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

arXiv: https://arxiv.org/abs/2206.09506 · HTML: https://mlsanity.com/paper/2206.09506/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jun 2022.

## Built on by (most cited first, 4 of 4)

- [PIN-SLAM: LiDAR SLAM Using a Point-Based Implicit Neural Representation for Achieving Global Map Consistency](https://mlsanity.com/paper/2401.09101/) (2024)
- [HIO-SDF: Hierarchical Incremental Online Signed Distance Fields](https://mlsanity.com/paper/2310.09463/) (2023)
- [Distance and Collision Probability Estimation from Gaussian Surface Models](https://mlsanity.com/paper/2402.00186/) (2024)
- [Learning Scene-Level Signed Directional Distance Function with Ellipsoidal Priors and Neural Residuals](https://mlsanity.com/paper/2503.20066/) (2025)

## Abstract (arXiv)

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.