Zermelo-Markov-Dubins with two trailers

We study the minimum time problem for a simplified model of a ship towing a long spread of cables. Constraints are on the curvature of the trajectory as well as on the shape of what represent the spread of cables here. This model turns out to be the same as a cart towing two trailers and rolling without sleeping on a plane in uniform translation. We analyse the Hamiltonian system describing the extremal flow given by Pontrjagin maximum principle. We detail the equilibria of the system and prove that, contrary to the case of one trailer studied previously by part of the authors, it is not solvable by quadratures. Preliminary numerical results are given.