Primer Vector Theory Applied to Global Low-Thrust Trade Studies

The low-thrust spacecraft trajectory problem can be reduced to only a few parameters using calculus of variations and the well-known primer vector theory. This low dimensionality combined with the extraordinary speed of modern computers allows for rapid exploration of the parameter space and invites...

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Bibliographic Details
Published in:Journal of guidance, control, and dynamics control, and dynamics, 2007-03, Vol.30 (2), p.460-472
Main Author: Russell, Ryan P
Format: Article
Language:English
Subjects:
Applied sciences
Calculus
Computer science
control theory
systems
Computers
Control theory. Systems
Copyright
Exact sciences and technology
Laboratories
Lagrange multiplier
Methods
Optimization
Orbits
Velocity
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Summary:The low-thrust spacecraft trajectory problem can be reduced to only a few parameters using calculus of variations and the well-known primer vector theory. This low dimensionality combined with the extraordinary speed of modern computers allows for rapid exploration of the parameter space and invites opportunities for global optimization. Accordingly, a general low-thrust trade analysis tool is developed based on a global search for local indirect method solutions. An efficient propagator is implemented with an implicit 'bang-bang'thrusting structure that accommodates an a priori unknown number of switching times. An extension to the standard adjoint control transformation is introduced that provides additional physical insight andcontrol over the anticipated evolution of the thrust profile. The uniformly random search enjoys a perfect linear speedup for parallel implementation. The method is applied specifically on multirevolution transfers in the Jupiter-Europa and Earth-moon restricted three body problems. In both cases, thousands of solutions are found in a single parallel run. The result is a global front of Pareto optimal solutions across the competing objectives of flight time and final mass.
ISSN:0731-5090
1533-3884
DOI:10.2514/1.22984