Inspection robotics is attracting much attention on overhead power transmission lines to replace manual inspection tour. In this paper, based on a benchmark of underactuated Acrobot, we mainly focus on movements and control of a two-link bionic-robot for online inspection by adding grippers at the end of connecting links. Firstly, a movement planning is proposed for brachiating suspended on high-voltage aerial lines. Considering motion efficiency and some obstacles on the lines, two movements consisting of line-walking and obstacle-navigation are analyzed in details. Then, according to the Lyapunov-based analysis and the theory of energy conservation, an energy-based controller is presented for obstacle-navigation to track and stabilize the planned movement. Finally, Simulation results show that the bionic-robot can realize obstacle-navigation motion and proves the valid of the controller.