Robust Geometric Control of Catenary Robots under Unstructured Force Uncertainties

Researchers Alexandre Anahory Simoes and Leonardo Colombo have developed a robust geometric control framework for catenary robots—systems where two quadrotors are connected by an inextensible cable. Published on arXiv (2604.27705), the paper models the entire system on SE(3), the special Euclidean group that captures 3D rotations and translations. Crucially, the cable is not treated as an independent dynamical element but as a geometric subsystem induced by the UAVs' configuration. The catenary shape generates configuration-dependent forces that couple the translational dynamics of both quadrotors, creating a challenging control problem.

The team proposes a geometric tracking controller for the relative configuration between the two agents and analyzes its robustness under unstructured uncertainties in the catenary-induced forces. The main theoretical result establishes local input-to-state stability (ISS) of the closed-loop tracking errors: in the nominal case, the errors converge asymptotically, and under bounded perturbations (e.g., wind gusts or payload shifts), an explicit ultimate bound is guaranteed. This work provides a mathematically rigorous foundation for controlling tethered drone pairs in applications such as aerial towing, suspended load transport, or search-and-rescue operations where precise relative positioning is critical.