Lagrange-Poincaré reduction for optimal control of underactuated mechanical systems

2013/06/25 by Colombo, Leonardo
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1306.6005

Abstract

We deal with regular Lagrangian constrained systems which are invariant under the action of a symmetry group. Fixing a connection on the higher-order principal bundle where the Lagrangian and the (independent) constraints are defined, the higher-order Lagrange-Poincaré equations of classical mechanical systems with higher-order constraints are obtained from classical Lagrangian reduction. Higher-order Lagrange-Poincaré operator is introduced to characterize higher-order Lagrange-Poincaré equations. Interesting applications are derived as, for instance, the optimal control of an underactuated Elroy's Beanie and a snakeboard seens as an optimization problem with higher-order constraints.

Related

• The variational discretization of the constrained higher-order Lagrange-Poincaré equations
• Variational integrators for underactuated mechanical control systems with symmetries
• A new Lagrangian approach to optimal control of second-order systems
• Control problems with differential constraints of higher order
• On the geometry of higher-order variational problems on Lie groups