Optimal control-based design and feasibility assessment of rendezvous trajectories for ‘In-Air Capturing’ of a reusable launcher stage

‘In-Air Capturing’ is an innovative mid-air recovery technique where a winged reusable launch vehicle (RLV) is retrieved by a towing aircraft and transported back to the launch site. This approach eliminates landing fuel requirements and increases payload capacity. During ‘In-Air Capturing’, the RLV must execute a precise rendezvous maneuver and maintain stable formation within a designated, wake-free mating zone behind the aircraft. A tethered capturing device is deployed in advance and awaits connection as the RLV arrives in position. This paper presents a comprehensive trajectory optimisation and control framework for the rendezvous phase, addressing multiple objectives, strict path constraints, capturing device range limits, and external disturbances such as aircraft wake and wind. The trajectory is optimized using Legendre–Gauss–Radau pseudospectral method, with refinement of initial conditions and evaluation of both single- and multiple-capture attempt scenarios. For control, a gain-scheduled Linear Quadratic Regulator (LQR) based on the RLV's energy is developed. To improve robustness, a disturbance observer is integrated into the controller to estimate and correct for wind and wake-induced disturbances during flight. Capture feasibility is assessed through a Monte-Carlo analysis, and the results are used to identify critical boundaries and conditions that determine when re-planning of the guidance trajectory is necessary.