Conjugate points in nilpotent sub-Riemannian problem on the Engel group
  The left-invariant sub-Riemannian problem on the Engel group is considered. This problem is very important as nilpotent approximation of nonholonomic systems in four-dimensional space with two-dimensional control, for instance of a system which describes movement of mobile trailer robot. We study the local optimality of extremal trajectories and estimate conjugate time in this article. 
A. A. Ardentov, Yu. L. Sachkov
math.OC