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2013, 2013(special): 149-158. doi: 10.3934/proc.2013.2013.149

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, Spain
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  November 2013

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: optimal control, Euler-Poincaré, underactuated systems..
Mathematics Subject Classification: Primary: 70Q05, 70G75, 70G65; Secondary: 70H50, 70H0.
Citation: Leonardo Colombo, David Martín de Diego. Optimal control of underactuated mechanical systems with symmetries. Conference Publications, 2013, 2013 (special) : 149-158. doi: 10.3934/proc.2013.2013.149
References:
[1]

A. Bloch, Nonholonomic Mechanics and Control, Interdisciplinary Applied Mathematics Series vol.24, Springer-Verlag, New-York, 2003.

[2]

F. Bullo and A. Lewis, Geometric control of mechanical systems: Modeling, Analysis, and Design for Simple Mechanical Control Systems, Texts in Applied Mathematics, Springer Verlang, New York, 2005.

[3]

H. Cendra, J. Marsden, T. Ratiu., Lagrangian reduction by stages. Memoirs of the American Mathematical Society, 152 (722). pp. 1-108. (2001)

[4]

L. Colombo and D. Martín de Diego, On the geometry of higher-order variational problems on Lie groups, arXiv:1104.3221v1 (2011).

[5]

A. Lewis, R. Murray, Variational principles for constrained systems: Theory and experiment. Int. J. nonlinear mech. 30 (1995), no. 6, 793-815.

show all references

References:
[1]

A. Bloch, Nonholonomic Mechanics and Control, Interdisciplinary Applied Mathematics Series vol.24, Springer-Verlag, New-York, 2003.

[2]

F. Bullo and A. Lewis, Geometric control of mechanical systems: Modeling, Analysis, and Design for Simple Mechanical Control Systems, Texts in Applied Mathematics, Springer Verlang, New York, 2005.

[3]

H. Cendra, J. Marsden, T. Ratiu., Lagrangian reduction by stages. Memoirs of the American Mathematical Society, 152 (722). pp. 1-108. (2001)

[4]

L. Colombo and D. Martín de Diego, On the geometry of higher-order variational problems on Lie groups, arXiv:1104.3221v1 (2011).

[5]

A. Lewis, R. Murray, Variational principles for constrained systems: Theory and experiment. Int. J. nonlinear mech. 30 (1995), no. 6, 793-815.

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