GPmap: A Unified Framework for Robotic Mapping Based on Sparse Gaussian Processes

Abstract

This paper proposes a unified framework called GPmap for reconstructing surface meshes and building continuous occupancy maps using sparse Gaussian processes. Previously, Gaussian processes have been separately applied for surface reconstruction and occupancy mapping with different function definitions. However, by adopting the signed distance function as the latent function and applying the probabilistic least square classification, we solve two different problems in a single framework. Thus, two different map representations can be obtained at a single cast, for instance, an object shape for grasping and an occupancy map for obstacle avoidance. Another contribution of this paper is reduction of computational complexity for scalability. The cubic computational complexity of Gaussian processes is a well-known issue limiting its applications for large-scale data. We address this by applying the sparse covariance function which makes distant data independent and thus divides both training and test data into grid blocks of manageable sizes. In contrast to previous work, the size of grid blocks is determined in a principled way by learning the characteristic length-scale of the sparse covariance function from the training data. We compare theoretical complexity with previous work and demonstrate our method with structured indoor and unstructured outdoor datasets.