Extension of the Proximity-Quotient Control Law for Low-Thrust Propulsion

Paper number

IAC-08.C1.5.3

Author

Ms. Christie Maddock, University of Glasgow, United Kingdom

Coauthor

Dr. Massimiliano Vasile, University of Glasgow, United Kingdom

Year

2008

Abstract

The proximity-quotient control law, or Q-law, was first proposed by Petropoulos (2003) to generate first guess approximations for propellant-optimal, low-thrust transfers between two Keplerian orbits. It is based on a Lyapunov feedback control law and calculates the optimal direction of thrust based on the proximity to the target orbit (i.e. the difference in the static Keplerian parameters) and the current location of the spacecraft on the orbit (i.e. true anomaly). The basic Q-law was developed for the restricted two-body problem, based on Gauss’ planetary equations. 
In this paper, this Q-law is extended to account for both third body effects and solar radiation pressure. The perturbing effect of solar radiation pressure becomes relevant when dealing with solar sails, or large optics in space. Equations for the disturbing acceleration and disturbing potential function were derived for the perturbations, then analysed to determine the minimum and maximum rate of changes of the Keplerian elements given the thrust vector and true anomaly of the spacecraft. These were then analytically incorporated into the Q-law feedback function. The complete mathematical derivations are presented. By accounting for the additional perturbations within the control law, this allows for a better optimisation of the resulting transfer.
The resulting Q-law is compared to the fully optimal control law, stemming from optimal control theory, for the same dynamical model. Two missions are used as test cases. The first calculates the transfer trajectories following the initial deployment of a formation of spacecraft, into their final formation orbits. The second covers a more complex test case based on an asteroid deviation mission, where each spacecraft in the formation is required to constantly adjust their orbits in order to maintain a periodic motion with respect to the asteroid. 

Abstract document

IAC-08.C1.5.3.pdf

Manuscript document

IAC-08.C1.5.3.pdf (🔒 authorized access only).

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