Minimum-Fuel Closed-Loop Powered Descent Guidance with Stochastically Derived Throttle Margins

If during a guided powered descent maneuver the descent vehicle deviates from the planned trajectory, then the vehicle may need to adjust the commanded thrust in order to still reach the target landing site or to avoid violating mission constraints. However, often the nominal thrust command at any time along a minimum-fuel powered descent trajectory is either at the maximum or the minimum throttle, and as a result the corrective thrust command may be outside the allowable throttle range. A margin must therefore be added between the planned throttle command and the engine throttle limits, but this margin may be overly conservative to the detriment of performance. In this paper, the powered descent trajectory is modeled as a stochastic process in order to nonconservatively adjust the bounds on the feed-forward optimal thrust magnitude command to allow for sufficient feedback authority. The margin on the nominal throttle is computed as a function of the covariance of the closed-loop thrust commands so that if the nominal throttle is within the limits, plus the margin, then the closed-loop throttle is within the allowable limits with high probability. The proposed method can be solved onboard without iteration.