The concept of Urban Air Mobility (UAM) has gained significant attention recently. In this vibrant domain, the capability of generating an optimal flight trajectory is of essential importance. This study aims to provide analytical solutions to generate the optimal trajectory in the three most common UAM scenarios. The first case is the comfort-optimal trajectory for drone package delivery and air taxis carrying passengers. The cost is evaluated as a linear combination of acceleration (or specific support force) and flight time. The second case is the control-effort-optimal trajectory for hovering vehicles. Hovering vehicles are expected to be the dominant model of air taxi. The objective function is a linear combination of thrust and flight time. The third case is the Direct-Operating-Cost (DOC) optimal trajectory for electric fixed-wing aircraft, on which all major aerospace companies are working. DOC is a linear combination of energy consumption and flight time.
The trajectory optimization problems are formulated as optimal control problems and the Pontryagen’s Minimum Principle is applied to solve them. The solution is the reference position as a function of time, which is a guidance law and is fed to the downstream flight controller. The biggest advantage of an analytical solution is to reduce the computational time. It can also be integrated with other flight path planning methods. Several simulation examples will be presented to show the effectiveness of the proposed method
