A 2D Laser SLAM Graph Optimization Based On A Position And Angle Partition And Cholesky Decomposition

Liangliang  Gao; Chaoyi  Dong; Xiaoyang  Liu; Qifan  Ye; Kang  Zhang; Xiaoyan  Chen

doi:10.6180/jase.202309_26(9).0006

A 2D Laser SLAM Graph Optimization Based On A Position And Angle Partition And Cholesky Decomposition

Liangliang Gao^1,2, Chaoyi Dong ^1,2, Xiaoyang Liu^1,2, Qifan Ye^1,2, Kang Zhang^1,2, and Xiaoyan Chen^1,2

¹College of Electric Power, Inner Mongolia University of Technology, Hohhot 0100801.
²Intelligent Energy Technology and Equipment Engineering Research Centre of Colleges and Universities in Inner Mongolia Autonomous Region, Inner Mongolia, Hohhot 010051, China.

Received: August 28, 2022
Accepted: October 23, 2022
Publication Date: November 24, 2022

Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

Download Citation: ||https://doi.org/10.6180/jase.202309_26(9).0006

ABSTRACT

The traditional 2D laser slam back-end graph optimization (LSBGO) is not efficient in some special situations, such as fast scene switching, limited computing time, and limited hardware facilities. This paper presents a partitioned pose vector method (PPVM) to optimize a pose vector by dividing it into two parts: a position term and an angle term. Based on this partition, the traditional graph optimization problem has been transformed into two linear equations. The least square solutions of the two equations help to find the pose vector. Furthermore, the paper applies a Cholesky decomposition (CD) to improve the speed of solving the two linear equations. Cholesky decomposition has great advantages in solving linear equations with symmetric positive definite coefficient matrix. The effectiveness of PPVM-CD is numerically verified by MATLAB simulation. Compared with the traditional LSBGO method, PPVM-CD improves the optimization speed by 26% and the optimization accuracy by 11.1%.

Keywords: Laser SLAM; Graph Optimization; Cholesky Decomposition; MATLAB

REFERENCES

[1] K. He, X. Zhang, S. Ren, and J. Sun. “Deep residual learning for image recognition”. In: Proceedings of the IEEE conference on computer vision and pattern recognition. 2016, 770–778. DOI: 10.1109/CVPR.2016.90.
[2] M. Shafiq, Z. Gu, O. Cheikhrouhou, W. Alhakami, and H. Hamam, (2022) “The Rise of “Internet of Things”: Review and Open Research Issues Related to Detection and Prevention of IoT-Based Security Attacks" Wireless Communications and Mobile Computing 2022: DOI: 10.1155/2022/8669348.
[3] M. Shafiq, Z. Tian, A. K. Bashir, X. Du, and M. Guizani, (2020) “IoT malicious traffic identification using wrapper-based feature selection mechanisms" Computers & Security 94: 101863. DOI: 10.1016/j.cose.2020.101863.
[4] M. Shafiq, Z. Tian, A. Bashir, A. Jolfaei, and X. Yu, “Data mining and machine learning method for sustainable cities traffic classification" Sustainable Cities and Society 60: DOI: 10.1016/j.scs.2020.102177.
[5] M. Shafiq, Z. Tian, Y. Sun, X. Du, and M. Guizani, (2020) “Selection of effective machine learning algorithm and Bot-IoT attacks traffic identification for internet of things in smart city" Future Generation Computer Systems 107: 433–442. DOI: 10.1016/j.future.2020.02.017.
[6] R. Gao, L. Zhang, and S. Zhang. “Research on Mobile Robot SLAM Based on Laser Range Finder”. In: Proceedings of the 2017 The 7th International Conference on Computer Engineering and Networks. 2017, 22–23. DOI: 10.22323/1.299.0016.
[7] J. J. Leonard and H. F. Durrant-Whyte, (1991) “Mobile robot localization by tracking geometric beacons" IEEE Transactions on robotics and Automation 7(3): 376–382. DOI: 10.1109/70.88147.
[8] M. G. Dissanayake, P. Newman, S. Clark, H. F. Durrant-Whyte, and M. Csorba, (2001) “A solution to the simultaneous localization and map building (SLAM) problem" IEEE Transactions on robotics and automation 17(3): 229–241. DOI: 10.1109/70.938381.
[9] H. Wang, S. Huang, K. Khosoussi, U. Frese, G. Dissanayake, and B. Liu, (2015) “Dimensionality reduction for point feature SLAM problems with spherical covariance matrices" Automatica 51: 149–157. DOI: 10.1016/j.automatica.2014.10.114.
[10] T. Oh, D. Lee, H. Kim, and H. Myung, (2015) “Graph structure-based simultaneous localization and mapping using a hybrid method of 2D laser scan and monocular camera image in environments with laser scan ambiguity" Sensors 15(7): 15830–15852. DOI: 10.3390/s150715830.
[11] H. Wang and J. Leng. “Summary on development of permanent magnet synchronous motor”. In: 2018 Chinese Control And Decision Conference (CCDC). IEEE.2018, 689–693. DOI: 10.1109/CCDC.2018.8407219.
[12] J. Zhang and S. Singh. “LOAM: Lidar odometry and mapping in real-time.” In: Robotics: Science and Systems.2. 9. Berkeley, CA. 2014, 1–9. DOI: 10.15607/RSS.2014.X.007.
[13] B. Wang, Y. Han, and J. Jin. “Research on Global Map Construction and Location of Intelligent Vehicles Based on Lidar”. In: International Symposium on Cyberspace Safety and Security. Springer. 2020, 210–224. DOI: 10.1007/978-3-030-73671-2_19.
[14] X. G. S. [14] J. Q. Wu, “Summary of the development of synchronous positioning and mapping technology" Journal of Shandong University 51(5): 16–31.
[15] R. Smith, M. Self, and P. Cheeseman. “Estimating uncertain spatial relationships in robotics”. In: Autonomous robot vehicles. Springer, 1990, 167–193. DOI: 10.1016/B978-0-444-70396-5.50042-X.
[16] W. Zhongli, Z. Jie, and C. Hegao, (2015) “A survey of front-end method for graph-based slam under large-scale environment" J. Harbin Inst. Technol 47: 75–85. DOI: 10.11918/j.issn.0367-6234.2015.01.012.
[17] Y. Cheng, J. Bai, and C. Xiu. “Improved RGB-D vision SLAM algorithm for mobile robot”. In: 2017 29th Chinese Control And Decision Conference (CCDC). IEEE.2017, 5419–5423. DOI: 10.1109/CCDC.2017.7979460.
[18] K. Murphy and S. Russell. “Rao-Blackwellised particle filtering for dynamic Bayesian networks”. In: Sequential Monte Carlo methods in practice. Springer, 2001, 499–515.
[19] S. Thrun and M. Montemerlo, (2006) “The graph SLAM algorithm with applications to large-scale mapping of urban structures" The International Journal of Robotics Research 25(5-6): 403–429. DOI: 10.1177/0278364906065387.
[20] L. M. Paz, P. Jensfelt, J. D. Tardos, and J. Neira. “EKF SLAM updates in O (n) with Divide and Conquer SLAM”. In: Proceedings 2007 IEEE International Conference on Robotics and Automation. IEEE. 2007, 1657–1663. DOI: 10.1109/ROBOT.2007.363561.
[21] F. Lu and E. Milios, (1997) “Globally consistent range scan alignment for environment mapping" Autonomous robots 4(4): 333–349. DOI: 10.1023/A:1008854305733.
[22] E. Olson, J. Leonard, and S. Teller. “Fast iterative alignment of pose graphs with poor initial estimates”. In: Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006. IEEE.2006, 2262–2269. DOI: 10.1109/ROBOT.2006.1642040.
[23] G. Grisetti, C. Stachniss, andW. Burgard, (2009) “Nonlinear constraint network optimization for efficient map learning" IEEE Transactions on Intelligent Transportation Systems 10(3): 428–439. DOI: 10.1109/TITS.2009.2026444.
[24] F. Dellaert and M. Kaess, (2006) “Square Root SAM: Simultaneous localization and mapping via square root information smoothing" The International Journal of Robotics Research 25(12): 1181–1203. DOI: 10.1177/0278364906072768.
[25] M. Kaess, A. Ranganathan, and F. Dellaert, (2008) “iSAM: Incremental smoothing and mapping" IEEE Transactions on Robotics 24(6): 1365–1378. DOI: 10.1109/TRO.2008.2006706.
[26] W. Hess, D. Kohler, H. Rapp, and D. Andor. “Realtime loop closure in 2D LIDAR SLAM”. In: 2016 IEEE international conference on robotics and automation (ICRA). IEEE. 2016, 1271–1278. DOI: 10.1109/ICRA.2016.7487258.
[27] B. Liu, Z. Guan, B. Li, G.Wen, and Y. Zhao. “Research on SLAM Algorithm and Navigation of Mobile Robot Based on ROS”. In: 2021 IEEE International Conference on Mechatronics and Automation (ICMA). IEEE. 2021, 119–124. DOI: 10.1109/ICMA52036.2021.9512584.
[28] L. Polok, V. Ila, M. Solony, P. Smrz, and P. Zemcik. “Incremental Block Cholesky Factorization for Nonlinear Least Squares in Robotics.” In: Robotics: Science and Systems. 2013, 328–336. DOI: 10.3182/20130626-3-AU-2035.00027.