From Angular Manifolds to the Integer Lattice: Guaranteed Orientation Estimation With Application to Pose Graph Optimization
Open accessAbstract
Pose graph optimization from relative measurements is challenging because of the angular component of the poses: the variables live on a manifold product with nontrivial topology and the likelihood function is nonconvex and has many local minima. Because of these issues, iterative solvers are not robust to large amounts of noise. This paper describes a global estimation method, called multi-hypothesis orientation-from-lattice estimation in 2-D (MOIE2D), for the estimation of the nodes' orientation in a pose graph. We demonstrate that the original nonlinear optimization problem on the manifold product is equivalent to an unconstrained quadratic optimization problem on the integer lattice. Exploiting this insight, we show that, in general, the maximum likelihood estimate alone cannot be considered a reliable estimator. Therefore, MOIE2D returns a set of point estimates, for which we can derive precise probabilistic guarantees. Experiments show that the method is able to tolerate extreme amounts of noise, far above all noise levels of sensors used in applications. Using MOIE2D's output to bootstrap the initial guess of iterative pose graph optimization methods improves their robustness and makes them avoid local minima even for high levels of noise.
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State-of-the-art iterative solvers fail to converge to a global minimum of the cost for relatively small noise levels.
“State-of-the-art iterative solvers fail to converge to a global minimum of the cost for relatively small noise levels [32, 37].”
From Past, Present, and Future of Simultaneous Localization and Mapping: Toward the Robust-Perception Age (2016) · cites this paper as [32]
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Cites
iSAM2: Incremental smoothing and mapping using the Bayes tree
Kaess, M., Johannsson, H., Roberts, R., Ila, V., Leonard, J. J., & Dellaert, F. (2012) · The International Journal of Robotics Research · doi:10.1177/0278364911430419 · Cited by 1,362 · see citing works
Fast iterative alignment of pose graphs with poor initial estimates
Olson, E., Leonard, J., & Teller, S. (2006) · Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006. · doi:10.1109/robot.2006.1642040 · Cited by 427 · see citing works
Nonlinear Constraint Network Optimization for Efficient Map Learning
Grisetti, G., Stachniss, C., & Burgard, W. (2009) · IEEE Transactions on Intelligent Transportation Systems · doi:10.1109/tits.2009.2026444 · Cited by 222 · cited 9× · see citing works
“Section VIII-C discusses the use of the orientation estimate produced by MOLE2D as the initial guess for iterative techniques for pose graph optimization, such as Toro and g2o.”
BackgroundMethodInfluentialTowards a robust back-end for pose graph SLAM
Sunderhauf, N., & Protzel, P. (2012) · 2012 IEEE International Conference on Robotics and Automation · doi:10.1109/icra.2012.6224709 · Cited by 198 · see citing works
On frame and orientation localization for relative sensing networks
Piovan, G., Shames, I., Fidan, B., Bullo, F., & Anderson, B. D. O. (2013) · Automatica · doi:10.1016/j.automatica.2012.09.014 · Cited by 105 · see citing works
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Past, Present, and Future of Simultaneous Localization and Mapping: Toward the Robust-Perception Age
Cadena, C., Carlone, L., Carrillo, H., Latif, Y., Scaramuzza, D., Neira, J., Reid, I., & Leonard, J. J. (2016) · IEEE Transactions on Robotics · doi:10.1109/tro.2016.2624754 · Cited by 3,596 · see citing works
Self-citationCarlone, L., Tron, R., Daniilidis, K., & Dellaert, F. (2015) · 2015 IEEE International Conference on Robotics and Automation (ICRA) · doi:10.1109/icra.2015.7139836 · Cited by 237 · see citing works
Self-citationLagrangian duality in 3D SLAM: Verification techniques and optimal solutions
Carlone, L., Rosen, D. M., Calafiore, G., Leonard, J. J., & Dellaert, F. (2015) · 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) · doi:10.1109/iros.2015.7353364 · Cited by 95 · see citing works
Self-citationA convex relaxation for approximate global optimization in simultaneous localization and mapping
Rosen, D. M., DuHadway, C., & Leonard, J. J. (2015) · 2015 IEEE International Conference on Robotics and Automation (ICRA) · doi:10.1109/icra.2015.7140014 · Cited by 56 · see citing works
“One notable example is [20], which guarantees the recovery of the globally optimal orientation estimates in the 2D pose-graph SLAM problem with high (user-selectable) probability; however, this approach depends upon the identification SO (2) ∼ = R / 2 π Z , and so appears to be limited to the…”
BackgroundDuality-based verification techniques for 2D SLAM
Carlone, L., & Dellaert, F. (2015) · 2015 IEEE International Conference on Robotics and Automation (ICRA) · doi:10.1109/icra.2015.7139835 · Cited by 49 · see citing works
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- Authors
- Carlone, L., & Censi, A.
- Affiliations
- Georgia Institute of Technology (US)
- Massachusetts Institute of Technology (US)
- Venue
- IEEE Transactions on Robotics
- Published
- 2014-04
- Volume
- 30
- Issue
- 2
- Pages
- 475-492
- ISSN
- 1552-3098 (ISSN-L)
- 1941-0468
- OpenAlex
- W1994292819
- Cited by
- 79
- References
- 5
- Citations by year
- 2026: 2 · 2025: 6 · 2024: 6 · 2023: 6 · 2022: 2 · 2021: 6 · 2020: 5 · 2019: 8 · 2018: 10 · 2017: 8 · 2016: 8 · 2015: 8 · 2014: 4
- FWCI
- 13.77
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- IEEE Transactions on Robotics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Engineering › Aerospace Engineering › Robotics and Sensor-Based Localization
- Physical Sciences › Computer Science › Artificial Intelligence › Target Tracking and Data Fusion in Sensor Networks
- Physical Sciences › Engineering › Aerospace Engineering › Inertial Sensor and Navigation
- Keywords
- pose graph optimization, attitude estimation, integer lattice, probabilistic guarantees, global optimization, relative measurement, noise robustness
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