∑ δ estimation is a simple non linear method of background estimation used in the field of estimation is a simple non linear method of background estimation used in the field of image processing. We propose the method of data transmission using the ∑ δ modulation under narrow bandwidth, which degrades the performance due to time-discretization. In this paper, the ∑ δ estimation is used as a method of motion detection of motors, and high priority is added to detected data. Hierarchical Token Bucket, which controls traffic in a link, discrimates motion data, and handles the packet with high priority preferentially. The motion detection algorithm based on traffic contonl is implemented into two degree-of-freedom robots to verify the validity of the proposed method. Effectiveness of the proposed method is verified through experiments..