Large-scale continuous 2.5D robotic mapping

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Autonomous robotic systems require building representations of the environment in order to accomplish their particular tasks. Creating rich, continuous probabilistic maps is essential for the robot to perceive the world. As the complexity of the task increases, robots need more sensors or more data to build maps. Noisy and incomplete data is common for the robotic sensors outputs; Gaussian Process (GP), a flexible and powerful statistical model, has become a popular method to cope with the incompleteness of sensory information, incorporate and handle uncertainties appropriately and allow a multi-resolution representation of space. GP regression has been applied in robotic mapping to predict spatial correlations and fill in gaps in unknown areas across the field. The key component of GP for robotic mapping is that it captures spatial correlations and thus increases the accuracy of the representation when fusing data. When multiple sources of data are available, spatial correlations also can be used in fusion to improve accuracy. For large datasets, however, exploiting correlations can become prohibitively expensive. One attractive strategy for reducing storage and computational cost is submapping, which works by dividing the environment into small regions. If no information is shared between maps, submaps are statistically independent. This thesis investigates how to effectively and efficiently model the necessary spatial correlations that are required to build accurate large-scale maps. Three near-optimal probabilistic mapping frameworks that exploit global and local strategies such as submapping are proposed. SubGPBF applies submapping techniques imposing the conditional independence between submaps. It develops a novel approach to propagate information forward and backwards, which allows spatial correlations to be transferred between submaps after fusing sensor data only within submaps. GMRF-BF is a global mapping approach, which exploits the inherent structure of the recently proposed continuous Gaussian Markov Random Field (GMRF) and Bayesian fusion in information form, to model spatial correlations using a sparse information matrix. This leads to information-form Bayesian fusion that is linear in cost. To further increase computational efficiency, this thesis combines ideas from the previous two approaches (the GMRF model and the information-form submapping) to propose another new framework named subGMRF-BF. The forward and backward update algorithms formulated in information form are introduced to produce a highly efficient approach due to the conditional independence between submaps when assuming Gaussian distribution. All three frameworks lend themselves to generate accurate 2.5D probabilistic maps at high resolution. They can handle varying noise from disparate sensor sources and incorporate spatial correlations in a statistically sound way. They are all efficient in memory requirements as there is no need to recover the full covariance matrix or information matrix. The performance of the three frameworks was evaluated on one controlled terrain elevation dataset and a real water pipe thickness dataset. Five other methods, including one optimal global (fully correlated) method and one without spatial correlations, were used to benchmark the proposed methods. The experiments show that the accuracy, reliability and consistency are improved when the spatial correlations are correctly modelled and incorporated. The experiments also show that all three frameworks achieve storage and computational gain compared with the fully correlated benchmark approach, while subGMRF-BF outperforms all others.
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