Efficient Constellation-Based Map-Merging for Semantic SLAM

Data association in SLAM is fundamentally challenging, and handling ambiguity well is crucial to achieve robust operation in real-world environments. When ambiguous measurements arise, conservatism often mandates that the measurement is discarded or a new landmark is initialized rather than risking an incorrect association. To address the inevitable `duplicate' landmarks that arise, we present an efficient map-merging framework to detect duplicate constellations of landmarks, providing a high-confidence loop-closure mechanism well-suited for object-level SLAM. This approach uses an incrementally-computable approximation of landmark uncertainty that only depends on local information in the SLAM graph, avoiding expensive recovery of the full system covariance matrix. This enables a search based on geometric consistency (GC) (rather than full joint compatibility (JC)) that inexpensively reduces the search space to a handful of `best' hypotheses. Furthermore, we reformulate the commonly-used interpretation tree to allow for more efficient integration of clique-based pairwise compatibility, accelerating the branch-and-bound max-cardinality search. Our method is demonstrated to match the performance of full JC methods at significantly-reduced computational cost, facilitating robust object-based loop-closure over large SLAM problems.Comment: Accepted to IEEE International Conference on Robotics and Automation (ICRA) 201

Lagrangian Duality in 3D SLAM: Verification Techniques and Optimal Solutions

State-of-the-art techniques for simultaneous localization and mapping (SLAM) employ iterative nonlinear optimization methods to compute an estimate for robot poses. While these techniques often work well in practice, they do not provide guarantees on the quality of the estimate. This paper shows that Lagrangian duality is a powerful tool to assess the quality of a given candidate solution. Our contribution is threefold. First, we discuss a revised formulation of the SLAM inference problem. We show that this formulation is probabilistically grounded and has the advantage of leading to an optimization problem with quadratic objective. The second contribution is the derivation of the corresponding Lagrangian dual problem. The SLAM dual problem is a (convex) semidefinite program, which can be solved reliably and globally by off-the-shelf solvers. The third contribution is to discuss the relation between the original SLAM problem and its dual. We show that from the dual problem, one can evaluate the quality (i.e., the suboptimality gap) of a candidate SLAM solution, and ultimately provide a certificate of optimality. Moreover, when the duality gap is zero, one can compute a guaranteed optimal SLAM solution from the dual problem, circumventing non-convex optimization. We present extensive (real and simulated) experiments supporting our claims and discuss practical relevance and open problems.Comment: 10 pages, 4 figure

Past, Present, and Future of Simultaneous Localization And Mapping: Towards the Robust-Perception Age

Simultaneous Localization and Mapping (SLAM)consists in the concurrent construction of a model of the environment (the map), and the estimation of the state of the robot moving within it. The SLAM community has made astonishing progress over the last 30 years, enabling large-scale real-world applications, and witnessing a steady transition of this technology to industry. We survey the current state of SLAM. We start by presenting what is now the de-facto standard formulation for SLAM. We then review related work, covering a broad set of topics including robustness and scalability in long-term mapping, metric and semantic representations for mapping, theoretical performance guarantees, active SLAM and exploration, and other new frontiers. This paper simultaneously serves as a position paper and tutorial to those who are users of SLAM. By looking at the published research with a critical eye, we delineate open challenges and new research issues, that still deserve careful scientific investigation. The paper also contains the authors' take on two questions that often animate discussions during robotics conferences: Do robots need SLAM? and Is SLAM solved

A review of optimisation strategies used in simultaneous localisation and mapping

© 2018, © 2018 Northeastern University, China. This paper provides a brief review of the different optimisation strategies used in mobile robot simultaneous localisation and mapping (SLAM) problem. The focus is on the optimisation-based SLAM back end. The strategies are classified based on their purposes such as reducing the computational complexity, improving the convergence and improving the robustness. It is clearly pointed out that some approximations are made in some of the methods and there is always a trade-off between the computational complexity and the accuracy of the solution. The local submap joining is a strategy that has been used to address both the computational complexity and the convergence and is a flexible tool to be used in the SLAM back end. Although more research is needed to further improve the SLAM back end, nowadays there are quite a few relatively mature SLAM back end algorithms that can be used by SLAM researchers and users

Novel insights into the impact of graph structure on SLAM

© 2014 IEEE. SLAM can be viewed as an estimation problem over graphs. It is well known that the topology of each dataset affects the quality of the corresponding optimal estimate. In this paper we present a formal analysis of the impact of graph structure on the reliability of the maximum likelihood estimator. In particular, we show that the number of spanning trees in the graph is closely related to the D-optimality criterion in experimental design. We also reveal that in a special class of linear-Gaussian estimation problems over graphs, the algebraic connectivity is related to the E-optimality design criterion. Furthermore, we explain how the average node degree of the graph is related to the ratio between the minimum of negative log-likelihood achievable and its value at the ground truth. These novel insights give us a deeper understanding of the SLAM problem. Finally we discuss two important applications of our analysis in active measurement selection and graph pruning. The results obtained from simulations and experiments on real data confirm our theoretical findings

Towards a reliable SLAM back-end

In the state-of-the-art approaches to SLAM, the problem is often formulated as a non-linear least squares. SLAM back-ends often employ iterative methods such as Gauss-Newton or Levenberg-Marquardt to solve that problem. In general, there is no guarantee on the global convergence of these methods. The back-end might get trapped into a local minimum or even diverge depending on how good the initial estimate is. Due to the large noise in odometry data, it is not wise to rely on dead reckoning for obtaining an initial guess, especially in long trajectories. In this paper we demonstrate how M-estimation can be used as a bootstrapping technique to obtain a reliable initial guess. We show that this initial guess is more likely to be in the basin of attraction of the global minimum than existing bootstrapping methods. As the main contribution of this paper, we present new insights about the similarities between robustness against outliers and robustness against a bad initial guess. Through simulations and experiments on real data, we substantiate the reliability of our proposed method. © 2013 IEEE

Exploiting the separable structure of SLAM

© 2015, MIT Press Journals. All rights reserved. In this paper we point out an overlooked structure of SLAM that distinguishes it from a generic nonlinear least squares problem. The measurement function in most common forms of SLAM is linear with respect to robot and features' positions. Therefore, given an estimate for robot orientation, the conditionally optimal estimate for the rest of state variables can be easily obtained by solving a sparse linear-Gaussian estimation problem. We propose an algorithm to exploit this intrinsic property of SLAM by stripping the problem down to its nonlinear core, while maintaining its natural sparsity. Our algorithm can be used together with any Newton-based iterative solver and is applicable to 2D/3D pose-graph and feature-based problems. Our results suggest that iteratively solving the nonlinear core of SLAM leads to a fast and reliable convergence as compared to the state-of-the-art back-ends

Dimensionality reduction for point feature SLAM problems with spherical covariance matrices

© 2014 Elsevier Ltd. All rights reserved. The main contribution of this paper is the dimensionality reduction for multiple-step 2D point feature based Simultaneous Localization and Mapping (SLAM), which is an extension of our previous work on one-step SLAM (Wang et al.; 2013). It has been proved that SLAM with multiple robot poses and a number of point feature positions as variables is equivalent to an optimization problem with only the robot orientations as variables, when the associated uncertainties can be described using spherical covariance matrices. This reduces the dimension of original problem from 3m+2n to m only (where m is the number of poses and n is the number of features). The optimization problem after dimensionality reduction can be solved numerically using the unconstrained optimization algorithms. While dimensionality reduction may not provide computational saving for all nonlinear optimization problems, for some SLAM problems we can achieve benefits such as improvement on time consumption and convergence. For the special case of two-step SLAM when the orientation information from odometry is not incorporated, an algorithm that can guarantee to obtain the globally optimal solution (in the maximum likelihood sense) is derived. Simulation and experimental datasets are used to verify the equivalence between the reduced nonlinear optimization problem and the original full optimization problem, as well as the proposed new algorithm for obtaining the globally optimal solution for two-step SLAM