Optimization of three-dimensional waypoint ordering for energy-optimal multirotor operation

Air mobility enabled by multirotor aircraft is an emerging transportation mode with wide real-world applications. Maximum range and flight duration are critical aspects of the performance, governed by the vehicle energy efficiency. This paper studies the energy-optimal planning of the multirotor, which aims at finding the optimal ordering of waypoints with the minimum energy consumption for missions in 3D space. The study uses a system model capturing first-principle energy dynamics of the multirotor. It is found that in most cases (up to 95%) the energy-optimal order is different from the minimum-distance order, which is the solution to the traditional traveling salesman problem. The difference can be as high as 14.9%, with the average at 1.6%-3.4% and 90th percentile at 3.8%-6.6% depending on the range and other parameters of the mission. To validate these results, three sample missions were tested in real-world flight, and the minimum-energy order was shown to reduce energy cost by 3.9%-9.4% relative to the minimum-distance order. These results were used to identify and explain the key features of the minimum-energy order by correlating to the underlying flight energy dynamics. It is shown that instead of minimizing the distance, coordination of vertical and horizontal motion to promote aerodynamic efficiency is the key to optimizing energy consumption. In addition, the combination of minimum-energy order planning and energy-optimal trajectory control could achieve energy savings of up to 29.9% over the combined minimum-distance order and a commonly used type of baseline controller.