Time and Energy Efficient Descent Trajectories for Quadcopters that Avoid the Vortex Ring State

We investigate the problem of computing time-optimal and energy-optimal vertical descent trajectories for quadcopters, while avoiding the Vortex Ring State (VRS). The VRS is a region in the velocity space of the quadcopter in which disturbances on the thrust produced by the propellers result in a reduced control effectiveness and can eventually lead to a crash. A new model is proposed for the VRS dynamics for quadcopters, which is shown to be more complete in comparison with existing approaches. Based on this novel model, time-optimal and energy-optimal trajectories are computed using GPOPS II and compared in a numerical case study.