Rapid Optimal Multiburn Ascent Planning and Guidance

Abstract

This paper provides detailed development of an analytical multiple-shooting method for rapid and reliable generation of the optimal exo-atmospheric ascent trajectory of a launch vehicle. The trajectory consists of multiple burns (stages) and optimal coast arc between two burns. The problem solution is in closed-form and quadratures. An expanded analysis of the problem allows us to reduce the complexity of the constraints. A dogleg trust-region method that is more robust than the classical Newton-Raphson method is employed for the numerical solution. The multiple-shooting formulation, constraint simplification, and more sophisticated numerical method are all aimed at enhancing the robustness of the algorithm for this otherwise challenging problem. The essential equations necessary for implementing the algorithm are presented. Such an algorithm can be a valuable tool in rapid planning of launch missions and in on-board applications for closed-loop ascent guidance.