Hilbert maps: scalable continuous occupancy mapping with stochastic gradient descent
Robotics: Science and Systems XI
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
... ationships 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 optimisation where each measurement is only processed once during learning in an online manner. We present results with three types of approximations, Random Fourier, Nyström and a novel sparse projection. 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.