@inproceedings{55ce9baefc3a491590f914954a2b58b0,

title = "A discrete variational integrator for optimal control problems on SO(3)",

abstract = "In this paper we study a discrete variational optimal control problem for the rigid body. The cost to be minimized is the external torque applied to move the rigid body from an initial condition to a pre-specified terminal condition. Instead of discretizing the equations of motion, we use the discrete equations obtained from the discrete Lagrange-d'Alembert principle, a process that better approximates the equations of motion. Within the discrete-time setting, these two approaches are not equivalent in general. The kinematics are discretized using a natural Lie-algebraic formulation that guarantees that the flow remains on the Lie group SO(3) and its algebra so (3). We u{\v s}e Lagrange's method for constrained problems in the calculus of variations to derive the discrete-time necessary conditions. We give a numerical example for a three-dimensional rigid body maneuver.",

author = "Hussein, {Islam I.} and Melvin Leok and Sanyal, {Amit K.} and Bloch, {Anthony M.}",

year = "2006",

doi = "10.1109/cdc.2006.377818",

language = "English (US)",

isbn = "1424401712",

series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "6636--6641",

booktitle = "Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC",

note = "45th IEEE Conference on Decision and Control 2006, CDC ; Conference date: 13-12-2006 Through 15-12-2006",

}