Robust Geometric Control of Catenary Robots under Unstructured Force Uncertainties

This paper considers the robust control of a catenary robot composed of two quadrotors connected by an inextensible cable. The system is modeled on $SE(3)$, with the cable treated as a geometric subsystem induced by the UAV configuration rather than as an independent dynamical element. The catenary shape determines configuration-dependent forces that couple the translational dynamics of the vehicles. We propose a geometric tracking controller for the relative configuration of the agents and analyze its robustness with respect to unstructured uncertainties in the catenary-induced forces. The main theoretical result establishes local input-to-state stability of the closed-loop tracking errors. In particular, we obtain asymptotic convergence in the nominal case and an explicit ultimate bound for the tracking errors under bounded catenary-force perturbations.