A quadrotor with a cable-suspended load with eight degrees of freedom and four degrees underactuation is considered and a coordinate-free dynamic model, defined on the configuration space SE(3)×S2, is obtained by taking variations on manifolds. The quadrotor-load system is established to be a differentially-flat hybrid system with the load position and the quadrotor yaw serving as the flat outputs. A nonlinear geometric control design is developed, that enables tracking of outputs defined by (a) quadrotor attitude, (b) load attitude, and (c) position of the load. In each case, the closed-loop system exhibits almost-global properties. Stability proofs for the controller design, as well as simulations of the proposed controller are presented.
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