Several position identification methods have been used for mobile robots. Dead reckoning is a popular method, but is not reliable for long distances or uneven surfaces because of variations in wheel diameter and slippage. The landmark method, which estimates current position relative to landmarks, cannot be used in an uncharted environment. We have proposed a new method called "Cooperative Positioning System (CPS) ." For CPS, we divide the robots into two groups, A and B. One group, A, remains stationary and acts as a landmark while group B moves. Group B then stops and acts as a landmark for group A. This "dance" is repeated until the target position is reached. CPS has a far lower accumulation of positioning error than dead reckoning, and can work in three-dimensions which is not possible with dead reckoning. Also, CPS has inherent landmarks and therefore works in uncharted environments. In this paper, we discuss CPS with redundancy that consists of a number of moving robots and show a new computational theory that is to integrate positional information obtained from various combinations of multiple robots. Experimental results with a second prototype CPS machine model (CPS-II) give a positioning accuracy of 0.32% for position and 0.43 [degree] for attitude without redundancy, and 0.12% for position and 0.32 [degree] for attitude with redundancy.