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Spectral Graph Theory in Pose-Graph ApplicationsAuthor: Sayantan Datta Date: 2017-12-05 Report no: IIIT/TH/2017/85 Advisor:Madhava Krishna AbstractIn this thesis, we investigate spectral graph theoretic techniques especially heat-kernel embedding as a route to graph representation, in order to solve commonly known Pose-Graph applications in Robotics such as Simultaneous Localization and Mapping problem and mining Multi-Trajectory Pose Correspondences. The Simultaneous Localization and Mapping problem (SLAM) in robotics is typically modeled as a dyadic graph of relative pose measurements taken by the robot. The graph nodes store the values representing the absolute pose of the robot at a given point of time. An edge connecting two nodes represents robot movement and it stores the measurements taken by the robot sensor while moving between two nodes. The objective of the SLAM problem is to find the optimal global measurements best satisfying the noisy relative measurements [29]. This problem of optimal estimation on a graph given relative measurements is a well-studied problem , for which several results and algorithms are known [6, 7]. In this thesis, we explore the applications of spectral graph theory in assisting the problem of single and multi-robot SLAM. SLAM is generally solved as a least squares problem. Robust kernels which are less sensitive to outliers are used to deal with noise and outlier measurements. However, robust kernels tend to be dependent on initialization and can fail as the number of outliers increase. Therefore, it’s important to identify and prune the outlier (noisy) measurements represented by incorrect loop closure edges for an accurate pose estimate. Therefore, we propose a multi-scale Heat-Kernel analysis based loop closure edge pruning algorithm for the SLAM graph. We show that compared to other pruning algorithms, our algorithm has a substantially higher precision and recall when compared and is able to handle a large amount of outlier measurements. We have corroborated results on several publicly available datasets and several types of noise. Our algorithm is not restricted to SLAM graphs only, but has a much wider applicability to other types of geometric graphs. Furthermore, in the case of multi-robot SLAM problem, we consider the problem of finding pose matches between trajectories of multiple robots in their respective coordinate frames or equivalent matches between trajectories obtained during different sessions. Pose correspondences between trajectories are mediated by common landmarks represented in a topological map lacking distinct metric coordinates. Despite such lack of explicit metric level associations, we mine preliminary pose level correspondences between trajectories through a novel multi-scale heat-kernel descriptor and correspondence graph framework. These serve as an improved initialization for ICP (Iterative Closest Point) to yield dense pose correspondences. The set of models and framework proposed in this thesis could act as the basic building blocks in the future works attempting to advance the science of building smarter SLAM systems. Full thesis: pdf Centre for Robotics |
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