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Considering the structure of single split high-voltage transmission line and the feature of its magnetic density distribution, this paper propose a kind of methodology of autonomously collision-free obstacles overcoming for high-voltage power transmission-line inspection robot. The main features are listed as follows: (1) Six electromagnetic sensors are installed in the robot body and its two arms for obstacle-detection and obstacle-overcoming navigation. (2) A, B and C, three groups - amounting 20 sensors -are installed in each arm to detect the robot's pose and lead the obstacle-passing arm to grasp the conductor object. (3) There are three types of obstacles passing modes, namely, crossing-obstacle, spanning-obstacle, and crossing-spanning hybrid passing obstacle. Based on the response signals of the obstacles-detecting sensors and pose-detection sensors, the algorithms for obstacles detection, recognition, and pose detection are explored. The experimental and field tests show that the proposed method is capable of locating and recognizing the obstacles, as well as navigating the robot to pass obstacles autonomously and grasping the conductor object.