Optimal guidance and control for space missions on asteroids and planetary bodies

This thesis deals with innovative and reliable solutions for optimal guidance and control of space exploration missions on small and large planetary bodies, such as Moon, Mars and asteroids. These solutions are based on the combination of artificial intelligence algorithms (metaheuristics and machine learning) and functional interpolation techniques (simple polynomials, B-spline curves and Theory of Functional Connections). In order to compute optimal trajectories, the associated optimal control problems are solved by using both direct and indirect methods. If the direct method is used, metaheuristic algorithms are employed to obtain the optimal solution. In this case, for most of the analyzed problems, the inverse dynamics approach is pursued together with a polynomial approximation of the trajectory, achieved through simple polynomials or B-spline curves. Following this methodology allows to ease the original optimal control problems and obtain faster algorithms, with the advantage of having less optimization parameters and automatically satisfying the boundary conditions. On the other hand, when the indirect method is exploited, a particular Physics-Informed Neural Network framework, called PoNNs, is used to learn the solution of the Two-Point Boundary Value Problems, in terms of states and costates, arising from the application of the Pontryagin Minimum Principle. PoNNs exploit the so-called X-TFC, which is based on a recently-proposed theory for functional interpolation named Theory of Functional Connections. The advantage of using PoNNs to learn the solution of Optimal Control Problems resides in the analytical fulfillment of the boundary constraints. In addition, an analytical representation of the solution is obtained, which allows to compute the control even in points unseen during the training without applying any further interpolation. The aforementioned frameworks are applied to the optimal design and control of space trajectories, with emphasis on proximity maneuvers around asteroids, interplanetary transfers and landing trajectories. Comparisons with other state-of-the-art methods, commonly adopted in literature, are carried out to test the accuracy of the proposed approaches. Finally, an experimental simulation of a lunar landing is also performed through a robotic simulator facility, showing the feasibility of artificial intelligence techniques for real-time applications.