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In this work we present the first initialization methods equipped with explicit performance guarantees adapted to the pose-graph simultaneous localization and mapping (SLAM) and rotation averaging (RA) problems. SLAM and rotation averaging are typically formalized as large-scale nonconvex point estimation problems, with many bad local minima that can entrap the smooth optimization methods typically applied to solve them; the performance of standard SLAM and RA algorithms thus crucially depends upon the quality of the estimates used to initialize this local search. While many initialization methods for SLAM and RA have appeared in the literature, these are typically obtained as purely heuristic approximations, making it difficult to determine whether (or under what circumstances) these techniques can be reliably deployed. In contrast, in this work we study the problem of initialization through the lens of spectral relaxation. Specifically, we derive a simple spectral relaxation of SLAM and RA, the form of which enables us to exploit classical linear-algebraic techniques (eigenvector perturbation bounds) to control the distance from our spectral estimate to both the (unknown) ground-truth and the global minimizer of the estimation problem as a function of measurement noise. Our results reveal the critical role that spectral graph-theoretic properties of the measurement network play in controlling estimation accuracy; moreover, as a by-product of our analysis we obtain new bounds on the estimation error for the maximum likelihood estimators in SLAM and RA, which are likely to be of independent interest. Finally, we show experimentally that our spectral estimator is very effective in practice, producing initializations of comparable or superior quality at lower computational cost compared to existing state-of-the-art techniques.

2022 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) October 23-27, 2022, Kyoto, Japan, Simultaneous localization and mapping (SLAM) is a critical capability in autonomous navigation, but in order to scale SLAM to the setting of "lifelong" SLAM, particularly under memory or computation constraints, a robot must be able to determine what information should be retained and what can safely be forgotten. In graph-based SLAM, the number of edges (measurements) in a pose graph determines both the memory requirements of storing a robot's observations and the computational expense of algorithms deployed for performing state estimation using those observations; both of which can grow unbounded during long-term navigation. To address this, we propose a spectral approach for pose graph sparsification which maximizes the algebraic connectivity of the sparsified measurement graphs, a key quantity which has been shown to control the estimation error of pose graph SLAM solutions. Our algorithm, MAC (for "maximizing algebraic connectivity"), which is based on convex relaxation, is simple and computationally inexpensive, and admits formal post hoc performance guarantees on the quality of the solutions it provides. In experiments on benchmark pose-graph SLAM datasets, we show that our approach quickly produces high-quality sparsification results which retain the connectivity of the graph and, in turn, the quality of corresponding SLAM solutions, as compared to a baseline approach which does not consider graph connectivity.

2023 IEEE International Conference on Robotics and Automation (ICRA 2023) May 29 - June 2, 2023. London, UK, We present a novel initialization technique for the range-aided simultaneous localization and mapping (RASLAM) problem. In RA-SLAM we consider measurements of point-to-point distances in addition to measurements of rigid transformations to landmark or pose variables. Standard formulations of RA-SLAM approach the problem as nonconvex optimization, which requires a good initialization to obtain quality results. The initialization technique proposed here relaxes the RA-SLAM problem to a convex problem which is then solved to determine an initialization for the original, non-convex problem. The relaxation is a second-order cone program (SOCP), which is derived from a quadratically constrained quadratic program (QCQP) formulation of the RASLAM problem. As a SOCP, the method is highly scalable. We name this relaxation Second-order COnic RElaxation for RASLAM (SCORE). To our knowledge, this work represents the first convex relaxation for RA-SLAM. We present real-world and simulated experiments which show SCORE initialization permits the efficient recovery of quality solutions for a variety of challenging single- and multi-robot RA-SLAM problems with thousands of poses and range measurements.