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CLOSURE: Fast Quantification of Pose Uncertainty Sets (2403.09990v3)

Published 15 Mar 2024 in cs.RO

Abstract: We investigate uncertainty quantification of 6D pose estimation from learned noisy measurements (e.g. keypoints and pose hypotheses). Assuming unknown-but-bounded measurement noises, a pose uncertainty set (PURSE) is a subset of SE(3) that contains all possible 6D poses compatible with the measurements. Despite being simple to formulate and its ability to embed uncertainty, the PURSE is difficult to manipulate and interpret due to the many abstract nonconvex polynomial constraints. An appealing simplification of PURSE is to find its minimum enclosing geodesic ball (MEGB), i.e., a point pose estimation with minimum worst-case error bound. We contribute (i) a geometric interpretation of the nonconvex PURSE, and (ii) a fast algorithm to inner approximate the MEGB. Particularly, we show the PURSE corresponds to the feasible set of a constrained dynamical system or the intersection of multiple geodesic balls, and this perspective allows us to design an algorithm to densely sample the boundary of the PURSE through strategic random walks. We then use the miniball algorithm to compute the MEGB of PURSE samples, leading to an inner approximation. Our algorithm is named CLOSURE (enClosing baLl frOm purSe boUndaRy samplEs) and it enables computing a certificate of approximation tightness by calculating the relative size ratio between the inner approximation and the outer approximation. Running on a single RTX 3090 GPU, CLOSURE achieves the relative ratio of 92.8% on the LM-O dataset, 91.4% on the 3DMatch dataset and 96.6% on the LM dataset with the average runtime less than 0.3 second. Obtaining comparable worst-case error bound but 398x 833x and 23.6x faster than the outer approximation GRCC, CLOSURE enables uncertainty quantification of 6D pose estimation to be implemented in real-time robot perception applications.

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References (57)
  1. Bijan Afsari. Riemannian lp center of mass: existence, uniqueness, and convexity. Proceedings of the American Mathematical Society, 139(2):655–673, 2011.
  2. A gentle introduction to conformal prediction and distribution-free uncertainty quantification. arXiv preprint arXiv:2107.07511, 2021.
  3. Outlier-robust estimation: Hardness, minimally tuned algorithms, and applications. IEEE Transactions on Robotics, 38(1):281–301, 2021.
  4. On approximating the riemannian 1-center. Computational Geometry, 46(1):93–104, 2013a.
  5. On approximating the riemannian 1-center. Computational Geometry, 46(1):93–104, 2013b.
  6. Least-squares fitting of two 3-d point sets. IEEE Transactions on pattern analysis and machine intelligence, (5):698–700, 1987.
  7. Smaller core-sets for balls. In Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA ’03, page 801–802, USA, 2003. Society for Industrial and Applied Mathematics. ISBN 0898715385.
  8. D P Bertsekas. Nonlinear programming. Journal of the Operational Research Society, 48(3):334–334, 1997. doi: 10.1057/palgrave.jors.2600425. URL https://doi.org/10.1057/palgrave.jors.2600425.
  9. On the unification of line processes, outlier rejection, and robust statistics with applications in early vision. International journal of computer vision, 19(1):57–91, 1996.
  10. Nicolas Boumal. An introduction to optimization on smooth manifolds. Cambridge University Press, 2023.
  11. Learning 6d object pose estimation using 3d object coordinates. In Computer Vision–ECCV 2014: 13th European Conference, Zurich, Switzerland, September 6-12, 2014, Proceedings, Part II 13, pages 536–551. Springer, 2014.
  12. Simulation of constrained mechanical systems—part i: An equation of motion. Journal of Applied Mechanics, 2012.
  13. Guaranteed outlier removal for point cloud registration with correspondences. IEEE transactions on pattern analysis and machine intelligence, 40(12):2868–2882, 2017.
  14. Luca Carlone et al. Estimation contracts for outlier-robust geometric perception. Foundations and Trends® in Robotics, 11(2-3):90–224, 2023.
  15. The maximum consensus problem: recent algorithmic advances. Springer Nature, 2022.
  16. Safe output feedback motion planning from images via learned perception modules and contraction theory. In International Workshop on the Algorithmic Foundations of Robotics, pages 349–367. Springer, 2022.
  17. Fully convolutional geometric features. In Proceedings of the IEEE/CVF international conference on computer vision, pages 8958–8966, 2019.
  18. Deep global registration. In CVPR, 2020.
  19. Measurement-robust control barrier functions: Certainty in safety with uncertainty in state. In 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 6286–6291. IEEE, 2021.
  20. Robust guarantees for perception-based control. In Learning for Dynamics and Control, pages 350–360. PMLR, 2020.
  21. Self-supervised 6d object pose estimation for robot manipulation. In 2020 IEEE International Conference on Robotics and Automation (ICRA), pages 3665–3671. IEEE, 2020.
  22. Interval-based visual-inertial lidar slam with anchoring poses. In 2022 International Conference on Robotics and Automation (ICRA), pages 7589–7596. IEEE, 2022.
  23. Complete solution classification for the perspective-three-point problem. IEEE transactions on pattern analysis and machine intelligence, 25(8):930–943, 2003.
  24. Bernd Gärtner. Fast and robust smallest enclosing balls. In European symposium on algorithms, pages 325–338. Springer, 1999.
  25. Rotation averaging. International journal of computer vision, 103:267–305, 2013.
  26. Martin Henk. löwner-john ellipsoids. Documenta Math, 95:106, 2012.
  27. Peter J Huber. Robust statistics, volume 523. John Wiley & Sons, 2004.
  28. Robust and optimal control. Prentice hall, 1996.
  29. Upnp: An optimal o (n) solution to the absolute pose problem with universal applicability. In Computer Vision–ECCV 2014: 13th European Conference, Zurich, Switzerland, September 6-12, 2014, Proceedings, Part I 13, pages 127–142. Springer, 2014.
  30. Mvn: An r package for assessing multivariate normality. R JOURNAL, 6(2), 2014.
  31. Automatic generator of minimal problem solvers. In Computer Vision–ECCV 2008: 10th European Conference on Computer Vision, Marseille, France, October 12-18, 2008, Proceedings, Part III 10, pages 302–315. Springer, 2008.
  32. Peter Kunkel. Differential-algebraic equations: analysis and numerical solution, volume 2. European Mathematical Society, 2006.
  33. Jean B Lasserre. Global optimization with polynomials and the problem of moments. SIAM Journal on optimization, 11(3):796–817, 2001.
  34. Jean B Lasserre. A generalization of löwner-john’s ellipsoid theorem. Mathematical Programming, 152:559–591, 2015.
  35. Learning the uncertainty sets for control dynamics via set membership: A non-asymptotic analysis. arXiv preprint arXiv:2309.14648, 2023.
  36. Optimal estimation theory for dynamic systems with set membership uncertainty: An overview. Automatica, 27(6):997–1009, 1991.
  37. Guaranteed slam—an interval approach. Robotics and Autonomous Systems, 100:160–170, 2018.
  38. 6-dof object pose from semantic keypoints. In 2017 IEEE international conference on robotics and automation (ICRA), pages 2011–2018. IEEE, 2017.
  39. Pvnet: Pixel-wise voting network for 6dof pose estimation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4561–4570, 2019.
  40. Se-sync: A certifiably correct algorithm for synchronization over the special euclidean group. The International Journal of Robotics Research, 38(2-3):95–125, 2019.
  41. Aaron Roth. Uncertain: Modern topics in uncertainty estimation, 2022.
  42. Fast point feature histograms (fpfh) for 3d registration. In 2009 IEEE international conference on robotics and automation, pages 3212–3217. IEEE, 2009.
  43. Optimal and robust category-level perception: Object pose and shape estimation from 2-d and 3-d semantic keypoints. IEEE Transactions on Robotics, 2023.
  44. A right invariant extended kalman filter for object based slam. IEEE Robotics and Automation Letters, 7(2):1316–1323, 2021.
  45. Richard Szeliski. Computer vision: algorithms and applications. Springer Nature, 2022.
  46. Uncertainty quantification of set-membership estimation in control and perception: Revisiting the minimum enclosing ellipsoid. arXiv preprint arXiv:2311.15962, 2023.
  47. Constantin Udriste. Convex functions and optimization methods on Riemannian manifolds, volume 297. Springer Science & Business Media, 1994.
  48. Set-membership approach and kalman observer based on zonotopes for discrete-time descriptor systems. Automatica, 93:435–443, 2018.
  49. Foundationpose: Unified 6d pose estimation and tracking of novel objects. arXiv preprint arXiv:2312.08344, 2023.
  50. Miaolan Xie. Inner approximation of convex cones via primal-dual ellipsoidal norms. Master’s thesis, University of Waterloo, 2016.
  51. Certifiably optimal outlier-robust geometric perception: Semidefinite relaxations and scalable global optimization. IEEE transactions on pattern analysis and machine intelligence, 45(3):2816–2834, 2022.
  52. Object pose estimation with statistical guarantees: Conformal keypoint detection and geometric uncertainty propagation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 8947–8958, 2023.
  53. Teaser: Fast and certifiable point cloud registration. IEEE Transactions on Robotics, 37(2):314–333, 2020.
  54. Self-supervised geometric perception. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 14350–14361, 2021a.
  55. Dynamical pose estimation. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 5926–5935, 2021b.
  56. 3dmatch: Learning the matching of local 3d geometry in range scans. volume 1, page 4, 2017.
  57. First-order methods for geodesically convex optimization. In Conference on Learning Theory, pages 1617–1638. PMLR, 2016.
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