CPL-SLAM: Efficient and Certifiably Correct Planar Graph-Based SLAM Using the Complex Number Representation

Fan, Taosha; Wang, Hanlin; Rubenstein, Michael; Murphey, Todd D.

doi:10.1109/tro.2020.3006717

Cited by 27 publications

(18 citation statements)

References 53 publications

(180 reference statements)

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“…In some modern algorithms for solving pose-graph SLAM such as [21] and planar pose-graph and feature-based SLAM such as [7], the original SLAM problem is first reformulated as a rotation only problem, and then semidefinite relaxation and Riemannian staircase optimisation are applied. Similarly, in the proof of the region of attraction for GN in [5], the posegraph SLAM problem is also transferred into an orientation only problem first to facilitate the analysis.…”

Section: Discussionmentioning

confidence: 99%

“…[14] [13][2] [12][1] [19]). In particular, some recently developed algorithms can efficiently recover certifiably globally optimal solutions to the SLAM problems under certain conditions using techniques ranging from semidefinite relaxation and Riemannian Staircase procedure [21] [3], sparsebounded sum of squares programming [17], and complex number representation [7].…”

Section: Introductionmentioning

confidence: 99%

“…Similarly, Cartan-sync in [3] uses the same isotropic covariance matrices assumption and improved SE-sync by using the Cartan motion group and introducing a novel preconditioner to accelerate the algorithm. The isotropic noise covariance matrices assumption is also used in [7], where a more compact unit complex number representation instead of the matrix representation of SO (2) is used to speed up the semidefinite relaxation and Rienannian staricase optimisation for 2D pose-graph and 2D feature-based SLAM problems.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Feature-Based SLAM: Why Simultaneous Localisation and Mapping?

Zhao¹,

Mao²,

Huang³

2021

Robotics: Science and Systems XVII

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In this paper, we first prove an interesting result for point feature based SLAM. "When the covariance matrices of feature observation errors are isotropic, the robot poses and feature positions obtained in each Gauss-Newton iteration (when solving a reformulated least squares optimisation based SLAM) are independent of the feature positions in the previous step". That is, even if we reset the feature positions to different random values before each iteration, the results after the iteration never change. Building on this finding, we propose an algorithm to solve the robot poses only ("localisation") and show that the algorithm generates exactly the same robot poses in each iteration as the Gauss-Newton method (SLAM). The optimal feature positions can be easily recovered using a closed-form formula after the optimal robot poses are obtained.Similarly, when the covariance matrices of odometry translation errors are also isotropic, we can prove that the SLAM results are independent of both the feature positions and the robot positions. Thus, we can have an "rotation-only algorithm" which generates the same robot rotations as the full SLAM. Again, the optimal robot positions and the optimal feature positions can be computed from the obtained optimal robot rotations using a closed-form formula. We have used multiple 2D and 3D SLAM datasets to demonstrate our research findings. The video shows the interesting convergence results can be found at https://youtu.be/j1T8toqGtDE. We expect the findings in this paper can help SLAM researchers to further understand the special structure of the SLAM problems and to further develop more efficient and reliable SLAM algorithms.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Feature-Based SLAM: Why Simultaneous Localisation and Mapping?

Zhao¹,

Mao²,

Huang³

2021

Robotics: Science and Systems XVII

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“…The system can be seen as a spring-mass model [143] and solved by computing the minimal energy state of the model. Some of the popular open source graph-based algorithms are g2o [117], GTSAM [144], HOG-Man [145], KinectFusion [146], PTAM [147], TORO [148], CPL-SLAM [149], [150] etc. A comparative analysis of these three paradigms has been shown in Table 5.…”

Section: X K N and N Number Of Landmarks In The Map As M Kmentioning

confidence: 99%

Critical Design and Control Issues of Indoor Autonomous Mobile Robots: A Review

et al. 2021

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Robots that can move autonomously and can make intelligent decisions by perceiving their environments and surrounding objects are known as autonomous mobile robots. Such robots have rapidly moved from laboratories to automated industries to fill a variety of roles in our lives, homes, offices, hospitals, industries, and even on the streets. The interest in mobile robots is growing rapidly, prompting an enormous amount of research over the last 30 years, on critical factors of mobile robots such as locomotion, perception, localization, mapping, ego-motion tracking, and dynamic navigation. This article surveys these essential factors of autonomous mobile robots in terms of mathematical modeling, control issues, and challenging factors. Brief discussions are provided on the fundamentals of these technologies, popular algorithms in comprehensive mode, future challenges, and promising directions to guide the construction of an autonomous mobile robot with high accuracy and effectiveness. Since it is difficult to find complete coverage of those topics in a single location, this article provides a guideline for researchers entering the field or for innovators in the mobile robotics sector. The paper also examines open challenges in indoor mobile robots and identifies potential futures for autonomous mobile robots.

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“…The problem was further studied in [28] where it was shown that for low noise regimes, the SDP relaxation is always tight. In robotics, SDP relaxations for estimating rigid transformations in simultaneous localization and mapping (SLAM) have been explored in a number of recent papers [8,11,12,19,32]. Again, the empirical performance is generally good, the optimal solutions can be efficiently computed [5], and the relaxations are shown to be tight for bounded noise levels.…”

Section: Related Workmentioning

confidence: 99%

On the Tightness of Semidefinite Relaxations for Rotation Estimation

et al. 2021

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Why is it that semidefinite relaxations have been so successful in numerous applications in computer vision and robotics for solving non-convex optimization problems involving rotations? In studying the empirical performance, we note that there are few failure cases reported in the literature, in particular for estimation problems with a single rotation, motivating us to gain further theoretical understanding. A general framework based on tools from algebraic geometry is introduced for analyzing the power of semidefinite relaxations of problems with quadratic objective functions and rotational constraints. Applications include registration, hand–eye calibration, and rotation averaging. We characterize the extreme points and show that there exist failure cases for which the relaxation is not tight, even in the case of a single rotation. We also show that some problem classes are always tight given an appropriate parametrization. Our theoretical findings are accompanied with numerical simulations, providing further evidence and understanding of the results.

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CPL-SLAM: Efficient and Certifiably Correct Planar Graph-Based SLAM Using the Complex Number Representation

Cited by 27 publications

References 53 publications

Feature-Based SLAM: Why Simultaneous Localisation and Mapping?

Feature-Based SLAM: Why Simultaneous Localisation and Mapping?

Critical Design and Control Issues of Indoor Autonomous Mobile Robots: A Review

On the Tightness of Semidefinite Relaxations for Rotation Estimation

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