publication . Other literature type . Article . Preprint . 2017

Convergence and Consistency Analysis for a 3-D Invariant-EKF SLAM

Teng Zhang; Gamini Dissanayake; Jingwei Song; Kanzhi Wu; Shoudong Huang;
Open Access
  • Published: 22 Feb 2017
  • Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Abstract
In this paper, we investigate the convergence and consistency properties of an Invariant-Extended Kalman Filter (RI-EKF) based Simultaneous Localization and Mapping (SLAM) algorithm. Basic convergence properties of this algorithm are proven. These proofs do not require the restrictive assumption that the Jacobians of the motion and observation models need to be evaluated at the ground truth. It is also shown that the output of RI-EKF is invariant under any stochastic rigid body transformation in contrast to $\mathbb{SO}(3)$ based EKF SLAM algorithm ($\mathbb{SO}(3)$-EKF) that is only invariant under deterministic rigid body transformation. Implications of these ...
Persistent Identifiers
Subjects
arXiv: Computer Science::RoboticsComputer Science::OtherComputer Science::Systems and Control
free text keywords: Computer Science - Robotics, Kalman filter, Invariant extended Kalman filter, Mathematics, Rigid transformation, Estimator, Invariant (mathematics), Simultaneous localization and mapping, Invariant (physics), Extended Kalman filter, Control theory, Algorithm
24 references, page 1 of 2

[1] S. J. Julier and J. K. Uhlmann, “A counter example to the theory of simultaneous localization and map building,” in Robotics and Automation, 2001. Proceedings 2001 ICRA. IEEE International Conference on, vol. 4, 2001, pp. 4238-4243 vol.4.

[2] S. Huang and G. Dissanayake, “Convergence and consistency analysis for extended kalman filter based slam,” IEEE Transactions on Robotics, vol. 23, no. 5, pp. 1036-1049, Oct 2007.

[3] T. Bailey, J. Nieto, J. Guivant, M. Stevens, and E. Nebot, “Consistency of the ekf-slam algorithm,” in 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems, Oct 2006, pp. 3562-3568. [OpenAIRE]

[4] J. A. Castellanos, J. Neira, and J. D. Tardo´s, “Limits to the consistency of ekf-based slam,” in 5th IFAC Symp, Intell. Autonom. Veh. IAV'04, 2004.

[5] P. Lourenc¸o, B. J. Guerreiro, P. Batista, P. Oliveira, and C. Silvestre, “Simultaneous localization and mapping for aerial vehicles: a 3-d sensorbased gas filter,” Autonomous Robots, vol. 40, no. 5, pp. 881-902, 2016.

[6] G. P. Huang, A. I. Mourikis, and S. I. Roumeliotis, “Analysis and improvement of the consistency of extended kalman filter based slam,” in Robotics and Automation, 2008. ICRA 2008. IEEE International Conference on, May 2008, pp. 473-479. [OpenAIRE]

[7] J. Andrade-Cetto and A. Sanfeliu, “The effects of partial observability in slam,” in Robotics and Automation, 2004. Proceedings. ICRA '04. 2004 IEEE International Conference on, vol. 1, April 2004, pp. 397- 402 Vol.1.

[8] K. W. Lee, W. S. Wijesoma, and J. I. Guzman, “On the observability and observability analysis of slam,” in 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems, Oct 2006, pp. 3569- 3574.

[9] G. P. Huang, A. I. Mourikis, and S. I. Roumeliotis, “Observability-based rules for designing consistent ekf slam estimators,” The International Journal of Robotics Research, vol. 29, no. 5, pp. 502-528, 2010.

[10] J. A. Hesch, D. G. Kottas, S. L. Bowman, and S. I. Roumeliotis, “Consistency analysis and improvement of vision-aided inertial navigation,” IEEE Transactions on Robotics, vol. 30, no. 1, pp. 158-176, Feb 2014.

[11] G. Dissanayake, P. Newman, S. Clark, H. F. Durrant-Whyte, and M. Csorba, “A solution to the simultaneous localization and map building (slam) problem,” IEEE Transactions on Robotics and Automation, vol. 17, no. 3, pp. 229-241, Jun 2001. [OpenAIRE]

[12] A. I. Mourikis and S. I. Roumeliotis, “Analytical characterization of the accuracy of slam without absolute orientation measurements.” in Robotics: Science and systems, 2006, pp. 215-222.

[13] C. Forster, L. Carlone, F. Dellaert, and D. Scaramuzza, “On-manifold preintegration for real-time visual-inertial odometry,” IEEE Transactions on Robotics, vol. PP, no. 99, pp. 1-21, 2016.

[14] T. D. Barfoot and P. T. Furgale, “Associating uncertainty with threedimensional poses for use in estimation problems,” IEEE Transactions on Robotics, vol. 30, no. 3, pp. 679-693, June 2014. [OpenAIRE]

[15] R. Mahony, T. Hamel, and J. M. Pflimlin, “Nonlinear complementary filters on the special orthogonal group,” IEEE Transactions on Automatic Control, vol. 53, no. 5, pp. 1203-1218, June 2008. [OpenAIRE]

24 references, page 1 of 2
Abstract
In this paper, we investigate the convergence and consistency properties of an Invariant-Extended Kalman Filter (RI-EKF) based Simultaneous Localization and Mapping (SLAM) algorithm. Basic convergence properties of this algorithm are proven. These proofs do not require the restrictive assumption that the Jacobians of the motion and observation models need to be evaluated at the ground truth. It is also shown that the output of RI-EKF is invariant under any stochastic rigid body transformation in contrast to $\mathbb{SO}(3)$ based EKF SLAM algorithm ($\mathbb{SO}(3)$-EKF) that is only invariant under deterministic rigid body transformation. Implications of these ...
Persistent Identifiers
Subjects
arXiv: Computer Science::RoboticsComputer Science::OtherComputer Science::Systems and Control
free text keywords: Computer Science - Robotics, Kalman filter, Invariant extended Kalman filter, Mathematics, Rigid transformation, Estimator, Invariant (mathematics), Simultaneous localization and mapping, Invariant (physics), Extended Kalman filter, Control theory, Algorithm
24 references, page 1 of 2

[1] S. J. Julier and J. K. Uhlmann, “A counter example to the theory of simultaneous localization and map building,” in Robotics and Automation, 2001. Proceedings 2001 ICRA. IEEE International Conference on, vol. 4, 2001, pp. 4238-4243 vol.4.

[2] S. Huang and G. Dissanayake, “Convergence and consistency analysis for extended kalman filter based slam,” IEEE Transactions on Robotics, vol. 23, no. 5, pp. 1036-1049, Oct 2007.

[3] T. Bailey, J. Nieto, J. Guivant, M. Stevens, and E. Nebot, “Consistency of the ekf-slam algorithm,” in 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems, Oct 2006, pp. 3562-3568. [OpenAIRE]

[4] J. A. Castellanos, J. Neira, and J. D. Tardo´s, “Limits to the consistency of ekf-based slam,” in 5th IFAC Symp, Intell. Autonom. Veh. IAV'04, 2004.

[5] P. Lourenc¸o, B. J. Guerreiro, P. Batista, P. Oliveira, and C. Silvestre, “Simultaneous localization and mapping for aerial vehicles: a 3-d sensorbased gas filter,” Autonomous Robots, vol. 40, no. 5, pp. 881-902, 2016.

[6] G. P. Huang, A. I. Mourikis, and S. I. Roumeliotis, “Analysis and improvement of the consistency of extended kalman filter based slam,” in Robotics and Automation, 2008. ICRA 2008. IEEE International Conference on, May 2008, pp. 473-479. [OpenAIRE]

[7] J. Andrade-Cetto and A. Sanfeliu, “The effects of partial observability in slam,” in Robotics and Automation, 2004. Proceedings. ICRA '04. 2004 IEEE International Conference on, vol. 1, April 2004, pp. 397- 402 Vol.1.

[8] K. W. Lee, W. S. Wijesoma, and J. I. Guzman, “On the observability and observability analysis of slam,” in 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems, Oct 2006, pp. 3569- 3574.

[9] G. P. Huang, A. I. Mourikis, and S. I. Roumeliotis, “Observability-based rules for designing consistent ekf slam estimators,” The International Journal of Robotics Research, vol. 29, no. 5, pp. 502-528, 2010.

[10] J. A. Hesch, D. G. Kottas, S. L. Bowman, and S. I. Roumeliotis, “Consistency analysis and improvement of vision-aided inertial navigation,” IEEE Transactions on Robotics, vol. 30, no. 1, pp. 158-176, Feb 2014.

[11] G. Dissanayake, P. Newman, S. Clark, H. F. Durrant-Whyte, and M. Csorba, “A solution to the simultaneous localization and map building (slam) problem,” IEEE Transactions on Robotics and Automation, vol. 17, no. 3, pp. 229-241, Jun 2001. [OpenAIRE]

[12] A. I. Mourikis and S. I. Roumeliotis, “Analytical characterization of the accuracy of slam without absolute orientation measurements.” in Robotics: Science and systems, 2006, pp. 215-222.

[13] C. Forster, L. Carlone, F. Dellaert, and D. Scaramuzza, “On-manifold preintegration for real-time visual-inertial odometry,” IEEE Transactions on Robotics, vol. PP, no. 99, pp. 1-21, 2016.

[14] T. D. Barfoot and P. T. Furgale, “Associating uncertainty with threedimensional poses for use in estimation problems,” IEEE Transactions on Robotics, vol. 30, no. 3, pp. 679-693, June 2014. [OpenAIRE]

[15] R. Mahony, T. Hamel, and J. M. Pflimlin, “Nonlinear complementary filters on the special orthogonal group,” IEEE Transactions on Automatic Control, vol. 53, no. 5, pp. 1203-1218, June 2008. [OpenAIRE]

24 references, page 1 of 2
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