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.

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Professor Jonathan P. How

Mike Tillerson