Minimum energy route optimisation of a quad-copter UAV with landing incentivisation

Recent advancements in the technology surrounding UAVs have expanded the possibility of incorporating them into current logistical solutions. In order to accurately assess their capabilities, it is important that minimum energy trajectories can be generated to increase the travel range of a UAV as well as its possible number of visited locations. However, in current formulations of the optimisation problem, UAV dynamics do not incorporate a contact force on the ground. This results in hover-to-hover trajectories where the duration of the journey is exactly equal to an arrival time which is set as one of the problem's parameters. Those solutions are likely to be energetically sub-optimal if an unnecessarily large value of arrival time is chosen. This paper introduces landing capability by modifying gravitational acceleration in the dynamics using a sigmoid function which approaches zero at the destination. In this way, the trip can be conducted in a shorter amount of time if it results in lower energy consumption. The new model is compared against an example from the literature, where the corresponding solution results in a reduction of the travel time and energy consumption by approximately 80%. It is also applied to a real-world example where it is demonstrated that a UAV can provide energy savings if it replaces a van completing a delivery in the Solent region of the UK.