Relaxing loop-closing errors in 3D maps based on planar surface patches

3D mapping using large planar patches results in a compact and easily understandable representation of the environment as compared to point-cloud or voxel based representations. In this work, relaxation of loop-closing errors in a 3D map is presented. It is based on a plane-matching algorithm for correspondence-finding and least-squares registration of large planar patches fitted on 3D range-images. This method also provides covariance matrices for the pose-registration result. Based on this registration algorithm, a relaxation method utilizing these covariances is formulated. In particular, we exploit the plane-matcher properties that it provides an accurate rotation estimate, and that it can easily identify principal translational directions of uncertainty, to relax only the translation errors. This results in a closed-form solution that can be computed in a very fast manner, namely within a few milliseconds, as demonstrated by experimental results in an indoor locomotion test arena in form of a high bay rack.