Design of Observer-based Navigation Algorithms for a CubeSat Space Mission

Nowadays the design and operation of GNC of small satellites is widely being studied, due to the current and past space missions designed by several industries, research institutes, and space agencies. Some in-orbit demonstrations require heavy and bulky payload that must be embedded with complex set of sensors, actuators, and maintenance systems. Thus, the redundancy of elements is always inferior, so that a mathematical model estimating variables is needed to achieve the same goal with less sensors. At the same time, a good control of the state variables can be helpful in order to reduce fuel consumption, with the consequence of less space occupied by the actuation system or in an increase of the operational life span of the satellite. The aim of this thesis is to design an orbital simulator of a rendezvous manoeuvre of a 6U CubeSat. In particular, the main purpose is to design different observer-based navigation algorithms, to estimate all the system variables involved in the mission. At the same time, the system should be controlled to reach the desired values of attitude, position, and velocity. In this thesis, different state estimation methods are investigated, considering different Sliding Mode Observers (SMOs), and including a comparison with classical Kalman filters. The performance indices considered for the comparison are the estimation error, convergence time, and maintenance of performance in presence of disturbances. This thesis presents the results that can be obtained by applying the estimation techniques and the main disadvantages encountered during the development of the simulation model. Despite of the presence of external disturbances, process noise and measurements noise the performance of the studied filters always maintain good levels. A comparison of the proposed different techniques is performed for translational and rotational motions of the CubeSat. For example, the 1st order Sliding Mode Observer shows the best results in the estimation of the position along the y axis. On the other hand, as regard as the estimation of the position along the x and z axis, that have a coupled dynamics, the best result is given by the Kalman Filter and the 2nd order Sliding Mode Observer, in particular by the Super Twisting Observer. The Kalman filter and the Extended Kalman filter also shows the best results for the estimation of the Angular Velocities and the quaternion vector. Different control systems have been analyzed with the aim of identifying an optimal algorithm for the control of the attitude and the position. The first objective is to design a controller for the position control. Some controllers are studied, but only two of these are applied in the simulation model: the Sliding Mode Control and the PID controller. The second objective is to find a suitable controller for the attitude. The first model implemented is a Quaternion Feedback Controller (QFC), which is used as comparison with the second implemented technique, based on Linear Quadratic Gaussian (LQG) method. This consists of a Kalman Filter combined with a Linear Quadratic Regulator (LQR). Moreover, the Linear Quadratic Controller combined with different state observers. is studied and applied in simulations and compared with the result given by the classical LQG controller.