Delayed Target Tracking for Along-Track Formations

Abstract

The minimization of propellant consumption for maintenance of satellite formations is a key issue for efficient, cost-effective operations of such formations. An innovative and powerful solution to this problem for formations separated in along-track direction is presented using the Delayed Target Tracking method. The method avoids propellant consumptions associated to the compensation of differential perturbations arising from the complex Earth's gravity field by a guidance and control law that minimizes the separation of the chaser at any time with the target at the same time but delayed by a constant time offset. This offset is equivalent to an along-track separation and assures that, when formulated in an Earth-fixed frame, the chaser exactly follows the target's orbit, thus experiences identical accelerations, alleviating the need for any propellant consumption. The governing equations are presented along with an algorithm for implementation. The concept of Delayed Target Tracking is proven analytically, and demonstrated numerically in an open-loop configuration and in a closed-loop control scenario. The validity of the method has been analyzed including a demonstration of its applicability to eccentric orbits and perturbations other than from Earth's gravity alone.