Mixed-integer GA optimization for the tracking control of a formation of small satellites equipped with multi-constrained electric thrusters

A formation mission scenario is considered, consisting of small satellites (Chasers) that must keep a reference trajectory with respect to a larger and non-cooperating Target satellite. The Chaser must perform its formation guidance and control tasks within the framework of its thruster constraints: the case of a low thrust electrical engine is here considered. The constraints of such a thruster are relevant to number and orientation of thrusters, the admissible thrust levels and minimum and maximum ON time. The control algorithm developed to satisfy all these constraints is a model predictive control based on a mixed-integer genetic algorithm optimization, which provides a fast estimate of the necessary scheduled actions. The algorithm takes J2 and drag perturbations into account; at the scope a differential orbital parameters linear relative dynamics model has been used, while the real-world dynamics is represented by a high precision orbital propagator. The developed orbital controller is particularly effective when trajectory keeping is required; different relative configurations, like Helix or Train formations, are taken as benchmark trajectories. The results show promising and robust performance in counteracting differential perturbations, even in the case in which the Target satellite performs scheduled orbital maneuvers which are not timely communicated to the Chaser satellite.