TY - GEN
T1 - A discrete variational integrator for optimal control problems on SO(3)
AU - Hussein, Islam I.
AU - Leok, Melvin
AU - Sanyal, Amit K.
AU - Bloch, Anthony M.
N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2006
Y1 - 2006
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=39649097658&partnerID=8YFLogxK
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U2 - 10.1109/cdc.2006.377818
DO - 10.1109/cdc.2006.377818
M3 - Conference contribution
AN - SCOPUS:39649097658
SN - 1424401712
SN - 9781424401710
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 6636
EP - 6641
BT - Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 45th IEEE Conference on Decision and Control 2006, CDC
Y2 - 13 December 2006 through 15 December 2006
ER -