Implementable Epsilon-Propellant-Optimal Powered Descent Guidance

It is well known that propellant-optimal powered descent solutions require bang-bang thrust magnitude profiles. Although theoretically optimal, such thrust profiles are often challenging – and sometimes impossible – to implement practically. This paper addresses the optimal powered descent problem by introducing a regularization technique specifically designed to automatically produce continuous, practically implementable thrust profiles without compromising propellant efficiency. The formulated problem is thoroughly analyzed. A rigorous guarantee on the epsilon-optimality is established that the solution can achieve propellant performance arbitrarily close to the theoretical optimum of the bang-bang solution within any desired margin. A fully automated and still relatively simple guidance algorithm is designed to solve the problem reliably and quickly. The proposed approach and the guidance algorithm are demonstrated through closed-loop simulations applied to a crewed lunar landing mission.