A fixed-point framework for launch vehicle ascent guidance

Abstract

Recent interests in responsive launch have highlighted the need for rapid and fully automated ascent guidance planning and guidance parameter generation for launch ve­ hicles. This dissertation aims at developing the methodology and algorithms for ondemand generation of the optimal launch vehicle ascent trajectories from lift-off to achieving targeting conditions outside the atmosphere. The entire ascent trajectory from lift-off to the final target point is partitioned into two portions: the atmospheric ascent portion and the vacuum ascent portion. The two portions are seamlessly combined to­ gether via a fixed-point iteration based on the continuity condition at the junction point between the atmospheric ascent portion and the vacuum ascent portion. The previous research works on closed-loop endo-atmospheric ascent guidance shows that the classical finite difference method is well suited for fast solution of the con­ strained optimal three-dimensional ascent problem. The exploitation of certain unique features in the integration procedure between the atmospheric portion and vacuum por­ tion and the finite difference method, allows us to cast the atmospheric ascent problem into a nested fixed-point iteration problem. Therefore a novel Fixed-Point Iteration al­ gorithm is presented for solving the endo-atmospheric ascent guidance problem. Several approaches are also provided for facilitating the convergence of the fixed-point iteration. The exo-atmospheric ascent portion allows an optimal coast in between the two vacuum powered stages. The optimal coast enables more efficient usage of the propellant. The Analytical Multiple-Shooting algorithm is developed to find the optimal trajectory for this portion.