Rigid transformation is a popular method to estimate the robot motion given two sets of corresponding points seen from two different locations. Range imaging sensors, such as stereo camera and structured-light 3-D scanner, can be used to provide these corresponding points, however, such sensors have measurement uncertainty defined by intervals with upper and lower bounds. This paper presents a new approach to use interval analysis and simultaneously estimate the following: (1) the robot motion and, (2) the position of the landmarks with respect to the initial frame of reference, i.e. the robot initial pose. We will show that using this approach, the uncertainties of the landmark positions decrease over time, which causes the uncertainty of the robot pose to remain bounded. Our approach is illustrated with examples using simulated data, and real data acquired by Kinect sensor.
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