Design an optimal trajectory planner for pinpoint landing.

Future exploratory missions of celestial bodies in the solar system will require spacecraft capable of landing precisely near to predefined targets, such as places of high scientific interest usually on topographically hazardous terrains, human outposts and pre-positioned assets. This thesis work analyses and implements the guidance problem for a pinpoint landing on Mars. Which requires finding a feasible reference trajectory to safely land a spacecraft on the Martian surface precisely close to a predefined target, optimizing at the same time the fuel consumption. The Lossless Convexification (LCvx) theory is identified as a very promising method to solve this type of problem. The LCvx allows to formulate the guidance problem as a convex optimization problem, which can be quickly solved by efficient solvers. Then, based on the derived mathematical formulation, an algorithm is implemented, with particular attention to the reliability of the solutions. An optimization of the algorithm is needed, to increase its computational performance. Tests and simulations are carried out to analyze the performance and the robustness of the algorithm. Finally, a parametric analysis relates the behavior of the algorithm with respect to a selection of meaningful design parameters of the lander, such as the configuration of the Radar Doppler Altimeter, the performance of the parachute and the requirements of the Landing Vision System. In conclusion, the designed algorithm proves to compute optimal trajectories for feasible guidance problems and sub optimal solutions for unfeasible optimization problems. The sub optimal solutions result from a trade off between landing accuracy and fuel consumption. Finally, the parametric analysis highlights interesting correlations between the driver parameters of the analysis and the developed algorithm, leading to useful guidelines for spacecraft design choices.