Robust Trajectory Optimization with Orthogonal Collocation Methods for Ascending Rocket Stages in Early Phases of Mission Design

Abstract

This paper presents conora, a robust trajectory optimization software utilizing orthogonal collocation methods for ascending rocket stages, targeting applications in early phases of mission design. The proposed methodology leverages orthogonal collocation techniques, preferred over the multitude of available options for their robustness to inaccuracies in the initial guess. This, together with low amount of available data about the ascent profile, often makes preliminary optimization considerably complex, extremely case-specific and, consequently, very time consuming. The software here implemented addresses the problem of maximizing the payload mass of a rocket by providing the required flexibility to adapt to any mission scenario disregarding of the celestial body, launch site, vehicle design and target orbit. Proper functionality is demonstrated by replicating existing missions, simplifying and reducing to the bare minimum the number of inputs. Ariane V ascending to GTO, Electron launch to SSO, ALTO mission to LEO, Apollo XI Lunar Module ascent and Starship take-off to LMO are the multifaceted mission scenarios selected to demonstrate the capabilities of conora, resulting in accurate injection into orbit and relatively close estimation of optimized payload masses. The obtained outcomes grow more valuable when considering the small amount of inputs provided, the simplicity of the utilized physical model and the strong assumptions considered. The whole software development process followed a V-model, from requirement definition, passing by the actual implementation, to thorough code testing of each conora’s module. 64 are the top level identified requirements, for a verification process elaborated via more than 270 tests, from unit to system level. The entire work was performed in the context of an internship at DLR, at the Institute of Space Systems in Bremen, Germany.