In this study, we propose a synchronized motion-switching method for a robotic swarm comprising autonomous distributed mobile robots having only local communication ability. Assuming that a robot is equipped with a phase oscillator, we regarded the robotic swarm as a coupled oscillator system (COS). Furthermore, we propose wave-type local interactions among oscillators, which generate stationary-phase waves over a network of COS. Because a phase wave depends on the graph structure of the COS, a robot can determine the global changes in a swarm using spectrum analysis of its phase. The proposed system was applied to a robotic swarm to make synchronized decisions to change the direction of movement. Without a synchronization system, a robotic swarm can be split into pieces. Contrastingly, the proposed system can maintain a unified behavior even if a robot has no global communication or leader. We verified the feasibility of local interactions by building real robots, and examined the effectiveness of the simulations.