Rotorcraft Trajectory Optimization with Realizability Considerations

This paper considers the problem of computing optimal trajectories for rotorcraft systems. The vehicle is described through a flight mechanics model, and the optimal control problem is solved by discretizing the vehicle governing equations using a finite-element method, followed by optimization of the resulting finite-dimensional problem. It is found that the computed control policies exhibit oscillations and very high—and therefore unrealistic—time rates, especially for aggressive or emergency maneuvers. Highly oscillatory controls can affect the vehicle trajectory by, for example, exciting short period type oscillations. We argue that this behavior of the computed controls is due to the lack of modeling detail of the vehicle actuators, implied by the classical treatment of the system controls as algebraic variables. We propose a simple, low-cost solution that is based on the recovery of the control time rates through a Galerkin projection. This approach is motivated by the desire to avoid direct modeling of the actuator dynamics, which typically requires one to resolve fine temporal scales in the solution. The recovered control rates can then be constrained to remain within physically acceptable bounds during the solution and can also be included in the optimization cost functions. Numerical experiments are shown to demonstrate that smoother control time histories and vehicle trajectories are computed through this approach.