Zermelo-Markov-Dubins with two trailers

Ludovic Sacchelli (1) , Jean-Baptiste Caillau (2, 3, 4) , Thierry Combot (5) , Jean-Baptiste Pomet (4, 2, 3)

1 LAGEPP - Laboratoire d'automatique, de génie des procédés et de génie pharmaceutique
2 McTAO - Mathematics for Control, Transport and Applications
3 UniCA - Université Côte d'Azur
4 LJAD - Laboratoire Jean Alexandre Dieudonné
5 IMB - Institut de Mathématiques de Bourgogne [Dijon]

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.

Mots clés: turnpike; Zermelo navigation; minimum time; Kovacic algorithm; integrability

Domaines: Optimisation et contrôle [math.OC]

Ludovic Sacchelli, Jean-Baptiste Caillau, Thierry Combot, Jean-Baptiste Pomet. Zermelo-Markov-Dubins with two trailers. LHMNC 2021 - 7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, Oct 2021, Berlin, Germany. pp.249-245, ⟨10.1016/j.ifacol.2021.11.086⟩. ⟨hal-03211710v3⟩