Primer Vector Theory Applied to Global Low-Thrust Trade Studies

Abstract

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 and control 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.

Target sequence optimization for multiple debris rendezvous using low thrust based on characteristics of SSO

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“…(36), valid only when ε > 0. For the fuel optimal problem (ε = 0), a chain rule should be applied to string together a sequence of partial derivatives with "bangbang" switching point between them [21].…”

A survey on orbital dynamics and navigation of asteroid missions

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A fast, accurate, and smooth planetary ephemeris retrieval system

“…FIRE is particularly suited for problems that favor higher speeds and smooth derivatives, such as trajectory optimization (Russell 2007(Russell , 2004Hull 1979;Sauer 1989), orbit determination (Campbell and Speckman 2004;Russell and Lara 2007;Koon et al 1999;Lo et al 2004) and Monte Carlo sensitivity analysis (Desai and Cheatwood 1999;Aiello 2005). The new system generally favors speed in sacrifice of relatively more memory.…”