Optimal Longitudinal Trajectory Planning for a Quadrotor UAV Including Linear Drag Effects

This work proposes a methodology for determining the optimal trajectories of a quadrotor UAV in the sense of a trade-off between a control energy cost and a time-related cost under the influence of linear drag. The consideration of such a trade-off is motivated by the need to find efficient strategies to deal with battery-powered UAVs having limited battery charge. The problem is formulated as a free terminal time optimal control problem using a trade-off cost index and solutions are derived using the Pontryagin's Minimum Principle (PMP). The results show the sensitivity to drag effects of some important quantities such as trajectory smoothness, control energy, and final time. One of the important contributions of the methodology proposed in this paper is that it provides a Pareto optimal curve that is parameterized by the drag coefficient divided by the mass of the vehicle. Extensive simulation plots, including the Pareto optimal curve, show the results of the proposed method for different drag coefficients.