Finite thrust control for satellite formation flying with state constraints

This paper considers the problem of rotating a constellation of spacecraft using on/off thrusters such that the relative distance between the spacecraft is maintained to within a specified tolerance. The basic idea is to resolve all of the constraints into a sphere around the desired trajectory of each spacecraft. As the constellation rotates, the sphere sweeps out a tube that constrains the motion of the spacecraft. The control is activated when the spacecraft encounters the constraint sphere, the direction and magnitude of the thrust are calculated to maximize the travel of the spacecraft before the next required thrust, thus minimizing thrust.