Time-optimal Trajectory Planning for Landing Onto Moving Platforms

In this paper, an algorithm for time-optimal trajectory generation is developed for landing a 6 degree-of-freedom (DOF) quadrotor onto a moving platform (with tilt, heave and pitch). The overall control architecture has a standard guidance-and-tracking control inner-outer loop structure. The outer loop (guidance control) solves the time-optimal trajectory generation problem. Instead of directly solving the time-optimal control problem, the proposed method reformulates this into a nonlinear programming problem that transforms the constraints on the original system dynamics and inputs onto constraints on the system states. This transformation is based on the differential flatness property of the quadrotor dynamics. The proposed method is computationally efficient and can also incorporate the collision avoidance constraints. We further demonstrate that this time-optimal problem can be resolved at periodic intervals (if disturbances and unmodeled dynamics deviate the quadrotor from the optimal trajectory). For the inner loop, a trajectory tracking controller is also designed that can deal with system uncertainties and external disturbances that may affect the quadrotor’s dynamics. Simulation and experimental results show the effectiveness of the proposed method.