Dynamics and Control of a Quadrotor with a Payload Suspended through an Elastic Cable

We study the problem of a quadrotor transporting a payload suspended through a cable. While prior work has modeled the cable as a massless rigid link, in this paper, we consider the cable to be elastic with both spring stiffness and damping. We derive a coordinate-free dynamical model of the system. We use singular-perturbations to show that a geometric controller developed for the case of an inelastic cable still works for the case of an elastic cable to achieve almost global exponential tracking of a desired load position to within a certain bound. We provide numerical results to validate the proposed controller for various spring and damping coefficients for the cable.