Sensitivity Analysis for Powered Descent Guidance: Overcoming degeneracy

This paper exposes a method to handle inaccurate modeling and/or initial state errors during the Powered Descent Guidance (PDG), a critical phase of atmospheric rocket landing. For this, we develop a replanification method having reliable online computational capabilities. From a reference descent scenario, an optimal correction problem is formulated. After revisiting results on Non Linear Programming sensitivity for degenerate optimization problems, we conclude that Quadratic Programming (QP) provides a local solution to the replanification problem. Using three illustrative PDG scenarios, we stress degeneracy and show how QP is used to evaluate the upper Dini derivatives at stake. Further, we discuss to what extent QP also provides a quantitatively reasonable solution outside a small neighboorhood of the reference scenarios.