2000 character limit reached
An Analytic Solution to the 3D CSC Dubins Path Problem
Published 14 May 2024 in cs.RO | (2405.08710v1)
Abstract: We present an analytic solution to the 3D Dubins path problem for paths composed of an initial circular arc, a straight component, and a final circular arc. These are commonly called CSC paths. By modeling the start and goal configurations of the path as the base frame and final frame of an RRPRR manipulator, we treat this as an inverse kinematics problem. The kinematic features of the 3D Dubins path are built into the constraints of our manipulator model. Furthermore, we show that the number of solutions is not constant, with up to seven valid CSC path solutions even in non-singular regions. An implementation of solution is available at https://github.com/aabecker/dubins3D.
- L. E. Dubins, “On curves of minimal length with a constraint on average curvature, and with prescribed initial and terminal positions and tangents,” American Journal of mathematics, vol. 79, no. 3, pp. 497–516, 1957.
- S. Hota and D. Ghose, “Optimal path planning for an aerial vehicle in 3d space,” in 49th IEEE Conference on Decision and Control (CDC), Dec 2010, pp. 4902–4907.
- W.-H. Chen, W. Yang, L. Peach, D. E. Koditschek, and C. R. Sung, “Kinegami: Algorithmic design of compliant kinematic chains from tubular origami,” IEEE Transactions on Robotics, vol. 39, no. 2, pp. 1260–1280, 2023.
- P. Váňa, A. Alves Neto, J. Faigl, and D. G. Macharet, “Minimal 3D Dubins path with bounded curvature and pitch angle,” in 2020 IEEE International Conference on Robotics and Automation (ICRA), May 2020, pp. 8497–8503.
- Y. Wang, S. Wang, M. Tan, C. Zhou, and Q. Wei, “Real-time dynamic Dubins-helix method for 3-d trajectory smoothing,” IEEE Transactions on Control Systems Technology, vol. 23, no. 2, pp. 730–736, March 2015.
- R. Anderson and D. Milutinović, “A stochastic approach to dubins feedback control for target tracking,” in 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems. IEEE, 2011, pp. 3917–3922.
- H. Marino, M. Bonizzato, R. Bartalucci, P. Salaris, and L. Pallottino, “Motion planning for two 3d-dubins vehicles with distance constraint,” in 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2012, pp. 4702–4707.
- Y. Li, W. Lu, Y. Liu, D. Meng, X. Wang, and B. Liang, “Optimization design method of tendon-sheath transmission path under curvature constraint,” IEEE Transactions on Robotics, 2023.
- P. Cui, W. Yan, R. Cui, and J. Yu, “Smooth path planning for robot docking in unknown environment with obstacles,” Complexity, vol. 2018, pp. 1–17, 2018.
- H. Liu, T. B. Gjersvik, and A. Faanes, “Subsea field layout optimization (part i)–directional well trajectory planning based on 3d dubins curve,” Journal of Petroleum Science and Engineering, vol. 208, p. 109450, 2022.
- J. Herynek, P. Váňa, and J. Faigl, “Finding 3d Dubins paths with pitch angle constraint using non-linear optimization,” in 2021 European Conference on Mobile Robots (ECMR). IEEE, 2021, pp. 1–6.
- J. Lim, F. Achermann, R. Bähnemann, N. Lawrance, and R. Siegwart, “Circling back: Dubins set classification revisited,” in Workshop on Energy Efficient Aerial Robotic Systems, International Conference on Robotics and Automation 2023, 2023.
- G. Xu, D. Zhu, J. Cao, Y. Liu, and J. Yang, “Shunted collision avoidance for multi-uav motion planning with posture constraints,” in 2023 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2023, pp. 3671–3678.
- B. Moon, S. Sachdev, J. Yuan, and S. Scherer, “Time-optimal path planning in a constant wind for uncrewed aerial vehicles using dubins set classification,” IEEE Robotics and Automation Letters, 2023.
- A. T. Blevins, “Real-time path optimization for 3d uas line survey operations,” in AIAA SCITECH 2023 Forum, 2023, p. 0395.
- O. I. D. Bashi, H. K. Hameed, Y. M. Al Kubaisi, and A. H. Sabry, “Developing a model for unmanned aerial vehicle with fixed-wing using 3d-map exploring rapidly random tree technique,” Bulletin of Electrical Engineering and Informatics, vol. 13, no. 1, pp. 473–481, 2024.
- C. Consonni, M. Brugnara, P. Bevilacqua, A. Tagliaferri, and M. Frego, “A new markov–dubins hybrid solver with learned decision trees,” Engineering Applications of Artificial Intelligence, vol. 122, p. 106166, 2023.
- W. Wu, J. Xu, C. Gong, and N. Cui, “Adaptive path following control for miniature unmanned aerial vehicle confined to three-dimensional dubins path: From take-off to landing,” ISA transactions, vol. 143, pp. 156–167, 2023.
- C. Hague, A. Willis, D. Maity, and A. Wolek, “Planning visual inspection tours for a 3d dubins airplane model in an urban environment,” in AIAA SCITECH 2023 Forum, 2023, p. 0108.
- H. Liu, T. B. Gjersvik, and A. Faanes, “Practical application of 3d dubins curve method in directional well trajectory planning,” in Abu Dhabi International Petroleum Exhibition and Conference. SPE, 2023, p. D021S037R004.
- V. Patsko and A. Fedotov, “Three-dimensional reachability set for a dubins car: Reduction of the general case of rotation constraints to the canonical case,” Journal of Computer and Systems Sciences International, pp. 1–24, 2023.
- X. Tian, T. Xu, X. Luo, Y. Jia, and J. Yin, “Multi-uav reconnaissance task allocation in 3d urban environments,” IEEE Access, 2024.
- S. Hota and D. Ghose, “Optimal geometrical path in 3d with curvature constraint,” in 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems. IEEE, 2010, pp. 113–118.
- W. Wang and P. Li, “Towards finding the shortest-paths for 3D rigid bodies,” in Proceedings of Robotics: Science and Systems, Virtual, July 2021.
- ——, “Finding control synthesis for kinematic shortest paths,” 2022.
- D. Balkcom, A. Furtuna, and W. Wang, “The Dubins car and other arm-like mobile robots,” in 2018 IEEE International Conference on Robotics and Automation (ICRA), May 2018, pp. 380–386.
- M. Raghavan and B. Roth, “Inverse Kinematics of the General 6R Manipulator and Related Linkages,” Journal of Mechanical Design, vol. 115, no. 3, pp. 502–508, 09 1993. [Online]. Available: https://doi.org/10.1115/1.2919218
- E. T. Whittaker, “On Sylvester’s dialytic method of elimination,” Proceedings of the Edinburgh Mathematical Society, vol. 40, p. 62–63, 1921.
- D. Kapur, “Algorithmic elimination methods,” in Tutorial Notes, Intl. Symp. on Symbolic and Algebraic Computation (ISSAC), Montreal, 1995, pp. 1–32.
- D. Eberly, “Distance to circles in 3d,” 2023. [Online]. Available: https://www.geometrictools.com/Documentation/DistanceToCircle3.pdf
- G. Marsaglia, “Choosing a point from the surface of a sphere,” The Annals of Mathematical Statistics, vol. 43, no. 2, pp. 645–646, 1972.
- R. Diankov, “Automated construction of robotic manipulation programs,” Ph.D. dissertation, Carnegie Mellon University, The Robotics Institute Pittsburgh, 2010.
- D. Rakita, B. Mutlu, and M. Gleicher, “Relaxedik: Real-time synthesis of accurate and feasible robot arm motion.” in Robotics: Science and Systems, vol. 14. Pittsburgh, PA, 2018, pp. 26–30.
- P. E. Dupont, J. Lock, B. Itkowitz, and E. Butler, “Design and control of concentric-tube robots,” IEEE Transactions on Robotics, vol. 26, no. 2, pp. 209–225, 2009.
- Z. Mitros, S. H. Sadati, R. Henry, L. Da Cruz, and C. Bergeles, “From theoretical work to clinical translation: Progress in concentric tube robots,” Annual Review of Control, Robotics, and Autonomous Systems, vol. 5, pp. 335–359, 2022.
- H. Sussmann, “Shortest 3-dimensional paths with a prescribed curvature bound,” in Proceedings of 1995 34th IEEE Conference on Decision and Control, vol. 4, 1995, pp. 3306–3312 vol.4.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.