epsilon-Propellant Optimality in Powered Descent Guidance with Continuous Thrust

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 in planetary landing. 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 notion of epsilon-propellant-optimality is introduced. A rigorous guarantee on epsilon-optimality is established that such a solution with a continuous thrust profile can achieve propellant performance arbitrarily close to the theoretical optimum of the bang-bang solution within any desired margin. A fully automated and relatively simple guidance algorithm is presented 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.