Gpmaps: a bayesian nonparametric approach for mapping and reconstruction

Abstract

This thesis proposes new methods for robotic mapping using Bayesian nonparametric models such as Gaussian processes and Dirichlet processes. Particularly, we propose a unified framework for occupancy mapping and surface reconstruction using Gaussian processes which are called GPmaps. However, since Gaussian processes suffer from high computational complexity, it is not directly applicable to large-scale environmental mapping. Therefore, we take a divide and conquer strategy by introducing three spatial approximations, global, local and glocal (global + local) as well as a temporal approximation. The global approximation partitions training data into manageable subsets and applies a mixture of Gaussian process experts. For data partitioning, we employ Dirichlet process mixture models and line tracking. Individual Gaussian processes predict global maps with their own training subsets which are then merged into a final map using a gating network. However, because the clustering and prediction steps are separated in a mixture of expert scheme, clustering errors cause mis-predictions in the final map. Therefore, we combine both the clustering and prediction steps and further apply infinite mixtures of Gaussian process experts. However, in large-scale environments the size of test positions is as enormous as that of training data. Therefore, we introduce a local approximation which factorizes the whole map into block maps and predicts each block map with its own local observations. For doing that, we propose overlapping local Gaussian processes which partition both training and test data and apply local Gaussian processes to extended training subsets. Particularly, with octree-based data partitioning, GPmaps with local approximations are converted into a sliding window approach where we predict a block map with its local observations and move on to the next block iteratively. However, overlapping Gaussian processes generate no block maps where there exist no observations in the extended block. Therefore, we finally introduce a glocal approximation and propose hierarchical Gaussian processes which combine a global Gaussian process on top of the overlapping local Gaussian processes. On the other hand, we incorporate a temporal approximation of a static world assumption with the spatial approximations and propose Bayesian recursive updates to incrementally update GPmaps for sequential observations acquired from static environments. We demonstrate our GPmaps with simulated data and real datasets acquired from laser range finders and Microsoft Kinect depth cameras. Experimental results show that our GPmaps produce more accurate and reliable robotic maps as well as map uncertainties than occupancy grid maps and OctoMaps with additional computational time. We implemented GPmaps with spatial and temporal approximations in C++ and published on-line as open source software at GitHub. Show more