Geometric Control of a Quadrotor with a Load Suspended from an Offset

A quadrotor with a point-mass payload suspended with an offset from the center-of-mass of the quadrotor to the suspension point is studied in this paper. This system consists of eight degrees of freedom and four degrees of underactuation. A coordinate-free dynamic model is obtained by taking variations on manifolds. We also establish that under a mild assumption that the angular acceleration of quadrotor is small, the offset quadrotor-Ioad system is a differentially-flat system with the load position and the quadrotor yaw serving as the flat outputs. A nonlinear geometric control design based on this assumption is developed. With this controller, the following states (a) quadrotor attitude, (b) load attitude, and (c) load position can be tracked. Stability proofs for the controller design, as well as simulation of the proposed controller are presented. A comparison of a geometric controller developed for a zero offset quadrotor-Ioad model is also presented to motivate the need as well as demonstrate the advantages of our proposed geometric controller for the offset quadrotor-Ioad model.