Abstract
The celebrated minimum inertia line problem is reconsidered: a line is to be fitted to a planar cloud of points so that the sum of squared distances of all points to the line becomes minimal. The classical algebraic solution based on the tensor of inertia is complemented by a closed form trigonometric solution allowing various generalizations including the fit of elastic polygons. Proper polygons will be fitted numerically with non-closed partial solutions being reduced to the lowest dimension possible. This is complemented by segmentation heuristics for the measurement cloud.
The approach allows to solve the robot localization problem with high accuracy for position and orientation to be inferred from distance measurements in a known polygonal environment. The essential feature of the current approach is to fit the polygonal geometry as a whole.
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Kämpke, T., Strobel, M. Polygonal Model Fitting. Journal of Intelligent and Robotic Systems 30, 279–310 (2001). https://doi.org/10.1023/A:1008185412543
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DOI: https://doi.org/10.1023/A:1008185412543