Retraction maps in optimal control of nonholonomic systems
Numerical Analysis
2025-04-02 v1 Numerical Analysis
Differential Geometry
Optimization and Control
Abstract
In this paper, we compare the performance of different numerical schemes in approximating Pontryagin's Maximum Principle's necessary conditions for the optimal control of nonholonomic systems. Retraction maps are used as a seed to construct geometric integrators for the corresponding Hamilton equations. First, we obtain an intrinsic formulation of a discretization map on a distribution . Then, we illustrate this construction on a particular example for which the performance of different symplectic integrators is examined and compared with that of non-symplectic integrators.
Keywords
Cite
@article{arxiv.2504.00808,
title = {Retraction maps in optimal control of nonholonomic systems},
author = {Alexandre Anahory Simoes and María Barbero Liñán and Anthony Bloch and Leonardo Colombo and David Martín de Diego},
journal= {arXiv preprint arXiv:2504.00808},
year = {2025}
}
Comments
Conference paper