Probabilistic Implicit Surfaces for Localisation, Mapping and Planning
- Publication Type:
- Thesis
- Issue Date:
- 2023
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Digitising the unknown and unstructured environments as part of robotic perception raises varying requirements for its dedicated scene representations. Although the use of depth sensors e.g., Light Detection And Ranging Sensor (LiDAR) and depth cameras, makes this process cost-effective, it poses a challenge in the quality of the reconstructed representation. This type of sensor is generally noisy, with limited field of view or in some cases produces sparse measurements. Gaussian Process Implicit Surfaces (GPIS), a statistical and powerful probabilistic representation, has become a well-known approach to deal with the sparseness of sensory information, manage and handle uncertainty, and allow a continuous representation. This thesis focuses on the use of GPIS as a probabilistic representation to perform efficient and effective mapping, localisation and optimization-based path planning for depth sensors in perception robotic systems.
The main concern with GP-based algorithms, however, is the cubic computational complexity. Firstly, this thesis presents a novel submapping method for post-processing dense maps and reconstruction, following the topology of the scene to generate conditional independent GPIS. This allows inference and fusion mechanisms to be performed in parallel followed by information propagation through the submaps.
GPIS-based representations can be used to produce distance information. This thesis secondly introduces the Log-Gaussian Process Implicit Surfaces (Log-GPIS), a novel representation to estimate Euclidean Distance Field (EDF) for incremental mapping. The key contribution is the realisation that the solution of the regularised Eikonal equation can be simply approximated by applying the logarithmic transformation to a GPIS formulation to recover a faithful estimate of the EDF and, at the same time, the implicit surface. Our experiments show that Log-GPIS produces the most accurate results for the EDF and comparable results for surface reconstruction with respect to other methods.
The combination of the smooth, probabilistic nature and the improved EDF of Log-GPIS unlocks its potential as a unified representation for multiple robotic tasks. This thesis thirdly presents Log-Gaussian Process Implicit Surface for Mapping, Odometry and Planning (Log-GPIS-MOP): a probabilistic framework for surface reconstruction, localization and navigation based on a unified representation. 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 to produce an incremental map. Concurrently, an optimisation-based planner computes a collision-free path using the same Log-GPIS surface representation. We validate the proposed framework on simulated and real datasets and benchmark against the state-of-the-art approaches.
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