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