Abstract: This paper studies the trajectory optimization of helicopter autorotation landing in the event of one engine failure by applying the nonlinear optimal control theory. An augmented longitudinal three-dimensional rigid-body flight dynamic model of a helicopter is first presented. By selecting the appropriate objective function, path constraints and boundary constraints, the trajectory optimization problem of helicopter autorotation landing is then formulated into a nonlinear optimal control problem, which is further transcribed into a discrete nonlinear programming problem. Finally, the optimal trajectories and controls are obtained by solving the nonlinear programming problem. Using helicopter UH-60 as the sample helicopter, the optimal solutions are calculated to minimize autorotation landing distance, and these solutions are compared with those obtained using a two-dimensional point-mass model. It is found that the time histories of rotor speed, thrust coefficient and sink-rate using the two different models show great correlation, and that the optimal solutions obtained using the three-dimensional rigid-body model furthermore include pitch rate, pitch attitude, and more realistic longitudinal cyclic pitch control. Then the trajectory optimization problem of helicopter autorotation landing is solved to minimize the velocity at touchdown with 1 second constant-control pilot delay. The resulting optimal trajectories and controls show safer sink-rate and slower pitch control rates while the final time and autorotation landing distance also increase considerably.

Key words: autorotation landing, trajectory optimization, optimal control, one engine failure, helicopter, three-dimensional rigid-body model, nonlinear programming