Nonlinear Model Predictive Control of a Spacecraft Equipped with Reactions Wheels on SO(3)

In the present work, nonlinear model predictive control of a spacecraft equipped with reaction wheels as the actuators that generate the driving torque for the system is studied. The spacecraft body is also exposed to external disturbance originated from the existence of off-center in the system structure. The system configuration manifold is Lie group SO(3). Discrete equations of motion of the system, referred to as Lie group variational integrators and the NMPC formulation are much more complicated due to the terms added to the equations considering the effects of speed of the wheels and the angular momentum exchanges between the wheels and the spacecraft body and also due to the effects of external disturbances. However, the model of the system and consequently, the obtained results are much more realistic in return. The necessary conditions of optimality are extracted and solved using indirect shooting method based on sensitivity derivatives. Since the equations of motion are established based on Lie group properties, the geometric structure of the system is preserved in long time integration. In addition, the extracted equations are symplectic and momentum preserving and show good energy behavior. The system of a spacecraft with three reaction wheels with the off-center in the z-direction which impose external disturbance to the system is simulated using the extracted equations for NMPC control of spacecraft on SO(3) and the simplification of sensitivity equations is used to reduce the computation time of optimizations. The obtained results show that our method is able to bring the system to the zero position even when there is an off-center in the yaw direction of the spacecraft by structure.