Constant-Optic-Flow Lunar Landing: Optimality and Guidance

Neuromorphic architectures to robust and adaptive navigation based on visual clues have been proposed as automated landing systems. In particular, constant-optic-flow descents have been studied in relation to their bioinspired nature and to their promise for a substantial hardware and software simplification. The main body of work on the topic considers Earth-based systems as applications, such as micro air vehicles, and has only lately looked at planetary landings, but never in relation to their mass optimality. In this paper, constant-optic-flow descents are studied with respect to optimality, first from a theoretical point of view using Pontryagin’s maximum principle and then performing a numerical investigation on some selected cases (Apollo-like) and a comparison with unconstrained descents. The propellant mass introduced by forcing a constant optic flow during a lunar descent is estimated for typical high-gate/low-gate conditions. The effect of constraining the spacecraft pitch law during the constant-optic-flow descent is also studied, showing that an optimal pitch law is essential to lower the overall mass consumption and that linear or exponential laws may not be adequate. A guidance algorithm is then presented and discussed for use in automated planetary landing when a constant optic flow is regulated.