An attitude control by the functional series in the problem of nanosatellite reorientation

Abstract

The nanosatellite reorientation maneuver is one of the important elements of achieving the mission goal if it is required to ensure the transfer of the nanosatellite axes from the initial to the final attitude. This maneuver is used in the process of directing the sensitive axes of the onboard equipment of a nanosatellite according to a predetermined program. One of the features of the angular motion of a nanosatellite is that the control torque value is close to external one. The paper studies nanosatellite optimal reorientation maneuver trajectory, considering external torques under control torque constrains. We based the optimization procedure on the differential evolution algorithm. We studied the most effective structure of the control program. It was presented by a set of functional series: power, trigonometric, even and odd Fourier series and Schlömilch series. The paper proposes the localization approach for initialization of the differential evolution algorithm. Furthermore, the algorithm for finding the desired open-loop control program is suggested. We compared the most efficient structure of the control program with the results obtained by the inverse dynamics method and examined stability of the obtained solution. In addition, it is shown that the proposed approach can be extended to a larger spacecraft. We verify our approach by the comparison with the approach based on the use of the Pontryagin maximum principle.