No abstract
Pose graphs have become an attractive representation for solving Simultaneous Localization and Mapping (SLAM) problems. In this paper, we analyze the structure of the nonlinearities in the 2D SLAM problem formulated as the optimizing of a pose graph. First, we prove that finding the optimal configuration of a very basic pose graph with 3 nodes (poses) and 3 edges (relative pose constraints) with spherical covariance matrices, which can be formulated as a six dimensional least squares optimization problem, is equivalent to solving a one dimensional optimization problem. Then we show that the same result can be extended to the optimizing of a pose graph with "two anchor nodes" where every edge is connecting to one of the two anchor nodes. Furthermore, we prove that the global minimum of the resulting one dimensional optimization problem must belong to a certain interval and there are at most 3 minima in that interval. Thus the globally optimal pose configuration of the pose graph can be obtained very easily through the bisection method and closed-form formulas.
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.
This paper first demonstrates an interesting property of bundle adjustment (BA), "scale drift correction" property. Here "scale drift correction" means that BA can converge to the correct solution (up to a scale) even if the initial values of the camera pose translations and point feature positions are calculated using different scale factors. This property together with other properties of BA makes BA the best approach for monocular SLAM when no camera motion information is available, although the computational cost of BA is an issue. This naturally leads to the idea of using local BA and map joining to solve large-scale monocular SLAM problem, which is proposed in this paper. The local maps are built through Scale-Invariant Transform Feature (SIFT) detector and matching, random sample consensus paradigm (RANSAC) at different levels for robust outlier removal, and BA for optimization. To reduce the computational cost of the large-scale map building, the features in each local map are properly selected and then the local maps are combined using a recently developed 3D map joining algorithm. The proposed large-scale monocular SLAM algorithm is evaluated using a publicly available dataset. It is shown that the camera poses estimate is very accurate as compared with the ground truth provided.
In recent SLAM (simultaneous localization and mapping) literature, Pose Only or Graph Based optimization methods have become increasingly popular. This is greatly supported by the fact that these algorithms are computationally more efficient, as they focus more on the robots trajectory rather than dealing with complex map. Implantation simplicity allows these to handle both 2D and 3D environments with ease. This paper presents a detailed evaluation of the reliability and the accuracy of Pose Only SLAM, and aims at providing a definitive answer to whether optimizing poses is more advantages than optimizing features. Focus is centered around TORO, a Tree based network optimization algorithm, which has gained increase recognition within the robotics community. We compare this with Least Squares, which is considered one of the best Maximum Likelihood method available. Results based on both simulated and real data in 2D environments, are presented to substantiate the conclusions.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.