Nilpotent approximation of a trident snake robot controlling distribution

TL;DR

This paper develops a local nilpotent approximation for the controlling distribution of a trident snake robot, enabling comparison of its actual motions with simplified models.

Contribution

It introduces a method to construct privileged coordinates and a nilpotent approximation specific to the robot's controlling distribution.

Findings

Constructed privileged coordinate system for the robot

Developed a nilpotent approximation of the controlling distribution

Compared motions of original and approximated systems

Abstract

We construct a privileged system of coordinates with respect to the controlling distribution of a trident snake robot and, furthermore, we construct a nilpotent approximation with respect to the given filtration. Note that all constructions are local in the neighbourhood of a particular point. We compare the motions corresponding to the Lie bracket of the original controlling vector fields and their nilpotent approximation.