Time-Optimal Trajectory Generation for Landing a Quadrotor Onto a Moving Platform

We propose a time-optimal trajectory generation algorithm for landing a quadrotor onto a translating (heaving) and tilting (pitching) platform. The proposed algorithm exploits the differential flatness of the system dynamics and optimizes the trajectory in the space of system flat outputs, i.e., system states and their derivatives. This reformulation of the problem improves computational efficiency and can incorporate input and state constraints during the landing maneuver, such as collision avoidance and time-varying final state constraints. In order to verify the optimality of the solution obtained from the proposed algorithm, a switching time search mechanism is also proposed for a subclass of time-optimal trajectory generation problems. Experimental results demonstrating the landing of a quadrotor onto a moving platform are presented to verify the effectiveness of the proposed trajectory generation algorithm.