A cell-to-cell mapping method is introduced and applied to the analysis a fuzzy-knowledge-based mobile robot motion control system. The cell-to-cell mapping was originally used in nonlinear system analysis. This method is found to be very compatible with the fuzzy-knowledge-based system. By dividing the state space into cell state space, the multi-image fuzzy mapping is transformed to a fuzzy cell-to-cell mapping. The periodic solutions of the fuzzy dynamic system are located by using an algorithm. The global behavior of the fuzzy mapping is described by finding the domain of attraction of a periodic solution.