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

TL;DR

This paper introduces Log-GPIS-MOP, a unified probabilistic framework that uses a single surface representation for mapping, odometry, and planning in robotics, demonstrating competitive results across tasks.

Contribution

The paper presents Log-GPIS-MOP, a novel unified surface representation framework that integrates mapping, odometry, and planning using a probabilistic approach based on a logarithmic transformation of GPIS.

Findings

Accurately captures Euclidean distance field and gradients.

Provides competitive performance in odometry, mapping, and obstacle avoidance.

Validated on both simulated and real datasets in 2D and 3D.

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.