Optimal control of underactuated mechanical systems with symmetries

Pages: 149 - 158, Issue special, November 2013

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Leonardo Colombo - Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), Calle Nicolás Cabrera 15, 28049, Madrid, Spain (email)
David Martín de Diego - Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM, Campus de Cantoblanco, UAM, C/Nicolás Cabrera, 15, 28049 Madrid, Spain (email)

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:  Euler-Poincaré, optimal control, underactuated systems.
Mathematics Subject Classification:  Primary: 70Q05, 70G75, 70G65; Secondary: 70H50, 70H03.

Received: August 2012;      Revised: November 2012;      Published: November 2013.