Retraction maps in optimal control of nonholonomic systems

2025/04/01 by Alexandre Anahory Simoes, María Barbero-Liñán, Simoes, Alexandre Anahory +7
Engineering · Mathematics · #Control and Dynamics of Mobile Robots #Differential Geometry (math.DG) #Extremum Seeking Control Systems #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2504.00808

openalex publication_date 2025/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 D. 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.

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