The article presents self-excitation methods that aim to achieve the locomotion of a tensegrity robotic snake. The snake-like robot usually forms locomotion by a travelling wave. In this paper, we try to achieve travelling wave locomotion of a tensegrity robotic snake by self-excitation controllers. Two types of self-excitation methods are introduced in this study. These two types of methods are constructed by Kuramoto oscillators and cross-feedback controllers respectively. We derive the total dynamic model of a tensegrity robotic snake and the friction model between wheels and ground. To verify the effectiveness of self-excitation methods, a total dynamic model and two self-excitation controller models are built by numerical software and several simulations are performed. The results of simulations show that travelling wave locomotion can be generated by different self-excitation methods. We also find that controllers, the robotic snake and the environment are coupled to induce limit cycle locomotion of the robot.