Review of station keeping strategies for elliptically orbiting constellations in along-track formation

Three techniques for station keeping an orbiting constellation of satellites in an elliptical orbit are developed: (1) based on an application of the linearized Tschauner–Hempel (TH) equations for the motion of a daughter satellite relative to a reference (mother) satellite together with the linear quadratic regulator (LQR) control strategy which can be used in a piecewise adaptive manner; (2) since the mathematical model is inherently nonlinear and time varying, a control law based on a non-linear Lyapunov function is applied to daughter satellites’ osculating orbital elements; (3) by carefully selecting relative orbital design parameters so that the relative secular drifts due to the non-spherical Earth’s perturbation in the longitude of the ascending node, the argument of perigee and mean anomaly could vanish or be constrained to a desired value.