Constrained Reachability and Controllability Sets for Planetary Precision Landing via Convex Optimization

This paper presents a convex optimizations-based method to compute the set of initial conditions from which a given landing accuracy to a target can be achieved (constrained controllability set) and the set of states that can be reached from a given set of initial states (constrained reachability set) for a planetary landing vehicle with all the relevant control and mission constraints. The proposed method is based on the lossless convexification of the powered-descent landing guidance problem and methods of convex optimization and computational geometry. These techniques are used to generate approximations that can be arbitrarily close to the actual reachability or controllability sets. The quantification of these sets allows evaluation of the feasibility of a prescribed landing accuracy for a given vehicle and an expected set of dispersions from the parachute descent phase of a planetary landing mission. Since these sets are generated systematically and quickly, a wide range of design options can be evaluated for different mission requirements. Consequently, the proposed method can enable lander vehicle design optimization as a reliable analysis tool for systematic design and system engineering.