Regeneration of Normal Distributions Transform for Target Lattice Based on Fusion of Truncated Gaussian Components

In this letter, we propose a method that can be used to regenerate the 3-D normal distributions transform (NDT) for target lattice. When a pose is updated by simultaneous localization and mapping (SLAM), the lattice at the pose is also transformed. Given that NDT is a Gaussian mixture model generated by regular cells, the fusion of NDTs transformed with updated poses can distort the shapes of the Gaussian components (GCs). Moreover, when robots without information about other robots’ initial poses share and fuse NDT maps, the simple fusion of NDT maps built in different lattices can distort GCs. To overcome this problem, we propose a method by which GCs are subdivided into truncated GCs by the target lattices on each axis iteratively, and the truncated GCs in the same target cell are fused. To determine whether the GC should be subdivided, we define a weight threshold assigned to the weight corresponding to the truncated GC. In an experiment, we evaluated the receiver operating characteristics, the accuracy, the $L_2$ value, the mean error, the mean covariance distance based on Frechet distance to assess the similarity of the regenerated NDT, and ground truth NDT. Also, we evaluated the computational performance of the proposed method. Moreover, we evaluated the application of map fusion. It was found that the NDT regenerated by the proposed method showed improvement in the $L_2$ value, mean error, and mean covariance distance.