As power demand across communities increases, focus has been given to the maintenance of power lines against harsh environments such as wind-induced vibration (WIV). Inspection robots and fixed vibration absorbers (FVAs) are the current solutions. However, both solutions are currently facing many challenges. Inspection robots are limited by their size and considerable power demand, while FVAs are narrowband and unable to adapt to changing wind characteristics and thus are unable to reposition themselves at the antinodes of the vibrating loop. In view of these shortcomings, we propose a mobile damping robot (MDR) that integrates inspection robots mobility and FVAs WIV vibration control to help maintain power lines. In this effort, we model the conductor and the MDR by using Hamilton’s principle, and we consider the two-way nonlinear interaction between the MDR and the cable. The MDR is driven by a proportional-derivative (PD) controller to the optimal vibration location (antinodes) as the wind characteristics vary. The numerical simulations suggest that the MDR outperforms FVAs for vibration mitigation. Furthermore, the key parameters that influence the performance of the MDR are identified through a parametric study. The findings could setup a platform to design a prototype and experimentally evaluate the performance of the MDR.