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Detection of obstacles on a plane is important for a mobile robot that moves in a living space, especially for a humanoid that falls down even with a small obstacle. In this paper, a range image sensor for detecting small obstacles on a plane is constructed using a multi-slit laser projector. The sensor consists of a commercially available laser projector and a CCD camera. It measures a relative disparity map (RDMap) whose measurement errors are not affected by the distance. From the obtained RDMap, a plane is estimated using RANSAC and regions out of the plane are detected as obstacles. Experiments show that planes can be obtained with small errors in RDMaps with the constructed sensor, and that a humanoid with the constructed sensor can detect small obstacles such as a moving ping-pong ball and a LAN cable on a plane by the proposed methods while walking.