Mixed-Integer GA optimization for the 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 acquire and maintain 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: (a) single-axis orientation of the thrust (since only one engine is present); (b) the thrust level (only two levels are possible: maximum and zero); (c) maximum ON time (due to power consumption and temperature issues); (d) minimum ON time (because of the time required to prepare the motor ignition, it is preferrable not to have very short ignitions); (e) maximum number of ignitions; (f) minimum time between two subsequent ignitions. 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, while a different (not optimal) controller is used when large reconfigurations are needed. Developing a guidance logic that opportunely switches between the two controllers, the results show that even such a multi-constrained control system can perform a wide range of typical formation operations, such as station keeping in normal mode and during Target's scheduled operations, and acquisition of different relative configurations, like Helix or Train formations.