Robust Concurrent Attitude-Position Control of a Swarm of Underactuated Nanosatellites

In this paper, we address the formation flying problem of underactuated nanosatellites by concurrent attitude-position control. Lack of space in nanosatellites hinders us from having omnidirectional motion capabilities. Hence, a practical model for nanosatellites is to employ a one-directional propulsion system together with the reaction wheels. To achieve the formation flying of such nanosatellites, we develop a strategy based on the simultaneous control of attitude and position. The proposed formation flying method consists of three sublevels: first for each underactuated nanosatellite, a virtual fully actuated system is considered and a finite-time translational control method together with a disturbance estimator is developed for the fully actuated system. Subsequently, an adaptive finite-time attitude tracking is proposed to align the thruster of each underactuated nanosatellite with the obtained translational input of the corresponding virtual fully actuated system. Finally, by using the attitude and the obtained virtual input, the thrust for each underactuated nanosatellite is computed. Unlike the existing methods that are merely limited to control of fully actuated satellites, the proposed method presents a robust concurrent formation flying control for a group of underactuated nanosatellites, and accounts for disturbances such as air drag. A rigorous mathematical formulation and the stability analysis of the system are provided. Simulation results are presented to illustrate the performance of the proposed method.