In this paper, methods for detecting obstacles on a plane using a relative disparity map (RDMap) are proposed and discussed. The RDMap, which was formerly introduced by the author Umeda, is relative to a plane that is observed at first as the reference. It has an interesting feature that a plane in real 3D space also becomes a plane in the map, and has homogeneous characteristics compared to an ordinary range image. The proposed methods work even when the pose of the sensor changes significantly, which is the case in humanoid walking. First, a method to detect planar regions and obstacles by fitting a plane to the RDMap and a method to obtain the pose parameters from the RDMap are introduced. Fundamental experiments are then conducted to verify that a plane in real 3D space becomes a plane in the RDMap and that obstacles can be detected using the residual sum of squares for the fitted plane, and measurement errors in pose parameters are then evaluated. Finally, an experimental system with a humanoid and a small range image sensor is constructed, and it is demonstrated that the humanoid can detect obstacles on a plane by the proposed methods while walking.