Optimal Trajectory Tracking for Differentially Flat Systems with Singularities

The purpose of this paper is twofold: on one hand to analyse some properties of a class of differentially flat systems having particular singularities, and, on the other hand, to propose an adaptation of existing online optimal control strategies like NTG in order to take into account those singularities as well as constraints like bounds on the inputs.The system we are interested in is a mobile robot with several steering wheels, but we will present the main ideas for a simpler system called "symmetric crane" which has similar structural properties. The optimal control problem considered is to minimize an error w.r.t. a reference trajectory.