We present a simultaneous localization and mapping (SLAM) algorithm that uses Bézier curves as static landmark primitives rather than feature points. Our approach allows us to estimate the full 6-DOF pose of a robot while providing a structured map which can be used to assist a robot in motion planning and control. We demonstrate how to reconstruct the 3-D location of curve landmarks from a stereo pair and how to compare the 3-D shape of curve landmarks between chronologically sequential stereo frames to solve the data association problem. We also present a method to combine curve landmarks for mapping purposes, resulting in a map with a continuous set of curves that contain fewer landmark states than conventional point-based SLAM algorithms. We demonstrate our algorithm's effectiveness with numerous experiments, including comparisons to existing state-of-the-art SLAM algorithms.
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