The Powered Descent Guidance (PDG) algorithm and software for generating Mars pinpoint or precision landing guidance profiles has been enhanced to incorporate thrust-pointing constraints. Pointing constraints would typically be needed for onboard sensor and navigation systems that have specific field-of-view requirements to generate valid ground proximity and terrain-relative state measurements.
The original PDG algorithm was designed to enforce both control and state constraints, including maximum and minimum thrust bounds, avoidance of the ground or descent within a glide slope cone, and maximum speed limits. The thrust-bound and thrustpointing constraints within PDG are non-convex, which in general requires nonlinear optimization methods to generate solutions. The short duration of Mars powered descent requires guaranteed PDG convergence to a solution within a finite time; however, nonlinear optimization methods have no guarantees of convergence to the global optimal or convergence within finite computation time.
A lossless convexification developed for the original PDG algorithm relaxed the non-convex thrust bound constraints. This relaxation was theoretically proven to provide valid and optimal solutions for the original, non-convex problem within a convex framework. As with the thrust bound constraint, a relaxation of the thrust-pointing constraint also provides a lossless convexification that ensures the enhanced relaxed PDG algorithm remains convex and retains validity for the original non-convex problem. The enhanced PDG algorithm provides guidance profiles for pinpoint and precision landing that minimize fuel usage, minimize landing error to the target, and ensure satisfaction of all position and control constraints, including thrust bounds and now thrust-pointing constraints.