of the transformed distribution with respect to the given filtration. We compute normal extremals of sub-Riemanian structure, where the Hamiltonian point of view was used. We demonstrated that the extremals of sub-Riemannian structure based on this distribution play the similar role as classical periodic imputs in control theory with respect of our mechanism.To solve trident snake robot local controllability by differential geometry tools, we construct a privileged system of coordinates with respect to the distribution given by Pffaf system based on local nonholonomic conditions and, furthermore, we construct a nilpotent approximation of the transformed distribution with respect to the given filtration. We compute normal extremals of sub-Riemanian structure, where the Hamiltonian point of view was used. We demonstrated that the extremals of sub-Riemannian structure based on this distribution play the similar role as classical periodic imputs in control theory with respect of our mechanism.