A discrete variational integrator for optimal control problems on SO(3)

Islam I. Hussein; Melvin Leok; Amit K. Sanyal; Anthony M. Bloch

doi:10.1109/cdc.2006.377818

A discrete variational integrator for optimal control problems on SO(3)

Islam I. Hussein, Melvin Leok, Amit K. Sanyal, Anthony M. Bloch

Department of Mechanical & Aerospace Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

25 Scopus citations

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 uše 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.

Original language	English (US)
Title of host publication	Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	6636-6641
Number of pages	6
ISBN (Print)	1424401712, 9781424401710
DOIs	https://doi.org/10.1109/cdc.2006.377818
State	Published - 2006
Event	45th IEEE Conference on Decision and Control 2006, CDC - San Diego, CA, United States Duration: Dec 13 2006 → Dec 15 2006

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0191-2216

Other

Other	45th IEEE Conference on Decision and Control 2006, CDC
Country	United States
City	San Diego, CA
Period	12/13/06 → 12/15/06

ASJC Scopus subject areas

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

Access to Document

10.1109/cdc.2006.377818

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Hussein, I. I., Leok, M., Sanyal, A. K., & Bloch, A. M. (2006). A discrete variational integrator for optimal control problems on SO(3). In Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC (pp. 6636-6641). [4177888] (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/cdc.2006.377818

A discrete variational integrator for optimal control problems on SO(3). / Hussein, Islam I.; Leok, Melvin; Sanyal, Amit K.; Bloch, Anthony M.

Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC. Institute of Electrical and Electronics Engineers Inc., 2006. p. 6636-6641 4177888 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Hussein, II, Leok, M, Sanyal, AK & Bloch, AM 2006, A discrete variational integrator for optimal control problems on SO(3). in Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC., 4177888, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 6636-6641, 45th IEEE Conference on Decision and Control 2006, CDC, San Diego, CA, United States, 12/13/06. https://doi.org/10.1109/cdc.2006.377818

Hussein II, Leok M, Sanyal AK, Bloch AM. A discrete variational integrator for optimal control problems on SO(3). In Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC. Institute of Electrical and Electronics Engineers Inc. 2006. p. 6636-6641. 4177888. (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/cdc.2006.377818

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