Parallel iterative methods for variational integration applied to navigation problems

FERRARO, SEBASTIÁN J.; MARTÍN DE DIEGO, DAVID; SATO MARTÍN DE ALMAGRO, RODRIGO T.

Berlin

Workshop; 7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control; 2021

International Federation of Automatic Control

Discrete variational methods have shown an excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative method for discrete variational methods appropriate for boundary value problems. More concretely, we explore a parallelization strategy that leverages the power of multicore CPUs and GPUs(graphics cards). We study this parallel method for first-order and second-order Lagrangians and we illustrate its excellent behavior in some interesting applications, namely Zermelo’s navigation problem, a fuel-optimal navigation problem, and an interpolation problem.