Section: New Results

Extensions of the Zermelo-Markov-Dubins problem in optimal control

Participants : Ahmed Dieng, Jean-Baptiste Caillau, Jean-Baptiste Pomet, Sofya Maslovskaya.

Motivated by a collaboration with CGG in 2018, we continued investigating minimum time problems for simplified kinematic models of a marine vessel towing some equipments, with various curvature constraints. These are extensions (by adding the towed equipment) of the so-called Zermelo-Markov-Dubins problem. In [12], we describe the problem with the simplest possible model of the trailer, and show that the Hamiltonian system resulting from Pontryagin Principle for minimum time is integrable in that case, both for the “regular” flow and for the flow giving singular extremals; without giving an explicit analytic soltuon, this drastically simplifies the computation of optimal solutions; a description of the marine application solution is also given.

Ahmed Dieng's internship was the opportunity to test more complex models numerically and to have a qualitative approach of the results from [12].

Note that the collaboration with CGG (we had a short bilateral contract with this company in 2018) did not continue mainly because they stopped this activity and more generally marine acquisition. This recent press release details the transactions.