We show that the Lagrange dynamics of quadrotor-manipulator systems can be completely decoupled into: 1) the center-of-mass dynamics in E(3), which, similar to the standard quadrotor dynamics, is point-mass dynamics with under-actuation and gravity effect; and 2) the “internal rotational” dynamics of the quadrotor's rotation and manipulator configuration, which assumes the form of standard Lagrange dynamics of robotic manipulator with full-actuation and no gravity effect. Relying on this structure, we propose a novel backstepping-like end-effector tracking control law, which can allow us to assign different roles for the center-of-mass control and for the internal rotational dynamics control according to task objectives. Simulations using a planar quadrotor with a 2-DOF arm are also performed to show the theory.
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Yang et al. (2014) studied this question.