State Constraint Analysis for Powered Descent Guidance

We study the powered-descent guidance problem for soft planetary landing. This optimal control problem seeks the best trajectory for propulsively landing a vehicle at a given point while consuming as little propellant as possible and satisfying constraints on the control (thrust direction) and the state (obstacle avoidance). As such, it is very relevant to applications to reusable launchers. The problem and its variants have been extensively studied using finite-dimensional optimization techniques (e.g. convex solvers), and less so with indirect methods. Even the variant with the simplest dynamics is not yet completely understood mathematically, as highlighted by the recent study of Leparoux and Jean (2022). We provide the expression of the control along state-constrained arcs, which allows us to implement the indirect method accounting for the control and state constraints. We then explore the space of trajectory structures by sampling the initial condition. This highlights the richness of the problem, and lets us envision, as future work, low computation MPC-style real-time controllers.