Optimal control of underactuated mechanical systems with symmetries

Leonardo Colombo; David Martín de Diego

doi:10.3934/proc.2013.2013.149

Article Contents

2013, Volume 2013: 149-158. Doi: 10.3934/proc.2013.2013.149 open access

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Optimal control of underactuated mechanical systems with symmetries

Leonardo Colombo^1, and
David Martín de Diego^2,

1.
Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), Calle Nicolás Cabrera 15, 28049, Madrid
2.
Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM, Campus de Cantoblanco, UAM, C/Nicolás Cabrera, 15, 28049 Madrid

Received: August 2012

Revised: November 2012

Published: October 2013

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Abstract

The aim of this paper is to study optimal control problems for underactuated mechanical systems with symmetries using higher-order Lagrangian mechanics. We variationally derive the corresponding Lagrange -Poincaré equations for second-order Lagrangians with constraints defined on trivial principal bundles and apply them to study an optimal control problem for an underactuated vehicle.

Keywords:

Mathematics Subject Classification: Primary: 70Q05, 70G75, 70G65; Secondary: 70H50, 70H03.

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References

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