A novel closed-form solution for pose-graph SLAM is presented. It optimizes pose-graphs of particular structure called pose-chains by employing an extended version of trajectory bending. Our solution is designed as a back-end optimizer to be used within systems whose front-end performs state-of-the-art visual odometry and appearance based loop detection. The optimality conditions of our closed-form method and that of state-of-the-art iterative methods are discussed. The practical relevance of their theoretical differences is investigated by extensive experiments using simulated and real data. It is shown using 49 kilometers of challenging binocular data that the accuracy obtained by our closed-form solution is comparable to that of state-of-the-art iterative solutions while the time it needs to compute its solution is a factor 50 to 200 times lower. This makes our approach relevant to a broad range of applications and computational platforms.
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