This paper presents the design and analysis of an underactuated 2D, 2-link brachiating robot intended for operation on medium voltage transmission power lines. The study incorporates modeling of wind torques to reflect realistic field conditions that the robot is likely to encounter. The initial optimal trajectory planning is performed under zero wind conditions. Subsequently, the system’s robustness is evaluated by applying winds of varying speeds to assess its ability to adhere to the precomputed optimal trajectory. To enhance the system’s robustness and ensure precise trajectory following, a Proportional-Derivative (PD) and partial feedback linearization controller is developed. This controller uses the optimal trajectory as a reference, providing feedback that compensates for disturbances and model uncertainties. The results demonstrate the efficacy of the proposed control strategy in maintaining accurate trajectory tracking despite environmental disturbances and parameter variations for this particular configuration, highlighting its potential for practical deployment in power line maintenance and inspection tasks.