Cooperative Deployment of satellite formation into Highly Elliptic Orbit

Space trajectory optimization and mission design analysis have not general standards and procedures suitable for any kind of problems. Methods and results improve thanks the progress in computer science, numerical analysis, and engineering. The aim of this thesis is to enlarge the field of application of indirect optimization methods, which are based on the theory of optimal control, to trajectory optimization problems characterized by a complex dynamical model, which considers Earth oblateness, gravitational perturbations from Moon and Sun, and solar radiation pressure. The case study is the finite-thrust deployment of a two-satellite formation into a highly elliptic orbit. The optimization procedure provides the engine switching times and the thrust direction during each burn in order to transfer the satellites to the same prescribed final orbit with assigned distance between them at the apogee passage; the total final mass is maximized. A minimum-distance constraint is introduced when required to avoid collision risk. Different deployment strategies are analyzed; in particular, the classical chaser-target approach is compared to cooperative deployment. Necessary conditions for optimality corresponding to the different strategies are derived and numerical results presented. The optimal solution exhibits remarkable changes depending on the departure date, and a procedure has been developed to assure convergence with the use of a single tentative solution. The same problem was also solved using a suboptimal control law with thrust angles that remain constant in the inertial frame during each thrust arc. A preliminary study for considering errors introduced by thrust dispersion was carried on. The use of a re-optimization procedure after each apogee burn allows for a remarkable reduction of the errors on the final orbit achievement both in the single satellite case and in the formation deployment. In particular, intrinsically robust deployment strategies, characterized by a short final burn, have been identified.