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This paper presents a solution to the autonomous vertical autorotation problem of unmanned helicopters using a novel nonlinear model predictive controller (NMPC) enhanced by a recurrent neural network (RNN) that handles the nonlinear optimization. The controller utilizes an internal, nonlinear autorotation model and is capable of handling input and output constraints that directly map to quality, efficiency and safety requirements. The RNN is employed to achieve real-time operation because it is capable of improving convergence performance, especially when hardware that supports task parallelization is available. This is of major importance when dealing with small unmanned helicopters with limited onboard computational power, where high update rates are required to successfully perform the autorotation maneuver. The proposed NMPC/RNN combination signifies the first use of a nonlinear model for online autorotation trajectory optimization, thus allowing for easier adaptation to other helicopter types without the need for retraining as in the case of machine learning techniques used by the state-of-the-art. An additional novelty of this research concerns the use of an objective function designed to eliminate the risk of fatalities to people on the ground. This is in contrast to previous works where the goal was to save the aircraft and is achieved by appropriately lowering the kinetic energy of the helicopter during the last phase of its descent. The paper discusses in detail the general design of the NMPC/RNN, before going into the specifics regarding the derivation, implementation and integration of the autonomous autorotation controller itself. The performance of the latter is validated using extensive simulation results.