Several position identification methods are being used for mobile robots. Dead reckoning is a popular method but due to the accumulation error from wheel slippage, reliability is low for the measurement of long distances especially on uneven surfaces. Another popular method is the landmark method, which estimates current position relative to known landmarks, but the landmark method's limitation is that it cannot be used in an uncharted environment. Thus, this paper proposes a new method called "Cooperative Positioning System (CPS)" that is able to overcome these shortcomings. The main concept of CPS is to divide the robots into two groups, A and B respectively, group A remains stationary and acts as a landmark while group B moves and then group B stops and acts as a landmark for group A. This process is repeated until the target position is reached. Compared with dead reckoning, CPS has a far lower accumulation of positioning error, and can also work in three-dimensions. Furthermore, CPS employs inherent landmarks and therefore can be used in uncharted environments unlike the landmark method. In this paper, focus will be on the discussion of the relationship between moving configurations of CPS and its positioning accuracy for the latest prototype CPS model, CPS-111, using simulation and analytical techniques. Optimum moving strategies in order to minimize positioning error are then discussed and verified through experiments.