Optimal control for high-precision repeat ground-track orbits via convex optimization

To satisfy the requirement of high-precision maintenance for repeat ground-track orbits, a method for the design and control for the orbits in high-fidelity dynamics is presented. The method is based on the use of high-order expansion of Poincaré maps to propagate regions of the phase space forward in time for one, or more, repeating cycles. This allows us to identify initial conditions that ensure repetition of ground-tracks with high accuracy. These conditions are targeted by the spacecraft with a multiple-impulse control strategy that is optimized via Second-Order Cone Programming. The resulting approach is suitable for both impulsive- and continuous-thrust propulsion systems and can be implemented onboard thanks to the convex formulation of the problem.