Several position identification methods have been used for mobile robots. Dead reckoning is a popular method, but is not reliable for the measurement in long distances especially on uneven surfaces because due to the accumulation error of 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 previous papers, we introduced the second prototype CPS machine model named CPS-II and its experimental result. In this paper, we show the relationship between the configuration of moving robots in CPS-II and its' positioning accuracy using analytical technique and propose optimum moving strategy to minimize positioning error even after robots move long distances.