Glide back recovery of a winged reusable launch vehicle with wind estimate
Creators: name:  P. EDORH 
name:   B. HERISSE 
name:   E. BOURGEOIS 
Publisher: name: Proceedings of  the 9th European Conference for Aerospace Sciences. Lille, France, 27 June - 1 July, 2022
Year: 2022
Subjects: REUSABLE SYSTEMS
FLIGHT PHYSICS
DYNAMICS

description: Commercial and scientific interests in partially or fully reusable launchers have increased considerably in recent years. Among various strategies which enable the recovery of the first stage of Reusable Launch Vehicles (RLVs), the glide back return (Figure 1) emerges as a promising alternative to the toss-back concept [2, 3]. While the latter has proved its worth on SpaceX Falcon 9 launchers, the former offers a more cost-effective solution in terms of both propellant consumption and ground infrastructure costs [1]. For a toss back recovery, a large amount of energy is lost to make the vehicle turn over. Instead, the glide back which is designed for winged vehicles, exploits the aerodynamic capacities of the vehicle to minimize the amount of energy to be consumed. Such strategy enables a horizontal landing which can be thus performed on an existing runway, close to the launch site. Moreover, the recovery of a winged first stage must be carried out while ensuring constraints on the dynamic pressure, the heat flow, the load factors, and the atmospheric re-entry. A robust and efficient guidance algorithm is then required as the vehicles aerodynamic performance is extremely sensitive to its environment (e.g., wind, air density, atmospheric pressure). Wind disturbances play an important role in vehicle dynamics and they should be taken into consideration. This paper thus provides a numerical guidance algorithm which computes online and in real time the optimal recovery trajectory of a winged vehicle from the stage separation to the landing maneuver, while minimizing propellant mass consumption. The recovery of the vehicle is described as an optimal control problem which is solved with an indirect method based on Pontryagins maximum principle. By augmenting the state of the system and its dynamics with a co-state, we derive a set of necessary conditions of optimality, written as a zero-finding problem, that can be quickly solved by a Newton-like algorithm. The optimal control problem then consists in finding the correct initialization of the costate. First, a reference trajectory is computed off-line to provide a first solution to the problem. This trajectory consists of a unique thrust maneuver (that cancels out the horizontal component of the vehicles velocity) and an unpowered atmospheric re-entry which encompasses several turn maneuvers. Then, with this solution as an initial guess, the guidance algorithm recomputes online the optimal control using the true current state of the vehicle at each time. With such an approach, highly accurate solutions are quickly provided, at a frequency that is compatible with actual embedded guidance components. Additionally, the guidance law has been found sufficiently robust to accommodate various uncertainties on parameters (e.g., initial state at the beginning of the recovery procedure, rocket engine, aerodynamic coefficients). The introduction of wind in the atmospheric and aerodynamic models will particularly impact the handling of the first stage during its descent. While the guidance model without any knowledge of the wind profile is quite effective in the absence of strong wind gusts, we propose to necessary to include a wind estimate in the guidance design to obtain a more robust solution.