In this paper, a non-visual robotic formation control method based on a streaming communication architecture and a leader-follower control model is studied. The proposed stream-based communication architecture is inspired by the flocking behavior of fish. We analogize it into a form resembling an N-ary tree for communication purposes. Communication proceeds to the next layer only when all nodes in the upper layer have completed the follower selection. We also introduce a fault-tolerance mechanism and a termination filtering mechanism to prevent multiple leaders from choosing the same follower, avoiding a scenario where the robots in the last layer enter an endless loop of follower selection. The proposed stream-based communication architecture, built upon serial and parallel tracking, can achieve more complex formations, such as rectangular formations, closely resembling real-world scenarios, significantly enhancing formation efficiency. Simulation experiments on the e-puck platform validate the effectiveness and robustness of this architecture.