Synchronization and Control of Attitude for Spacecrafts:

The topic of this paper is to control and synchronize sphere-shaped spacecrafts in a leader-follower synchronization scheme. In order to achieve this objective, a nonlinear mathematical model of the vehicles has been developed. The design is based on rigid body dynamics where the vessel is actuated by means of three orthogonally mounted reaction wheels. The attitude dynamics is derived using Euler parameters. In the pursuit of reaching the main goal of controlling and synchronizing the satellites, it is natural to first develop control algorithms for single vehicle control. A sliding mode controller and a backstepping controller have been derived for this matter, and are compared for optimality. Both controllers are based on nonlinear control theory and are designed to control the angular velocity of the satellite. The system in combination with both the controllers is proven to be asymptotically stable. Due to cases where the spacecraft does not have angular velocity measurements, an estimator for the angular velocity is derived. Using LaSalle’s theorem, asymptotic stability is proven for the observer in the time-invariant case, while Matrosov’s theorem is utilized for system explicitly dependent on time. For operational assignments where it is not sufficient with only one satellite, a synchronizing scheme for several satellites has been proposed. The scheme is based on a leader-follower synchronization design, and is derived assuming that none of the satellites are equipped with angular velocity measurements. It is therefore possible to implement and utilize the nonlinear observer for angular velocity estimation in each vehicle. The controllers are designed in a similar manner for both the leader and the follower using backstepping control. The leader is set to follow an arbitrarily smooth trajectory, while the follower’s objective is to track the leader’s attitude, given by measurements and estimations. The various systems are tested in a lab setup with the AUVSAT. The AUVSAT is a sphere shaped, autonomous underwater satellite actuated by means of three reaction wheels. The experiments are performed when the AUVSAT is submerged in a water tank, making it possible to emulate a gravity free environment equal to what a satellite traveling in space is experiencing. The AUVSAT build up is presented where hardware and software components are chosen with respect to simplicity, cost and space restrictions. Several experiments are carried out using the AUVSAT to evaluate the performance of the controllers, observer and the synchronization scheme. For all cases, the system tracks a time-varying sinusoidal reference signal in addition to a squareshaped sequence. In this way, one can truly validate transient responses, steady-state and tracking maneuvers to determine the performance of the various systems. The experiments show that the sliding mode controller and backstepping controller works quite similar and with a satisfactorily behavior throughout the experiments. However, there are some lack of performance of the combined observer and controller system when tracking the sinusoidal time-varying reference. In the synchronization scheme, the leader follows the desired trajectory and the follower tracks the leader’s attitude to some extent. Comments on the results are presented in addition to proposed strategies and thoughts on how to improve the overall performance of the various systems.