Mechanics, control and internal dynamics of quadrotor tool operation

We propose a novel control framework to enable a quadrotor to operate a tool attached on it. We first show that any Cartesian control at the tool-tip can be generated if and only if the tool-tip is located strictly above or below the quadrotor’s center-of-mass. We then fully characterize the internal dynamics of the spatial quadrotor tool operation, which arises due to the quadrotor’s under-actuation, and elucidate a seemingly counter-intuitive necessary condition for the internal stability, that is, the tool-tip should be located above the quadrotor’s center-of-mass. We further manifest that this internal dynamics can exhibit finite-time escape and propose a stabilizing action to prevent that. The theory is then illustrated for the problems of rotating tool operation and hybrid force/position control with relevant simulation results.