Memorias de investigación
Propagation and Optimal Control of Space Trajectories Using Perturbation Methods

Research Areas
  • Aeronautical engineering

The development of low-thrust, high-specific-impulse thrusters, such as ionic and Hall effect thrusters, has brought new possibilities and challenges into the field of space mission design. This is highlighted by missions such as Deep Space 1, SMART-1 and BepiColombo. The high specific impulse of these thrusters allows for important savings in propellant mass, while their capability to operate continuously confers greater flexibility and robustness to the design process. However, this flexibility comes at the cost of a greater design complexity compared to impulsive thrusters, since the control laws must now be expressed as time functions (instead of as a set of discrete maneuvers). Furthermore, this problem is aggravated by the fact that the low magnitude of the thrust implies a smaller control authority and longer mission times. In order to successfully address this challenges and fully exploit the advantages of low-thrust, high-specific-impulse thrusters, new mathematical tools have to be developed, both numerical and analytical. The aim is not just to be able to computationally solve increasingly complex practical problems, but also to gain a better insight into the underlying physics and to develop approximate analytical solutions for preliminary design and estimation. The main objective of this thesis is to develop mathematical methods and tools for the propagation and optimization of low-thrust trajectories, both Earth-bound and interplanetary, and apply them to different practical test cases. These families of optimal control problems (OCPs) are studied both numerically, by implementing algorithms for their accurate and efficient resolution, and analytically, by searching for approximate solutions. This works covers a wide range of techniques for solving OCPs, including both direct and indirect methods. With direct methods, the OCP is transcribed as a discrete nonlinear programming (NLP) problem, which is then solved numerically using iterative algorithms starting from an initial guess of the solution. Conversely, in indirect methods the solution is sought for by imposing the first order optimality conditions, derived from Pontryagin's Maximum Principle or using the calculus of variations, which yields a two-point boundary value problem (TPBVP). Said TPBVP is studied in this thesis in two different, yet complementary ways. On the one hand, approximate analytical solutions are sought for using perturbation methods. On the other hand, numerical solutions are obtained using iterative algorithms. The dissertation is structured around three different formulations for orbital dynamics: a novel relative motion formulation in curvilinear coordinates; the modified equinoctial elements, originally introduced by P. Cefola; and Dromo, an element-based orbital propagator developed by the Space Dynamics Group (Technical University of Madrid-UPM). The section devoted to the relative motion formulation focuses on obtaining approximate analytical solutions for the phase change, radius change and inclination change problems, identifying different operation regimes. In the next section a general framework for indirect optimization with element-based formulations is developed, which is then applied, together with the modified equinoctial elements, to the design of end-of-life dispossal maneuvers for satellites in the Galileo constellation. The final sections focuses on Dromo, studying its applicability to OCPs and presenting a multiple-scales solution to the radial thrust problem.
Mark Rating
Sobresaliente cum laude

Research Group, Departaments and Institutes related
  • Creador: Grupo de Investigación: Dinámica Espacial (SDG-UPM)
  • Departamento: Física Aplicada a Las Ingenierías Aeronáutica y Naval