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A Third-Order Gaussian Process Trajectory Representation Framework with Closed-Form Kinematics for Continuous-Time Motion Estimation

Published 30 Oct 2024 in cs.RO | (2410.22931v4)

Abstract: In this paper, we propose a third-order, i.e., white-noise-on-jerk, Gaussian Process (GP) Trajectory Representation (TR) framework for continuous-time (CT) motion estimation (ME) tasks. Our framework features a unified trajectory representation that encapsulates the kinematic models of both $SO(3)\times\mathbb{R}3$ and $SE(3)$ pose representations. This encapsulation strategy allows users to use the same implementation of measurement-based factors for either choice of pose representation, which facilitates experimentation and comparison to achieve the best model for the ME task. In addition, unique to our framework, we derive the kinematic models with the closed-form temporal derivatives of the local variable of $SO(3)$ and $SE(3)$, which so far has only been approximated based on the Taylor expansion in the literature. Our experiments show that these kinematic models can improve the estimation accuracy in high-speed scenarios. All analytical Jacobians of the interpolated states with respect to the support states of the trajectory representation, as well as the motion prior factors, are also provided for accelerated Gauss-Newton (GN) optimization. Our experiments demonstrate the efficacy and efficiency of the framework in various motion estimation tasks such as localization, calibration, and odometry, facilitating fast prototyping for ME researchers. We release the source code for the benefit of the community. Our project is available at https://github.com/brytsknguyen/gptr.

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References (45)
  1. M. Bosse and R. Zlot, “Continuous 3d scan-matching with a spinning 2d laser,” in 2009 IEEE International Conference on Robotics and Automation.   IEEE, 2009, pp. 4312–4319.
  2. M. Bosse, R. Zlot, and P. Flick, “Zebedee: Design of a spring-mounted 3-d range sensor with application to mobile mapping,” IEEE Transactions on Robotics, vol. 28, no. 5, pp. 1104–1119, 2012.
  3. P. Dellenbach, J.-E. Deschaud, B. Jacquet, and F. Goulette, “Ct-icp: Real-time elastic lidar odometry with loop closure,” in 2022 International Conference on Robotics and Automation (ICRA).   IEEE, 2022, pp. 5580–5586.
  4. T.-M. Nguyen, S. Yuan, M. Cao, Y. Lyu, T. H. Nguyen, and L. Xie, “Ntu viral: A visual-inertial-ranging-lidar dataset, from an aerial vehicle viewpoint,” The International Journal of Robotics Research, vol. 41, no. 3, pp. 270–280, 2022.
  5. T.-M. Nguyen, D. Duberg, P. Jensfelt, S. Yuan, and L. Xie, “Slict: Multi-input multi-scale surfel-based lidar-inertial continuous-time odometry and mapping,” IEEE Robotics and Automation Letters, vol. 8, no. 4, pp. 2102–2109, 2023.
  6. P. Furgale, T. D. Barfoot, and G. Sibley, “Continuous-time batch estimation using temporal basis functions,” in 2012 IEEE International Conference on Robotics and Automation.   IEEE, 2012, pp. 2088–2095.
  7. P. Furgale, J. Rehder, and R. Siegwart, “Unified temporal and spatial calibration for multi-sensor systems,” in 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems.   IEEE, 2013, pp. 1280–1286.
  8. J. Rehder, J. Nikolic, T. Schneider, T. Hinzmann, and R. Siegwart, “Extending kalibr: Calibrating the extrinsics of multiple imus and of individual axes,” in 2016 IEEE International Conference on Robotics and Automation (ICRA).   IEEE, 2016, pp. 4304–4311.
  9. L. Oth, P. Furgale, L. Kneip, and R. Siegwart, “Rolling shutter camera calibration,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2013, pp. 1360–1367.
  10. A. Patron-Perez, S. Lovegrove, and G. Sibley, “A spline-based trajectory representation for sensor fusion and rolling shutter cameras,” International Journal of Computer Vision, vol. 113, no. 3, pp. 208–219, 2015.
  11. E. Mueggler, G. Gallego, H. Rebecq, and D. Scaramuzza, “Continuous-time visual-inertial odometry for event cameras,” IEEE Transactions on Robotics, vol. 34, no. 6, pp. 1425–1440, 2018.
  12. X. Lang, J. Lv, J. Huang, Y. Ma, Y. Liu, and X. Zuo, “Ctrl-vio: Continuous-time visual-inertial odometry for rolling shutter cameras,” IEEE Robotics and Automation Letters, vol. 7, no. 4, pp. 11 537–11 544, 2022.
  13. K. Li, Z. Cao, and U. D. Hanebeck, “Continuous-time ultra-wideband-inertial fusion,” IEEE Robotics and Automation Letters, vol. 8, no. 7, pp. 4338–4345, 2023.
  14. J. Quenzel and S. Behnke, “Real-time multi-adaptive-resolution-surfel 6d lidar odometry using continuous-time trajectory optimization,” in 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).   IEEE, 2021, pp. 5499–5506.
  15. J. Lv, K. Hu, J. Xu, Y. Liu, X. Ma, and X. Zuo, “Clins: Continuous-time trajectory estimation for lidar-inertial system,” in 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).   IEEE, 2021, pp. 6657–6663.
  16. T.-M. Nguyen, X. Xu, T. Jin, Y. Yang, J. Li, S. Yuan, and L. Xie, “Eigen is all you need: Efficient lidar-inertial continuous-time odometry with internal association,” IEEE Robotics and Automation Letters, vol. 9, no. 6, pp. 5330 – 5337, 2024.
  17. C. Park, P. Moghadam, J. L. Williams, S. Kim, S. Sridharan, and C. Fookes, “Elasticity meets continuous-time: Map-centric dense 3d lidar slam,” IEEE Transactions on Robotics, vol. 38, no. 2, pp. 978–997, 2021.
  18. X. Zheng and J. Zhu, “Traj-lio: A resilient multi-lidar multi-imu state estimator through sparse gaussian process,” arXiv preprint arXiv:2402.09189, 2024.
  19. T. Y. Tang, D. J. Yoon, and T. D. Barfoot, “A white-noise-on-jerk motion prior for continuous-time trajectory estimation on se (3),” IEEE Robotics and Automation Letters, vol. 4, no. 2, pp. 594–601, 2019.
  20. X. Yan, V. Indelman, and B. Boots, “Incremental sparse gp regression for continuous-time trajectory estimation and mapping,” Robotics and Autonomous Systems, vol. 87, pp. 120–132, 2017.
  21. Y. Wu, D. J. Yoon, K. Burnett, S. Kammel, Y. Chen, H. Vhavle, and T. D. Barfoot, “Picking up speed: Continuous-time lidar-only odometry using doppler velocity measurements,” IEEE Robotics and Automation Letters, vol. 8, no. 1, pp. 264–271, 2022.
  22. K. Burnett, A. P. Schoellig, and T. D. Barfoot, “Continuous-time radar-inertial and lidar-inertial odometry using a gaussian process motion prior,” arXiv preprint arXiv:2402.06174, 2024.
  23. ——, “Imu as an input vs. a measurement of the state in inertial-aided state estimation,” arXiv preprint arXiv:2403.05968, 2024.
  24. J. Peršić, L. Petrović, I. Marković, and I. Petrović, “Spatiotemporal multisensor calibration via gaussian processes moving target tracking,” Ieee transactions on robotics, vol. 37, no. 5, pp. 1401–1415, 2021.
  25. S. Agarwal and K. Mierle, “Ceres solver: Tutorial & reference.” [Online]. Available: http://ceres-solver.org/
  26. T. D. Barfoot, C. H. Tong, and S. Särkkä, “Batch continuous-time trajectory estimation as exactly sparse gaussian process regression.” in Robotics: Science and Systems, vol. 10.   Citeseer, 2014, pp. 1–10.
  27. T. Qin, P. Li, and S. Shen, “Vins-mono: A robust and versatile monocular visual-inertial state estimator,” IEEE Transactions on Robotics, vol. 34, no. 4, pp. 1004–1020, 2018.
  28. C. Forster, L. Carlone, F. Dellaert, and D. Scaramuzza, “On-manifold preintegration for real-time visual–inertial odometry,” IEEE Transactions on Robotics, vol. 33, no. 1, pp. 1–21, 2016.
  29. N. Demmel, D. Schubert, C. Sommer, D. Cremers, and V. Usenko, “Square root marginalization for sliding-window bundle adjustment,” in Proceedings of the IEEE/CVF International Conference on Computer Vision, 2021, pp. 13 260–13 268.
  30. C. Sommer, V. Usenko, D. Schubert, N. Demmel, and D. Cremers, “Efficient derivative computation for cumulative b-splines on lie groups,” in Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2020, pp. 11 148–11 156.
  31. D. Schubert, T. Goll, N. Demmel, V. Usenko, J. Stueckler, and D. Cremers, “The TUM VI benchmark for evaluating visual-inertial odometry,” in International Conference on Intelligent Robots and Systems (IROS), 2018.
  32. V. Usenko, N. Demmel, and D. Cremers, “The double sphere camera model,” in 2018 International Conference on 3D Vision (3DV).   IEEE, 2018, pp. 552–560.
  33. W. Zhao, A. Goudar, X. Qiao, and A. P. Schoellig, “Util: An ultra-wideband time-difference-of-arrival indoor localization dataset,” The International Journal of Robotics Research, p. 02783649241230640, 2022.
  34. M. Grupp, “evo: Python package for the evaluation of odometry and slam.” https://github.com/MichaelGrupp/evo, 2017.
  35. T.-M. Nguyen, S. Yuan, T. H. Nguyen, P. Yin, H. Cao, L. Xie, M. Wozniak, P. Jensfelt, M. Thiel, J. Ziegenbein, and N. Blunder, “Mcd: Diverse large-scale multi-campus dataset for robot perception,” in Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, Jun. 2024. [Online]. Available: https://mcdviral.github.io/
  36. W. Yu, J. Xu, C. Zhao, L. Zhao, T.-M. Nguyen, S. Yuan, M. Bai, and L. Xie, “I2ekf-lo: A dual-iteration extended kalman filter based lidar odometry,” in 2024 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).   IEEE, 2024.
  37. X. Zheng and J. Zhu, “Traj-lo: In defense of lidar-only odometry using an effective continuous-time trajectory,” IEEE Robotics and Automation Letters, 2024.
  38. X. Liu, C. Yuan, and F. Zhang, “Targetless extrinsic calibration of multiple small fov lidars and cameras using adaptive voxelization,” IEEE Transactions on Instrumentation and Measurement, vol. 71, pp. 1–12, 2022.
  39. J. Li, T.-M. Nguyen, S. Yuan, and L. Xie, “Pss-ba: Lidar bundle adjustment with progressive spatial smoothing,” arXiv preprint arXiv:2403.06124, 2024.
  40. K. Li, M. Li, and U. D. Hanebeck, “Towards high-performance solid-state-lidar-inertial odometry and mapping,” IEEE Robotics and Automation Letters, vol. 6, no. 3, pp. 5167–5174, 2021.
  41. Y. Cai, W. Xu, and F. Zhang, “ikd-tree: An incremental kd tree for robotic applications,” arXiv preprint arXiv:2102.10808, 2021.
  42. C. Yuan, W. Xu, X. Liu, X. Hong, and F. Zhang, “Efficient and probabilistic adaptive voxel mapping for accurate online lidar odometry,” IEEE Robotics and Automation Letters, vol. 7, no. 3, pp. 8518–8525, 2022.
  43. D. Duberg and P. Jensfelt, “UFOMap: An efficient probabilistic 3D mapping framework that embraces the unknown,” IEEE Robotics and Automation Letters, vol. 5, no. 4, pp. 6411–6418, 2020.
  44. J. Jiao, H. Ye, Y. Zhu, and M. Liu, “Robust odometry and mapping for multi-lidar systems with online extrinsic calibration,” IEEE Transactions on Robotics, vol. 38, no. 1, pp. 351–371, 2021.
  45. J. Sola, J. Deray, and D. Atchuthan, “A micro lie theory for state estimation in robotics,” arXiv preprint arXiv:1812.01537, 2018.
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