Manifold learning for robot navigation

In this paper we introduce methods to build a SOM that can be used as an isometric map for mobile robots. That is, given a dataset of sensor readings collected at points uniformly distributed with respect to the ground, we wish to build a SOM whose neurons (prototype vectors in sensor space) correspond to points uniformly distributed on the ground. Manifold learning techniques have already been used for dimensionality reduction of sensor space in navigation systems. Our focus is on the isometric property of the SOM. For reliable path-planning and information sharing between several robots, it is desirable that the robots build an internal representation of the sensor manifold, a map, that is isometric with the environment. We show experimentally that standard Non-Linear Dimensionality Reduction (NLDR) algorithms do not provide isometric maps for range data and bearing data. However, the auxiliary low dimensional manifolds created can be used to improve the distribution of the neurons of a SOM (that is, make the neurons more evenly distributed with respect to the ground). We also describe a method to create an isometric map from a sensor readings collected along a polygonal line random walk.