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). Currently, Inspection robots are used for maintenance efforts while fixed tuned mass dampers (FTMDs) are used to prevent structural damages. However, both solutions are facing many challenges. Inspection robots are limited by their size and considerable power demand, while FTMDs 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 FTMDs 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 controller to the optimal vibration location (i.e, antinodes) as the wind characteristics vary. The numerical simulations suggest that the MDR outperforms FTMDs for vibration mitigation. Furthermore, the key parameters that influence the performance of the MDR are identified through a parametric study. The findings could set up a platform to design a prototype and experimentally evaluate the performance of the MDR. / Master of Science / Power lines are civil structures that span more than 160000 miles across the United States. They help electrify businesses, factories and homes. However, power lines are subject to harsh environments with strong winds, which can cause Aeolian vibration. Vibration in this context corresponds to the oscillation of power lines in response to the wind. Aeolian vibration can cause significant structural damages that impact public safety and result in a significant economic loss. Today, different solutions have been explored to limit the damages to these key structures. For example, the lines are commonly inspected by foot patrol, helicopters, or inspection robots. These inspection techniques are labor intensive and expensive. Furthermore, Stockbridge dampers, mechanical vibration devices, can be used to reduce the vibration of the power line. However, Stockbridge dampers can get stuck at location called nodes, where they have zero efficiency. To tackle this issue, we propose a mobile damping robot that can re-adjust itself to points of maximum vibration to maximize vibration reduction. In this thesis, we explore the potential of this proposed solution and draw some conclusions of the numerical simulations.