Overview of some optimal control methods adapted to expendable and reusable launch vehicle trajectories

Launcher trajectory optimization is a complex task, especially when considering the specific problems arising in the study of reusable launch vehicles. Part of the difficulty comes from the different characteristics of the trajectory arcs which make up the vehicle's mission (constraints and controls may not be the same). Another difficulty is the necessity, in some cases, of a global optimization between ascent and re-entry phases (branching optimisation). Finally, optimization tools devoted to this task should be polyvalent and robust, as the studies of reusable launch vehicles usually cover many different concepts, and also many different trajectory cases (such as abort scenarios). The purpose of this paper is to present different approaches used in France by CNES and ONERA to solve optimal control problems in the context of launcher trajectory optimization. These approaches, which are powerful implementations of classical optimization methods, were designed to cover the needs for both expendable and reusable launchers trajectory calculation. The first optimization tool presented is OPTAX, which uses an indirect shooting method. The second and third tools presented are CNES's ORAGE and ONERA's FLOP/OLGA, which use two different variants of the gradient method. The paper describes the equations and methodology behind these tools, and also presents their advantages and drawbacks.