Energy optimal attitude control of a satellite actuated by magnetorquers in minimum time^*

In this article we combine a previously introduced energy optimal cost function based on net power with a minimum-time cost for attitude control of a spacecraft. The benefit of such an approach over the previous optimization scheme which used a fixed control horizon is that the control horizon does not have to be set in advance, which can be desirable if it is difficult to set the final time of the optimization. This time optimal objective is combined with a cost function based on net energy, which is the integral of the difference between the power the satellite gains from solar power and the power it spends performing the attitude maneuvers. The weighting between these two objectives can be exploited to let the optimal solver choose the final time in cases where the exact final time of the maneuver is not critical. Magnetorquers produce a magnetic torque that can be used to control the attitude of a spacecraft, but due to their physical limitations it is not trivial to predict when the spacecraft attitude will reach its reference value. For this reason, an approach such as this where the final time is set by the optimal solver can be beneficial. The difficulties related to the use of two terms in the cost function for the distance from the reference attitude and angular velocity, together with net power cost function and time, is discussed.