Aerial Co-Manipulation with Cables: The Role of Internal Force for Equilibria, Stability, and Passivity

TLDR: It is proved that if a nonzero internal force is chosen, then the asymptotic stabilization of any desired beam attitude can be achieved with a decentralized and communicationless master–slave admittance controller.

Abstract: This paper considers the study of cooperative manipulation of a cable-suspended load with two generic aerial robots and without explicit communication. The role of the internal force for the asymptotic stability of the beam-position/beam-attitude equilibria is analyzed in depth. Using a nonlinear Lyapunov-based approach, we prove that if a non-zero internal force is chosen then asymptotic stabilization of any desired beam-pose configuration can be achieved with a decentralized and communication-less master-slave admittance controller. If, conversely, a zero internal force is chosen, as done in the majority of the state-of-the-art algorithms, the attitude of the beam is not controllable without communication. Non-zero internal force can be interpreted then as a fundamental factor that enables the use of cables as implicit communication means between the two vehicles in replacement of the explicit ones. Furthermore, the formal proof of the system output-strictly passivity with respect to an energy-like storage function and a certain input-output pair is given. This proves the stability and the robustness of the method even during motion. The theoretical findings are validated through numerical simulations.