Optimal Powered Descent Guidance Under Thrust Pointing Constraint

This paper proposes a method for solving a three-dimensional propellant-optimal powered descent guidance problem under a thrust pointing constraint, where the thrust direction is restricted. Incorporating a thrust pointing constraint is as essential as pursuing propellant optimality for modern powered descent guidance, particularly when a lander uses terrain relative navigation sensors. However, the theoretical knowledge of optimal solutions is limited. One of the paper’s contributions is a method for finding the optimal solution under an upward-pointing constraint with an active–inactive–active switching structure. Usually, there is a maximum–minimum–maximum structure for the optimal thrust magnitude. Another contribution is compact propellant-optimal powered descent guidance under a thrust pointing constraint. The guidance may find the solution by establishing analytical models to evaluate switching points from the switching functions and predict the final-state errors. Numerical simulations provide the solutions of lunar pinpoint-landing scenarios, in addition to demonstrating the excellent propellant optimality, smooth convergence, and fast execution.