Log-GPIS-MOP: A Unified Representation for Mapping, Odometry and Planning

Abstract--Whereas dedicated scene representations are required for each different task in conventional robotic systems, this paper demonstrates that a unified representation can be used directly for multiple key tasks. We propose the Log-Gaussian Process Implicit Surface for Mapping, Odometry and Planning (Log-GPIS-MOP): a probabilistic framework for surface reconstruction, localisation and navigation based on a unified representation. Our framework applies a logarithmic transformation to a Gaussian Process Implicit Surface (GPIS) formulation to recover a global representation that accurately captures the Euclidean distance field with gradients and, at the same time, the implicit surface. By directly estimating the distance field and its gradient through Log-GPIS inference, the proposed incremental odometry technique computes the optimal alignment of an incoming frame and fuses it globally to produce a map. Concurrently, an optimisation-based planner computes a safe collision-free path using the same Log-GPIS surface representation. We validate the proposed framework on simulated and real datasets in 2D and 3D and benchmark against the state-of-the-art approaches. Our experiments show that Log-GPIS-MOP produces competitive results in sequential odometry, surface mapping and obstacle avoidance. Using the built map and the key objective of the mapping task is to reconstruct an accurate, estimated location, a path planner may produce collision-free dense and high-resolution map of the scene for, e.g., inspection paths for the robot to navigate safely. Path planning similarly requires dense information raises varying requirements leading to dedicated environment such as obstacle occupancy or closest distance to collision representations. The choice of scene representation strongly in order to avoid obstacles. As a unified representation for affects the performance of the localisation, mapping, and path multiple purposes, a feature-based representation such as a set planning tasks. Personal use of this material is permitted.