A Comparison of Linear Guidance Techniques, Applied to a Low-Thrust Orbit Transfer Problem

Citation

Stoker, Pieter Wilhelm (1975) A Comparison of Linear Guidance Techniques, Applied to a Low-Thrust Orbit Transfer Problem. Engineer's thesis, California Institute of Technology. doi:10.7907/2a06-sk90. https://resolver.caltech.edu/CaltechTHESIS:09032021-212451524

Abstract

The problem considered is that of a three-dimensional, minimum time, heliocentric, Earth-Mars transfer of a continuous low-thrust rocket vehicle.

The first order necessary conditions of the calculus of variations define the optimal trajectory in terms of a nonlinear first order two-point boundary-value problem, which is solved by the backward-sweep method. The calculation of a set of feedback gain matrices, a cross-check on the numerical accuracy of these matrices, and the satisfaction of a set of necessary conditions for the trajectory to be at least locally minimizing are done simultaneously.

The spacecraft is then perturbed from the nominal trajectory, and two neighboring optimum feedback control laws, the so-called time-to-go guidance technique, and minimum distance guidance technique are compared.

In-plane and out-of-plane perturbations are considered, and both guidance techniques, in most cases, reduce the initial error, although not by a very large factor.

It is shown that the minimum distance technique, as applied in this study, performs much better than found by Lattimore.¹

¹Lattimore, J. P. "A Comparison of Open and Closed Loop Applications of the Minimum Distance Guidance Technique," University of Texas at Austin, Engineer's Degree Dissertation, 1972.

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