Robotics: Science and Systems XI

Hilbert maps: scalable continuous occupancy mapping with stochastic gradient descent

Fabio Ramos, Lionel Ott


The vast amount of data robots can capture today motivates the development of fast and scalable statistical tools to model the environment the robot operates in. We devise a new technique for environment representation through continuous occupancy mapping that improves on the popular occupancy grip maps in two fundamental aspects: 1) it does not assume an a priori discretisation of the world into grid cells and therefore can provide maps at an arbitrary resolution; 2) it captures statistical relationships between measurements naturally, thus being more robust to outliers and possessing better generalisation performance. The technique named Hilbert maps, is based on the computation of fast kernel approximations that project the data in a Hilbert space where a logistic regression classifier is learnt. We show that this approach allows for efficient stochastic gradient descent optimisation where each measurement is only processed once during learning or online updates. We present results with three types of kernel approximations, Random Fourier, Nystrom and a novel sparse projections. We also show how to extend the approach to accept probability distributions as inputs, i.e. when there is uncertainty over the position of laser scans due to sensor or localisation errors. Experiments demonstrate the benefits of the approach in popular benchmark datasets with several thousand laser scans.



    AUTHOR    = {Fabio Ramos AND Lionel Ott}, 
    TITLE     = {Hilbert maps: scalable continuous occupancy mapping with stochastic gradient descent}, 
    BOOKTITLE = {Proceedings of Robotics: Science and Systems}, 
    YEAR      = {2015}, 
    ADDRESS   = {Rome, Italy}, 
    MONTH     = {July},
    DOI       = {10.15607/RSS.2015.XI.002}