Autorotation-Based Descent with Trajectory Optimization

Abstract

The paper investigates the unpowered descent of a rotor system through the upper atmosphere. Axial and helical trajectories are investigated in the context of fixed points as well as an optimal control problem for maximizing flight time. The mathematical model considered in the paper incorporates the fuselage degrees of freedom, dynamic inflow model, and airfoil characteristics that depend on Mach and Reynolds numbers. Considering a potential application as a descent mechanism, trajectory generation is performed to maximize the flight time. As an example, the performance in the Venusian atmosphere for rotors with different airfoil characteristics is assessed. To delineate the role of constraints, initial conditions, and aerodynamic forces on the optimal descent, the axial trajectory is studied by dividing it into two phases. The first phase corresponds to the trajectory determination through an optimization process wherein control inputs are provided such that states are within bounds. The second phase trajectory (below 70 km), although determined by solving the optimal control problem as in phase-I, is shown to be close to that achieved using control inputs corresponding to fixed points corresponding to each altitude. Apart from the axial flight, helical trajectories and corresponding fixed points are investigated using a rotating constant sideslip frame. Furthermore, optimal helical trajectories are also determined, which could be useful for rotor-based descent mechanisms. A comparison between axial and helical fixed-point solutions is also presented.