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Keywords
(8)
Cost Function
Discrete Mechanics
Equation of Motion
eulerlagrange equation
Mechanical Systems
Optimal Control
Optimal Control Problem
Variational Analysis
Related Publications
(5)
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DISCRETE MECHANICS AND OPTIMAL CONTROL
DISCRETE MECHANICS AND OPTIMAL CONTROL,Oliver Junge,Jerrold E. Marsden,Sina OberBl
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DISCRETE MECHANICS AND OPTIMAL CONTROL
(
Citations: 37
)
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Oliver Junge
,
Jerrold E. Marsden
,
Sina OberBl
A new approach to the solution of
optimal control
problems for
mechanical systems
is proposed. It is based on a direct discretization of the Lagranged'Alembert principle for the system (as opposed to using, for example, collocation or multiple shooting to enforce the equations of motion as constraints). The resulting forced discrete EulerLagrange equations then serve as constraints for the optimization of a given cost functional. We numerically illustrate the method by optimizing a low thrust satellite orbit transfer as well as the reconfiguration of a group of hovercraft in the plane.
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Citation Context
(26)
...While standard optimization methods are based on shooting, multiple shooting, or collocation techniques, recent work on discrete mechanics and optimal control (DMOC) [
5
] employs variational integrators [6], [7] that are derived from the discretization of variational principles such as Hamilton’s principle for conservative systems or the DLA principle for dissipative systems...
Marin B. Kobilarov
,
et al.
Discrete Geometric Optimal Control on Lie Groups
...This kind of strategy is called Discrete Mechanics and Optimal Control (DMOC) and can be found at Marsden and West [75] and Junge et al. [
53
]...
C. Goerzen
,
et al.
A survey of motion planning algorithms from the perspective of autonom...
...These include undercontrolled systems, such as a group of hovercraft that have control in only two of their three degrees of freedom [
3
] and constrained multibody dynamcs [4]...
...A complete discussion and derivation of this discretization can be found in [2], whereas much of the following shorter derivation is taken from [1] and [
3
]...
Kristine L. Snyder
,
et al.
Secondorder DMOC using projection
...d’Alembert principle [
20
], which requires that (7)...
Weizhong Zhang
,
et al.
Opportunistic 3D trajectory generation for the JPL Aerobot with Nonlin...
...Next steps include deriving optimal control laws using DMOC [15], [
8
]; these optimal control laws take into account the angular moment conservation as well as potential impacts and will be more efficient than the simple PD control used here...
Corrina Gibson
,
et al.
Geometric integration of impact during an orbital docking procedure
References
(15)
A Multiple Shooting Algorithm for Direct Solution of Optimal Control Problems
(
Citations: 128
)
H. G. Bock
,
K. J. Plitt
Published in 1984.
A modified Newton method for the solution of illconditioned systems of nonlinear equations with applications to multiple shooting
(
Citations: 34
)
P. Deuflhard
Published in 1974.
SNOPT: An SQP Algorithm For LargeScale Constrained Optimization
(
Citations: 496
)
Philip E. Gill
,
Walter Murray
,
Michael A. Saunders
Journal:
Siam Journal on Optimization  SIAMJO
, 1997
Discrete mechanics and variational integrators
(
Citations: 303
)
J. E. Marsden
Journal:
Acta Numerica
, vol. 10, pp. 357514, 2001
Numerical Solution of Optimal Control Problems by Direct Collocation
(
Citations: 82
)
Oskar Von Stryk
Published in 1993.
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Citations
(37)
Discrete Geometric Optimal Control on Lie Groups
Marin B. Kobilarov
,
Jerrold E. Marsden
Journal:
IEEE Transactions on Robotics  TRob
, vol. 27, no. 4, pp. 641655, 2011
A survey of motion planning algorithms from the perspective of autonomous UAV guidance
(
Citations: 7
)
C. Goerzen
,
Zhaodan Kong
,
Bernard Mettler
Published in 2010.
Discrete mechanics and optimal control: An analysis
(
Citations: 5
)
Sina OberBlöbaum
,
Oliver Junge
,
Jerrold E. Marsden
Journal:
Esaimcontrol Optimisation and Calculus of Variations  ESAIM CONTROL OPTIM CALC VAR
, vol. 16, no. 3, 2010
Secondorder DMOC using projection
(
Citations: 2
)
Kristine L. Snyder
,
Todd D. Murphey
Conference:
Conference on Decision and Control  CDC
, pp. 18721878, 2010
Energy efficient trajectory generation for a statespace based JPL Aerobot
Weizhong Zhang
,
Tamer Inanc
,
Alberto Elfes
Conference:
International Conference on Intelligent RObots and Systems  IROS  IROS
, pp. 41074112, 2010