In minimally invasive endovascular interventional surgery, guidewire navigation is an indispensable process. However, even experienced physicians often encounter difficulties in manually manipulating the guidewire for branch selection, while also facing the risk of radiation exposure. In this study, we investigated robotic autonomous guidewire navigation methods. An electromagnetic system was used to track the real-time position and orientation of the guidewire tip, and a state space representing the guidewire within the vascular environment was constructed to guide the robot in precise guidewire manipulation. Experimental results demonstrated that the proposed trial-and-error and centerline-guided methods successfully completed navigation tasks in a static environment, outperforming human navigation performance in terms of trajectory smoothness, trajectory length, and incorrect branch entry counts. For dynamic environment navigation, dynamic time warping (DTW), a technique for measuring the similarity between two temporal sequences, was integrated into the centerline-guided method. The proposed approaches eliminate the need for visual feedback and thereby minimizing the risk of radiation exposure for both patients and medical staff present in the operating room during the procedure.