Abstract
In this article, 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 complex (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 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 SDP to Riemannian staircase optimization (RSO) on the complex oblique manifold that can be solved with the Riemannian trust region 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-of-the-art methods.
| Original language | English (US) |
|---|---|
| Article number | 9143200 |
| Pages (from-to) | 1719-1737 |
| Number of pages | 19 |
| Journal | IEEE Transactions on Robotics |
| Volume | 36 |
| Issue number | 6 |
| DOIs | |
| State | Published - Dec 2020 |
Funding
Manuscript received September 10, 2019; revised December 13, 2019 and April 14, 2020; accepted May 25, 2020. Date of publication July 17, 2020; date of current version December 3, 2020. This work was supported by the National Science Foundation under Award DCSD-1662233. This paper was recommended for publication by Associate Editor L. Carlone and Editor F. Chaumette upon evaluation of the reviewers’ comments. (Corresponding author: Todd Murphey.) Taosha Fan and Todd Murphey are with the Department of Mechanical Engineering, Northwestern University, Evanston, IL 60201 USA (e-mail: [email protected]; [email protected]).
Keywords
- certifiably correct algorithms
- pose graph optimization
- simultaneous localization and mapping
ASJC Scopus subject areas
- Control and Systems Engineering
- Computer Science Applications
- Electrical and Electronic Engineering