Using a hyper-ellipsoid clustering Kohonen for autonomous mobile robot map building, place recognition and motion planning

We show how a self-organizing Kohonen neural network using hyperellipsoid clustering (HEC) can build maps from actual sonar data. With the HEC algorithm we can use the Mahalanobis distance to learn elongated shapes (typical of sonar data) and obtain a stochastic measurement of data-node association. Hence, the HEC Kohonen can be used to build topographical maps and to recognize its own topographical cues for self-localization. The number of nodes can also be regulated in a self-organizing manner by measuring how well a node models the statistical properties of its associated data. This measurement determines whether a node should be divided (mitosis) or pruned completely. Because fewer nodes are needed for an HEC Kohonen than for a Kohonen that uses only Euclidean distance, the data size is smaller for the HEC Kohonen. Relative to grid-based approaches, the savings in data size is even more profound. By incorporating principal component analysis (PCA), the HEC Kohonen can handle problems with several dimensions (3D, time-series, etc.). The HEC Kohonen is also multifunctional in that it accommodates compact geometric motion planning and self-referencing algorithms. It can also be generalized to solve other pattern recognition problems