Geometric Control and Differential Flatness of a Quadrotor UAV with Load Suspended from a Pulley

We study a quadrotor with a cable-suspended load, where the cable length can be controlled by applying a torque on a pulley attached to the quadrotor. A coordinate-free dynamical model of the quadrotor-pulley-load system with nine degrees-of-freedom and four degrees-of-underactuation is obtained by taking variations on manifolds. Under the assumption that the radius of the pulley is much smaller than the length of cable, the quadrotor-pulley-load system is established to be a differentially-flat system with the load position, the quadrotor yaw angle and the cable length serving as the flat outputs. A nonlinear geometric controller is developed, that enables tracking of outputs defined by either (a) quadrotor attitude, (b) load attitude, (c) load position and cable length. Specifically, the design of the controllers for load position and cable length are taken into consideration as a whole unit due to the dynamical coupling of the quadrotor-pulley-load system. Stability proofs for the control design in each case and a simulation of the proposed controller to navigate through a sequence of windows of varying sizes is presented.