Practical and Accurate Generation of Energy-Optimal Trajectories for a Planar Quadrotor

Motivated by the limited flight time of battery-powered multi-rotor UAVs, in this paper we address the problem of generating energy-optimal trajectories for a planar quadrotor. More specifically, by considering an accurate electrical model for the brushless DC motors and rest-to-rest maneuvers between two predefined boundary states, we explicitly compute the minimum-energy curves by adopting a free and a fixed end-time optimal control formulation. The numerical solution of these optimal control problems hinges upon a simple yet effective indirect projected gradient method. Simulation experiments illustrate the theory in a variety of realistic flight scenarios.