# Formation Flying Control
in Eccentric Orbits

## Michael Tillerson and
Jonathan P. How

Proceedings of the AIAA Guidance, Navigation, and Control Conference,

Montreal, August 2001.

This paper extends recent
work on the control of a formation of spacecraft orbiting about an eccentric
(elliptic) reference orbit. The approach uses the equations for periodic relative
motion that were previously developed from Lawden's original work. This paper
presents fuel/time-optimal algorithms for the low-level station-keeping of one
satellite with respect to another satellite in the presence of disturbances.
The station-keeping algorithm is optimized by posing it as a linear programming
problem. The primary extension of this paper is to present the solution to the
linear programming problem using the time-varying linearized dynamics that occur
for an eccentric reference orbit. Numerous nonlinear simulations were performed
to demonstrate the effectiveness of this overall control approach. The results
indicate that, even in the presence of differential J2 disturbances, our formation
flying control approach is very effective, requiring a Delta V = 5 - 15 mm/s/orbit,
depending on the scenario. The simulations also show that Lawden's equations
are necessary for determining the desired state for periodic relative motion,
but Hill's equations are sufficient for the linear programming control problem.
This result is important because using the time-invariant Hill's equations significantly
reduces the computational effort required to formulate the linear program.

Download: SSL
Technical Report

Professor Jonathan P. How

jhow@mit.edu
Mike Tillerson

11/27/2001