Optimal Trajectory Generation for Transitioning Quadrotor Biplane Tailsitter Using Differential Flatness

This paper presents the development of an optimization-based trajectory planner for the autonomous transition of a quadrotor biplane tailsitter (QRBP) between the flight modes of hover to forward flight and forward flight to hover. The trajectory planner is formulated as an optimization problem with an  embedded dynamic model of the QRBP, vehicle design constraints (e.g. power), physical constraints (e.g. stall) and initial/terminal states for the transition. A differentially flat reformulation is employed to reduce the computational cost of the trajectory planner for on-board mission planning. The solution of this problem yields time-optimal state and input trajectories for transition. Using this trajectory planner, we generate trajectories for various transition flight missions (from hover to forward flight and vice versa) under various constraints. Further, we demonstrate how the proposed algorithm can also be used to assess the agility of a vehicle in terms of minimum space required to perform a specific maneuver or transition, given physical design constraints (such as maximum power). Finally, we demonstrate trajectory tracking on a high fidelity simulation of a QRBP with a cascaded dynamic-inversion based controller with a control blending strategy between the quadcopter and forward-flight control modes, for hover to forward flight.