Motivated by the reduced flight time of battery-powered UAVs, this thesis proposes a methodology for determining the optimal trajectories of a quadrotor in the sense of a trade-off between an energy-based cost and a time-related cost. Two main cost functionals are proposed to address the battery power consumption.
Firstly, a trade-off between costs associated with body acceleration and total time is studied for nonsteady maneuvers. An optimal state feedback solution that considers the nonlinearities of the quadrotor’s equations of motion and the drag force components were developed. The main advantage of this technique is that it provides a state-feedback analytical expression.
Secondly, a simplified energy consumption model based on the blade element momentum theory (BEMT) is developed to deal with the cruise portion of the flight. The analytical solution for the constant altitude steady state flight minimum-energy problem was obtained and was similar to the maximum range problem solution. Based on the nature of the solutions, a hypothesis of a geometrical bound for the optimal pitch angle is raised.
The problems are 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). Simulations show the suitability of the proposed method.