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Discrete Mechanics and Optimal Control for Space Trajectory Design


Moore, Ashley (2011) Discrete Mechanics and Optimal Control for Space Trajectory Design. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/ZXTG-V056.


Space trajectory design is often achieved through a combination of dynamical systems theory and optimal control. The union of trajectory design techniques utilizing invariant manifolds of the planar circular restricted three-body problem and the optimal control scheme Discrete Mechanics and Optimal Control (DMOC) facilitates the design of low-energy trajectories in the N-body problem. In particular, DMOC is used to optimize a trajectory from the Earth to the Moon in the 4-body problem, removing the mid-course change in velocity usually necessary for such a trajectory while still exploiting the structure from the invariant manifolds.

This thesis also focuses on how to adapt DMOC, a method devised with a constant step size, for the highly nonlinear dynamics involved in trajectory design. Mesh refinement techniques that aim to reduce discretization errors in the solution and energy evolution and their effect on DMOC optimization are explored and compared with trajectories created using time adaptive variational integrators.

Furthermore, a time adaptive form of DMOC is developed that allows for a variable step size that is updated throughout the optimization process. Time adapted DMOC is based on a discretization of Hamilton's principle applied to the time adapted Lagrangian of the optimal control problem. Variations of the discrete action of the optimal control Lagrangian lead to discrete Euler-Lagrange equations that can be enforced as constraints for a boundary value problem. This new form of DMOC leads to the accurate and efficient solution of optimal control problems with highly nonlinear dynamics. Time adapted DMOC is tested on several space trajectory problems including the elliptical orbit transfer in the 2-body problem and the reconfiguration of a cubesat.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:trajectory design; optimal control; variational integrators with time adaption; discrete mechanics; mesh refinement
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Control and Dynamical Systems
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Marsden, Jerrold E. (advisor)
  • Murray, Richard M. (advisor)
Thesis Committee:
  • Murray, Richard M. (chair)
  • Desbrun, Mathieu
  • Ortiz, Michael
  • Ober-Blobaum, Sina
Defense Date:17 May 2011
Non-Caltech Author Email:moore.ashley (AT)
Record Number:CaltechTHESIS:05252011-164957222
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6441
Deposited By: Ashley Moore
Deposited On:27 May 2011 22:05
Last Modified:09 Oct 2019 17:10

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