Robust optimal solution to the attitude/force control problem

Many spacecraft have an orbit control subsystem (OCS) which applies forces in order to maintain the orbital parameters within certain bounds. On the other hand, the attitude control subsystem (ACS) applies torques so that the spacecraft keeps its desired orientation. We explore the interaction of an orbital control maneuver with the attitude of a spacecraft. We propose to use the thrusters that provide the force for the orbit control as actuators to control the attitude as well. We obtain the conditions on the thruster configuration which guarantee that any perturbation torque can be compensated while performing the orbit control maneuver. We prove that the minimum number of thrusters which solve this problem is 4. Furthermore, we prove that the same problem can be solved with a minimum of 6 thrusters if a single failure in any thruster is accepted. We compute a robustness index which measures the maximum allowable uncertainty in the thruster configuration while still solving the problem stated previously. In the case of 4 thrusters with bounded thrusts, we solve the problem of maximizing the resulting force in a certain direction.