Geometric Optimal Trajectory Tracking of Nonholonomic Mechanical Systems

Colombo LJ, Martín de Diego D, Nayak A, Sato Martin de Almagro R (2020)

Publication Language: English

Publication Status: Published

Publication Type: Journal article, Original article

Future Publication Type: Journal article

Publication year: 2020

Journal

SIAM Journal on Control and Optimization Society for Industrial and Applied Mathematics

Publisher: Society for Industrial and Applied Mathematics

Edited Volumes: SIAM Journal on Control and Optimization

Book Volume: 58

Pages Range: 1652-1675

Journal Issue: 3

DOI: 10.1137/19M1243464

Abstract

We study the tracking of a trajectory for a nonholonomic system by recasting the problem as a constrained optimal control problem. The cost function is chosen to minimize the error in positions and velocities between the trajectory of a nonholonomic system and the desired reference trajectory, both evolving on the distribution which defines the nonholonomic constraints. The problem is studied from a geometric framework. Optimality conditions are determined by the Pontryagin Maximum Principle and also from a variational point of view, which allows the construction of geometric integrators. Examples and numerical simulations are shown to validate the results.

Authors with CRIS profile

Rodrigo Sato Martin de Almagro Institute of Applied Dynamics

Involved external institutions

Universidad Autónoma de Madrid (UAM) ES Spain (ES) Mines ParisTech / École Nationale Supérieure des Mines de Paris (ENSMP) FR France (FR) Spanish National Research Council / Consejo Superior de Investigaciones Científicas (CSIC) ES Spain (ES)

How to cite

APA:

Colombo, L.J., Martín de Diego, D., Nayak, A., & Sato Martin de Almagro, R. (2020). Geometric Optimal Trajectory Tracking of Nonholonomic Mechanical Systems. SIAM Journal on Control and Optimization, 58(3), 1652-1675. https://dx.doi.org/10.1137/19M1243464

MLA:

Colombo, Leonardo Jesús, et al. "Geometric Optimal Trajectory Tracking of Nonholonomic Mechanical Systems." SIAM Journal on Control and Optimization 58.3 (2020): 1652-1675.

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