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

Abstract

This paper presents conora (Collocated Orthogonal coNtrol Optimization for Rocketry Applications), 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 other available options for their robustness to poorly defined initial guesses. This robustness is particularly crucial considering the inherent complexity in computing initial guesses for launch trajectories, where dynamic variables such as atmospheric conditions, thrust variations, and gravitational influences pose significant challenges. 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 implemented software 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. Ariane V ascending to GTO, Electron launch to SSO, ALTO (Air Launch To Orbit) 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 close estimation of optimized payload masses. The obtained outcomes grow more valuable when considering the small number of inputs provided, the simplicity of the utilized physical model and the strong assumptions considered. Furthermore, these results were achieved using one of the most straightforward approaches for an initial guess: a stage-wise linear interpolation to bridge the launch and orbital injection conditions. 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. The requirements were carefully designed with a user-centric approach, guided by personae and user stories. The software development leveraged OpenMDAO and Dymos for implementation, ensuring efficient handling of complex computations. Testing was thoroughly conducted to verify the system's integrity, and an object-oriented requirements framework was used to maintain clarity and structure. The content of this work was produced under technical supervision by DLR (Deutsches Zentrum für Luft- und Raumfahr), at the Institute of Space Systems in Bremen, Germany, as the Master Thesis project of the Author.