Exploiting the Separable Structure of SLAM

Khosoussi, Kasra; Huang, Shoudong; Dissanayake, Gamini

doi:10.15607/rss.2015.xi.023

Cited by 12 publications

(22 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this regard, the idea of solving for the rotations first and to use the resulting estimate to bootstrap nonlinear iteration has been demonstrated to be very effective in practice [20,30,32,37]. Khosoussi et al [130] leverage the (approximate) separability between translation and rotation to speed up optimization.…”

Section: New Theoretical Tools For Slammentioning

confidence: 99%

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

Cadena¹,

Carlone²,

Carrillo³

et al. 2016

IEEE Trans. Robot.

3,141

1,742

View full text Add to dashboard Cite

Abstract-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 and consider future directions. 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?

show abstract

Section: New Theoretical Tools For Slammentioning

confidence: 99%

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

Cadena¹,

Carlone²,

Carrillo³

et al. 2016

IEEE Trans. Robot.

3,141

1,742

View full text Add to dashboard Cite

show abstract

“…respectively. It is possible to marginalize the translational states and landmarks and reformulate planar graph-based SLAM as an optimization problem on the rotational states only, which has been used in [27], [33], [49] to improve the computational efficiency. In a similar way, if rotational states z…”

Section: B Problem Simplificationmentioning

confidence: 99%

“…Similar to [24], [27], [56], PDL-GN uses the Gauss-Newton method and might not perform well if there are large residues of the measurements and strong nonlinearities of the objective function [21], [47], whereas CPL-SLAM uses the exact Hessian to compute the Newton direction, and thus, is expected to converge faster and have better efficiency. In addition, as mentioned before, when evaluating the descent direction, PDL-GN factorizes sparse matrices to solve linear equations.…”

Section: A Tree Datasetsmentioning

confidence: 99%

“…Carlone et al [25], [26] propose approximations for planar pose graph optimization that reduce the risks of getting stuck at local minima. Khosoussi et al [27] exploit the separable structure of SLAM problems using variable projection and propose algorithms to improve the efficiency of Gauss-Newton methods. However, all of the aforementioned nonlinear optimization techniques are local search methods, and as a result, there are no guarantees of the correctness for the resulting solutions.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

et al. 2020

View full text Add to dashboard Cite

In this paper, we consider the problem of planar graph-based simultaneous localization and mapping (SLAM) that involves both poses of the autonomous agent and positions of observed landmarks. We present CPL-SLAM, an efficient and certifiably correct algorithm to solve planar graph-based SLAM using the complex number representation. We formulate and simplify planar graph-based SLAM as the maximum likelihood estimation (MLE) on the product of unit complex numbers, and relax this nonconvex quadratic complex optimization problem to convex complex semidefinite programming (SDP). Furthermore, we simplify the corresponding complex semidefinite programming to Riemannian staircase optimization (RSO) on the complex oblique manifold that can be solved with the Riemannian trust region (RTR) method. In addition, we prove that the SDP relaxation and RSO simplification are tight as long as the noise magnitude is below a certain threshold. The efficacy of this work is validated through applications of CPL-SLAM and comparisons with existing state-of-the-art methods on planar graph-based SLAM, which indicates that our proposed algorithm is capable of solving planar graph-based SLAM certifiably, and is more efficient in numerical computation and more robust to measurement noise than existing state-ofthe-art methods.

show abstract

“…1 and 2). Recent works [4,6,17] have analyzed structural properties of SLAM with the aim of decoupling non-linearities that arise due to orientation. The works of [4,6] provided several important insights, demonstrating that estimating orientation as the first step and using these estimates to initialize pose graph optimization results in a robust solution.…”

Section: Related Workmentioning

confidence: 99%

RFM-SLAM: Exploiting relative feature measurements to separate orientation and position estimation in SLAM

Agarwal

Shree

Chakravorty

2017

2017 IEEE International Conference on Robotics and Automation (ICRA)

View full text Add to dashboard Cite

The SLAM problem is known to have a special property that when robot orientation is known, estimating the history of robot poses and feature locations can be posed as a standard linear least squares problem. In this work, we develop a SLAM framework that uses relative feature-to-feature measurements to exploit this structural property of SLAM. Relative feature measurements are used to pose a linear estimation problem for pose-to-pose orientation constraints. This is followed by solving an iterative non-linear on-manifold optimization problem to compute the maximum likelihood estimate for robot orientation given relative rotation constraints. Once the robot orientation is computed, we solve a linear problem for robot position and map estimation. Our approach reduces the computational burden of non-linear optimization by posing a smaller optimization problem as compared to standard graph-based methods for featurebased SLAM. Further, empirical results show our method avoids catastrophic failures that arise in existing methods due to using odometery as an initial guess for non-linear optimization, while its accuracy degrades gracefully as sensor noise is increased. We demonstrate our method through extensive simulations and comparisons with an existing state-of-the-art solver.

show abstract

Exploiting the Separable Structure of SLAM

Cited by 12 publications

References 26 publications

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

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

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

RFM-SLAM: Exploiting relative feature measurements to separate orientation and position estimation in SLAM

Contact Info

Product

Resources

About