Control of Spacecraft Formations Around the Libration Points Using Electric Motors with One Bit of Resolution

This paper investigates a formation control problem for two space vehicles in the vicinity of the L2 libration point of the Sun-Earth/Moon system. The objective is to accurately regulate the relative position vector between the vehicles to a desired configuration, under tight tolerances. It is shown that the formation control problem is solvable using six constant thrust electric actuators requiring only one bit of resolution, and bounded switching frequency. The proposed control law is hybrid, and it coordinates the sequence of on-off switches of the thrusters so as to achieve the control objective and, at the same time, avoid high-frequency switching.