Transporting objects using aerial robots has been widely studied in the literature. Still, those approaches always assume that the connection between the quadrotor and the load is made in a previous stage. However, that previous stage usually requires human intervention, and autonomous procedures to locate and attach the object are not considered. Additionally, most of the approaches assume cables as rigid links, but manipulating cables requires considering the state when the cables are hanging. In this work, we design and control a catenary robot. Our robot is able to transport hook-shaped objects in the environment. The robotic system is composed of two quadrotors attached to the two ends of a cable. By defining the catenary curve with five degrees of freedom, position in 3-D, orientation in the z-axis, and span, we can drive the two quadrotors to track a given trajectory. We validate our approach with simulations and real robots. We present four different scenarios of experiments. Our numerical solution is computationally fast and can be executed in real-time.
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