Real-time trajectory generation for interception maneuvers with quadrocopters

This paper presents an algorithm that permits the calculation of interception maneuvers for quadrocopters. The translational degrees of freedom of the quadrocopter are decoupled. Pontryagin's minimum principle is used to show that the interception maneuver that minimizes the time to rest after the interception is identical to the time-optimal maneuver that drives the vehicle to the position at which it comes to rest after the interception. This fact is leveraged to apply previously developed, computationally efficient methods for the computation of interception maneuvers. The resulting trajectory generation algorithm is computationally lightweight, permitting its use as an implicit feedback law by replanning the trajectory at each controller update. The validity and performance of the approach is demonstrated experimentally by intercepting balls mid-flight. The real-time trajectory generation permits to take into account changes in the predicted ball flight path at each controller update.