Computing the Forward Reachable Set for a Multirotor Under First-Order Aerodynamic Effects

Collision avoidance plays a crucial role in safe multirotor flight in cluttered environments. Even though a given reference trajectory is designed to be collision free, it might lead to collision due to imperfect tracking caused by external disturbances. In this work, we tackle this problem by computing the forward reachable set (FRS), which is the set of positions and velocities that a multirotor can reach while following a reference trajectory due to tracking errors. Hence, if the FRS is computed before flight, we can utilize it to check the safety of a given trajectory in terms of collision avoidance. To compute a realistic FRS that covers an agile flight envelope, we consider first-order aerodynamic effects, which have the most salient influence on the vehicle. For computing FRS, we conduct a thorough stability analysis including these aerodynamic effects. Then, we present an FRS computation method that can easily be adapted to newly given reference trajectories. The presented method is validated by comparing the FRS with real flight data collected during agile and high-speed flight. In addition, we compare the FRS computed with and without compensating for first-order aerodynamic effect to highlight their significance on the trajectory tracking performance. To the best of our knowledge, this is the first attempt to compute FRSs by incorporating first-order aerodynamic effects for multirotors.