On the Existence of Static Equilibria of a Cable-Suspended Load with Non-stopping Flying Carriers

Aerial cooperative robotic manipulation of cable-suspended objects has been largely studied as it allows handling large and heavy objects, and cables offer multiple advantages, such as their low weight and cost efficiency. Multirotors have been typically considered, which, however, can be unsuitable for long-lasting manipulation tasks due to their scarce endurance. Hence, this work investigates whether non-stop flights are possible for maintaining constant the pose of cable-suspended objects. First, we show that one or two flying carriers alone cannot perform non-stop flights while maintaining a constant pose of the suspended object. Instead, we demonstrate that \emph{three} flying carriers can achieve this task provided that the orientation of the load at the equilibrium is such that the components of the cable forces that balance the external force (typically gravity) do not belong to the plane of the cable anchoring points on the load. Numerical tests are presented in support of the analytical results.