Precise autonomous orbit control in low earth orbit: from design to flight validation

The main purpose of this research is the analysis, development and implementation of a precise autonomous orbit control system for a spacecraft in low Earth orbit. This thesis work represents a step forward in the theoretical formalization and implementation of an on-board orbit maintenance system. Two main approaches are identified for the realization of an on-board orbit control system. The first is the reconsideration and further development of state-of-the-art orbit control methods from the perspective of autonomy. A step forward is then taken in the direction of the definition of a general and rigorous formalization of the autonomous orbit control problem. The problem of the autonomous absolute orbit control is considered as a specific case of two spacecraft in formation in which one, the reference, is virtual and affected only by the Earth's gravitational field. A new parametrization, the relative Earth-Fixed elements, analogous to the relative orbital elements used for formation control, is introduced to describe the relative motion of the real and reference sub-satellite points on the Earth surface. An extensive discussion is dedicated to the reference orbit selection and generation process and the analysis of the free motion of a spacecraft in low Earth orbit. The reference orbit defines the spacecraft's nominal trajectory designed to satisfy the mission requirements. The actual orbit is kept within certain bounds defined with respect to the reference orbit. The generation process of the reference orbit is dealt in detail as it is the fundamental starting point of the orbit control chain. The free motion analysis is essential to understand the orbit perturbation environment which causes the deviation of the actual from the nominal trajectory. The use of the precise orbit determination data of the missions PRISMA and TerraSAR-X guarantee the reliability of the results of this analysis and the understanding of the orbit's perturbation environments at an altitude of 700 and 500 km. This study helps the definition of a proper control strategy. The control algorithms developed in the thesis can be divided into the two broad categories of analytical and numerical. An analytical algorithm for the maintenance of a repeat-track orbit is developed from the state-of-the-art methods and new analytical formulations for the reference orbit acquisition under different constraints and requirements are presented. The virtual formation method for the absolute orbit control is formalized by means of the relative Earth-fixed elements described previously. The state-space representation is used for the mathematical formulation of the problem. A linear and a quadratic optimal regulators, based on this model, are designed for the in-plane and out-of-plane absolute orbit control. Numerical simulations are performed for the validation of the control methods. The test platform includes a very accurate orbit propagator, the flight software and allows the simulation of actuators and navigation errors. The simulation results are evaluated from a performance and operational point of view in order to formulate a first conclusion about the advantages and disadvantages of the different control techniques. The main differences between the considered analytical and numerical control methods are outlined. The practical implementation of a precise autonomous orbit control system for a spacecraft in low Earth orbit is then described in detail. The on-board guidance, navigation and control software development, implementation and testing of the PRISMA mission, to which the author of this thesis contributed, is described. The attention is focused on the technological aspects implied by the realization of the autonomous orbit control system tested in-flight with the autonomous orbit keeping experiment on PRISMA. Among the several innovative aspects of the flight software development, some space is dedicated to the advanced software validation and testing realized on the formation flying test-bed at DLR, the German Aerospace Center, which played a fundamental role in the realization of the PRISMA mission and its experiments. Finally, the flight results of the autonomous orbit keeping experiment on the PRISMA mission, a fundamental milestone of this research work, are presented. This in-flight experiment took place in the summer of 2011 and demonstrated the capability of autonomous precise absolute orbit control using the analytical control method developed in this thesis