Analytical Mechanics of Space Systems

Consider a spacecraft that is to be reoriented to a new heading. It is possible to prescribe a corresponding trajectory and then derive the required control effort through inverse dynamics that will accomplish the desired maneuver. Such maneuvers are called open-loop maneuvers because no position or velocity feedback is present to indicate how accurately these maneuvers are being accomplished. Naturally, any real system will not be modeled perfectly and unmodeled dynamics and external influences will cause the spacecraft to drift from the desired trajectory or final state, i.e., the inverse solution for the open loop contains modeling approximations. To guarantee stability of the maneuver, a feedback control law is required. This control law operates on measured updates of the current states and compares them to where the spacecraft should be at any instant of time. The state errors are then used to modify the control input such that the spacecraft returns to the desired trajectory. Open-loop reference maneuvers are not always required to perform reorientations. In several control laws, spacecraft are reoriented to the new attitude by simply feeding the difference between current and final desired attitude to the control law.
This chapter will develop several control laws for both the regulator problem (maintaining a fixed orientation or configuration) and the trajectory tracking problem, and discuss their stability characteristics. Designing spacecraft attitude control laws combines the skills of rigid body kinematics and kinetics, as well as control methodology. In fact, the proper choice of attitude coordinates can be...