Nilpotent approximation of a trident snake robot controlling   distribution
  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. 
Jaroslav Hrdina, Ales Navrat, Petr Vasik
math.DG