Article Contents
Article Contents

# Optimal control of underactuated mechanical systems with symmetries

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

 Citation:

•  [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.
Open Access Under a Creative Commons license