Lossless convexification of Powered-Descent Guidance with non-convex thrust bound and pointing constraints

A numerically-efficient, convex formulation of PDG (Powered-Descent Guidance) for Mars pinpoint and precision landing has been enhanced to include thrust pointing constraints. The original algorithm was designed to enforce both control and state constraints, including maximum and minimum thrust bounds, maximum speed limits and descent within a glideslope cone (surface impact avoidance). The thrust bounds are non-convex, so the original formulation developed a lossless convexification of these constraints. Likewise, thrust pointing constraints are non-convex. In this paper we present a relaxation for the thrust pointing constraint such that the enhanced PDG algorithm generates a lossless convexification for both the thrust bound and thrust pointing constraints. Pointing constraints are needed for onboard terrain-relative sensors that have specific field-of-view requirements during landing.