In this paper, in order to get the better identification of motion and shape parameters of a plane dynamics, that is, in order to reduce the parameter ambiguity in the case of when we use only vision as the observation data, we now consider that we apply the laser range finder data with vision using both of a single laser range finder and a single CCD camera mounted on a mobile robot platform. The reason why we use the laser range finder is that it makes a line on the moving plane along a horizontal laser plane. Namely the laser range finder observes a cross section of the plane as a line. This line changes as the plane moves. We can add a line information for the identification problem. We show that when we use the laser range finder data with vision as the observation data the dimension of the parameter ambiguity in the only vision case can be reduced. Further, we introduce a suitable canonical form in order to identify orbits of the underlying a suitable subgroup of perspective group.