Abstract
Many real-world robotic operations that involve high-dimensional humanoid robots require fast reaction to plan disturbances and probabilistic guarantees over collision risks, whereas most probabilistic motion planning approaches developed for car-like robots cannot be directly applied to high-dimensional robots. In this paper, we present probabilistic Chekov (p-Chekov), a fast-reactive motion planning system that can provide safety guarantees for high-dimensional robots suffering from process noises and observation noises. Leveraging recent advances in machine learning as well as our previous work in deterministic motion planning that integrated trajectory optimization into a sparse roadmap framework, p-Chekov demonstrates its superiority in terms of collision avoidance ability and planning speed in high-dimensional robotic motion planning tasks in complex environments without the convexification of obstacles. Comprehensive theoretical and empirical analysis provided in this paper shows that p-Chekov can effectively satisfy user-specified chance constraints over collision risk in practical robotic manipulation tasks.
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Abadi M, Agarwal A, Barham P, Brevdo E, Chen Z, Citro C, Corrado GS, Davis A, Dean J, Devin M, Ghemawat S, Goodfellow I, Harp A, Irving G, Isard M, Jia Y, Jozefowicz R, Kaiser L, Kudlur M, Levenberg J, Mané D, Monga R, Moore S, Murray D, Olah C, Schuster M, Shlens J, Steiner B, Sutskever I, Talwar K, Tucker P, Vanhoucke V, Vasudevan V, Viégas F, Vinyals O, Warden P, Wattenberg M, Wicke M, Yu Y, Zheng X. TensorFlow: large-scale machine learning on heterogeneous systems (2015). https://www.tensorflow.org/. Software available from tensorflow.org Accessed May 2019.
Abramowitz M, Stegun IA. Handbook of mathematical functions: with formulas, graphs, and mathematical tables, vol. 55. US Government printing office Chelmsford: Courier Corporation; 1964.
Alterovitz R, Siméon T, Goldberg KY. The stochastic motion roadmap: A sampling framework for planning with Markov motion uncertainty. Robot Sci Syst. 2007;3:233–41.
Arslan O, Tsiotras P. Machine learning guided exploration for sampling-based motion planning algorithms. In: 2015 IEEE/RSJ International Conference on intelligent robots and systems (IROS), IEEE, 2015; p. 2646–52.
Atramentov A, LaValle SM. Efficient nearest neighbor searching for motion planning, vol. No. 02CH37292), In: Proceedings 2002 IEEE International Conference on robotics and automation (Cat. No. 02CH37292), vol. 1. IEEE 2002; p. 632–37.
Axelrod B, Kaelbling LP, Lozano-Pérez T. Provably safe robot navigation with obstacle uncertainty. Int J Robot Res. 2018;37(13–14):1760–74.
Bellman RE. Dynamic programming. Science. American Association for the Advancement of Science 1966.153(3731):34–7.
Bertsekas DP, Bertsekas DP, Bertsekas DP, Bertsekas DP. Dynamic programming and optimal control, vol. 1. Belmont: Athena Scientific; 1995.
Blackmore L, Li H, Williams B. A probabilistic approach to optimal robust path planning with obstacles. In: American Control Conference, 2006, pp. 7–pp. IEEE 2006.
Blackmore L, Ono M, Bektassov A, Williams BC. A probabilistic particle-control approximation of chance-constrained stochastic predictive control. IEEE Trans Rob. 2010;26(3):502–17.
Bohlin R, Kavraki LE. Path planning using lazy prm. In: Robotics and Automation, 2000. Proceedings. ICRA’00. IEEE International Conference on, IEEE 2000; vol. 1, pp. 521–28.
Bry A, Roy N. Rapidly-exploring random belief trees for motion planning under uncertainty. In: Robotics and Automation (ICRA), 2011 IEEE International Conference on, IEEE 2011; p. 723–30.
Burlet J, Aycard O, Fraichard T. Robust motion planning using Markov decision processes and quadtree decomposition. In: Robotics and automation, 2004. Proceedings. ICRA’04. 2004 IEEE International Conference on, IEEE 2004; vol. 3, pp. 2820–825.
Campana M, Lamiraux F, Laumond JP. A simple path optimization method for motion planning. Rapport LAAS n 15108. 2015.
Chen C, Rickert M, Knoll A. Motion planning under perception and control uncertainties with space exploration guided heuristic search. In: 2017 IEEE Intelligent Vehicles Symposium (IV), IEEE, 2017; p. 712–18.
Chollet F, et al. Keras 2015. https://keras.io. Accessed May 2019.
Choset HM. Principles of robot motion: theory, algorithms, and implementation. Cambridge: MIT Press; 2005.
Cohen BJ, Chitta S, Likhachev M. Search-based planning for manipulation with motion primitives. In: Robotics and automation (ICRA), 2010 IEEE International Conference on, IEEE 2010; p. 2902–908.
Dai S, Orton M, Schaffert S, Hofmann A, Williams BC. Improving trajectory optimization using a roadmap framework. In: Proceedings of the 2018 IEEE/RSJ International Conference on intelligent robots and systems (IROS) 2018. pp, 8674–81. https://doi.org/10.1109/IROS.2018.8594274.
Dai S, Schaffert S, Jasour A, Hofmann A, Williams BC. Chance constrained motion planning for high-dimensional robots. In: Proceedings of the 2019 IEEE/RSJ International Conference on robotics and automation (ICRA), 2019. pp, 8805–11. https://doi.org/10.1109/ICRA.2019.8793660.
Eaton ML. Multivariate statistics: a vector space approach. New York: Wiley; 1983. p. 512.
Gelb A. Applied optimal estimation. Cambridge: MIT Press; 1974.
Ha JS, Chae HJ, Choi HL. Approximate inference-based motion planning by learning and exploiting low-dimensional latent variable models. IEEE Robot Autom Lett. 2018;3(4):3892–9.
Hildebrand FB. Introduction to numerical analysis. USA Chelmsford: Courier Corporation; 1987.
Hoeffding W, Robbins H, et al. The central limit theorem for dependent random variables. Duke Math J. 1948;15(3):773–80.
Ichter B, Harrison J, Pavone M. Learning sampling distributions for robot motion planning. In: 2018 IEEE International Conference on robotics and automation (ICRA), IEEE 2018; p. 7087–94.
Janson L, Schmerling E, Pavone M. Monte Carlo motion planning for robot trajectory optimization under uncertainty. In: Bicchi A, Burgard W. (eds) Robotics research. Springer, 2018; p. 343–61. https://doi.org/10.1007/978-3-319-60916-4_20.
Kalakrishnan M, Chitta S, Theodorou E, Pastor P, Schaal, S. Stomp: stochastic trajectory optimization for motion planning. In: Robotics and automation (ICRA), 2011 IEEE International Conference on, IEEE, 2011; p. 4569–74.
Karaman S, Frazzoli E. Sampling-based algorithms for optimal motion planning. Int J Robot Res. 2011;30(7):846–94.
Kingma DP, Ba J. Adam: a method for stochastic optimization. arXiv preprint arXiv:1412.6980 2014.
Koenig S, Likhachev M. Fast replanning for navigation in unknown terrain. IEEE Trans Rob. 2005;21(3):354–63.
Kurniawati H, Hsu D, Lee WS. Sarsop: Efficient point-based pomdp planning by approximating optimally reachable belief spaces. In: Robotics: science and systems, vol. 2008. Zurich, Switzerland. 2008. https://doi.org/10.15607/RSS.2008.IV.009.
LaValle SM. Rapidly-exploring random trees: a new tool for path planning. 1998. https://www.cs.csustan.edu/~xliang/Courses/CS4710-21S/Papers/06%20RRT.pdf.
Lee A, Duan Y, Patil S, Schulman J, McCarthy Z, Van Den Berg J, Goldberg K, Abbeel P. Sigma hulls for Gaussian belief space planning for imprecise articulated robots amid obstacles. In: 2013 IEEE/RSJ International Conference on intelligent robots and systems, IEEE 2013; p. 5660–67.
Lenz D, Rickert M, Knoll A. Heuristic search in belief space for motion planning under uncertainties. In: 2015 IEEE/RSJ International Conference on intelligent robots and systems (IROS), IEEE 2015; p. 2659–65.
Li S, Shah JA. Safe and efficient high dimensional motion planning in space-time with time parameterized prediction. In: Proceedings of the 2019 IEEE/RSJ International Conference on robotics and automation (ICRA), 2019. pp, 5012–18. https://doi.org/10.1109/ICRA.2019.8793580.
Liaw A, Wiener M, et al. Classification and regression by random forest. R News. 2002;2(3):18–22.
Liu W, Ang MH. Incremental sampling-based algorithm for risk-aware planning under motion uncertainty. In: Robotics and automation (ICRA), 2014 IEEE International Conference on, IEEE 2014; p. 2051–508.
Luders B, Kothari M, How J. Chance constrained rrt for probabilistic robustness to environmental uncertainty. In: AIAA Guidance, Navigation, and Control Conference, 2010; p. 8160.
Luders BD, Karaman S, How JP. Robust sampling-based motion planning with asymptotic optimality guarantees. In: AIAA Guidance, Navigation, and Control (GNC) Conference, 2013; p. 5097.
Luenberger DG. Introduction to dynamic systems: theory, models, and applications, vol. 1. New York: Wiley; 1979.
Luna R, Şucan IA, Moll M, Kavraki LE. Anytime solution optimization for sampling-based motion planning. In: Robotics and automation (ICRA), 2013 IEEE International Conference on, IEEE 2013; p. 5068–74.
Luo Y, Bai H, Hsu D, Lee WS. Importance sampling for online planning under uncertainty. Int J Robot Res. 2019;38(2–3):162–81.
Mukadam M, Dong J, Yan X, Dellaert F, Boots B. Continuous-time gaussian process motion planning via probabilistic inference. Int J Robot Res. 2018;37(11):1319–40.
Murphy KP. Machine learning: a probabilistic perspective. Cambridge: MIT Press; 2012.
Ono M, Williams B. An efficient motion planning algorithm for stochastic dynamic systems with constraints on probability of failure. 2008.pp. 1376–82.
Ono M, Williams BC. Iterative risk allocation: a new approach to robust model predictive control with a joint chance constraint. In: Decision and control, 2008. CDC 2008. 47th IEEE Conference on, pp. 3427–3432. IEEE, 2008.
Ono M, Williams BC, Blackmore L. Probabilistic planning for continuous dynamic systems under bounded risk. J Artif Intell Res. 2013;46:511–77.
Orton M, Dai S, Schaffert S, Hofmann A, Williams BC. Improving incremental planning performance through overlapping replanning and execution. In: Proceedings of the 2019 IEEE/RSJ International Conference on robotics and automation (ICRA), 2019. pp, 2426–32. https://doi.org/10.1109/ICRA.2019.8793642.
Owen A. Monte Carlo theory, methods and examples (book draft). 2014. https://statweb.stanford.edu/~owen/mc/.
Pan J, Chitta S, Manocha D. Fcl: a general purpose library for collision and proximity queries. In: 2012 IEEE International Conference on robotics and automation, IEEE, 2012; p. 3859–66. https://doi.org/10.1109/ICRA.2012.6225337.
Pan J, Chitta S, Manocha D. Probabilistic collision detection between noisy point clouds using robust classification. In: Christensen H., Khatib O. (eds) Robotics research. Springer; 2017, p. 77–94. https://doi.org/10.1007/978-3-319-29363-9_5.
Pan J, Manocha D. Fast probabilistic collision checking for sampling-based motion planning using locality-sensitive hashing. Int J Robot Res. 2016;35(12):1477–96.
Park C, Pan J, Manocha D. Itomp: incremental trajectory optimization for real-time replanning in dynamic environments. In: ICAPS 2012.22(1):207–15. https://ojs.aaai.org/index.php/ICAPS/article/view/13513.
Park C, Park JS, Manocha D. Fast and bounded probabilistic collision detection for high-dof trajectory planning in dynamic environments. IEEE Trans Autom Sci Eng. 2018;15(3):980–91.
Park C, Rabe F, Sharma S, Scheurer C, Zimmermann UE, Manocha D. Parallel cartesian planning in dynamic environments using constrained trajectory planning. In: Humanoid robots (Humanoids), 2015 IEEE-RAS 15th International Conference on, IEEE 2015; p. 983–90.
Patil S, Duan Y, Schulman J, Goldberg K, Abbeel P. Gaussian belief space planning with discontinuities in sensing domains. In: 2014 IEEE International Conference on robotics and automation (ICRA), IEEE 2014; p. 6483–90.
Patil S, Kahn G, Laskey M, Schulman J, Goldberg K, Abbeel P. Scaling up gaussian belief space planning through covariance-free trajectory optimization and automatic differentiation. In: Algorithmic foundations of robotics XI, 107:515–33. Springer 2015.
Patil S, Van Den Berg J, Alterovitz R. Estimating probability of collision for safe motion planning under gaussian motion and sensing uncertainty. In: Robotics and automation (ICRA), 2012 IEEE International Conference on, IEEE 2012; p. 3238–44.
Pedregosa F, Varoquaux G, Gramfort A, Michel V, Thirion B, Grisel O, Blondel M, Prettenhofer P, Weiss R, Dubourg V, Vanderplas J, Passos A, Cournapeau D, Brucher M, Perrot M, Duchesnay E. Scikit-learn: machine learning in Python. J Mach Learn Res. 2011;12:2825–30.
Pfeiffer M, Schaeuble M, Nieto J, Siegwart R, Cadena C. From perception to decision: A data-driven approach to end-to-end motion planning for autonomous ground robots. In: 2017 IEEE International Conference on robotics and automation (ICRA), IEEE 2017; p. 1527–33.
Rasmussen C, Williams C. Gaussian processes for machine learning. Cambridge: MIT Press; 2006.
RethinkRobotics. Baxter. 2012. http://www.rethinkrobotics.com/baxter/. Accessed May 2019.
Schulman J, Duan Y, Ho J, Lee A, Awwal I, Bradlow H, Pan J, Patil S, Goldberg K, Abbeel P. Motion planning with sequential convex optimization and convex collision checking. Int J Robot Res. 2014;33(9):1251–70.
Schulman J, Ho J, Lee AX, Awwal I, Bradlow H, Abbeel P. Finding locally optimal, collision-free trajectories with sequential convex optimization. In: Robotics: science and systems, vol. 9. Citeseer; 2013, p. 1–10. https://doi.org/10.15607/RSS.2013.IX.031.
Stentz A. Optimal and efficient path planning for partially-known environments. In: Robotics and automation, 1994. Proceedings., 1994 IEEE International Conference on, pp. 3310–3317. IEEE, 1994.
Sun W, Patil S, Alterovitz R. High-frequency replanning under uncertainty using parallel sampling-based motion planning. IEEE Trans Rob. 2015;31(1):104–16.
Sun W, Torres LG, Van Den Berg J, Alterovitz R. Safe motion planning for imprecise robotic manipulators by minimizing probability of collision. In: Robotics research. Springer; 2016, 114:685–701. https://doi.org/10.1007/978-3-319-28872-7_39.
Thrun S, Burgard W, Fox D. Probabilistic robotics. Cambridge: MIT Press; 2005.
Van Den Berg J, Abbeel P, Goldberg K. Lqg-mp: optimized path planning for robots with motion uncertainty and imperfect state information. Int J Robot Res. 2011;30(7):895–913.
Van Den Berg J, Patil S, Alterovitz R. Motion planning under uncertainty using iterative local optimization in belief space. Int J Robot Res. 2012;31(11):1263–78.
Wang H, Chen J, Lau HY, Ren H. Motion planning based on learning from demonstration for multiple-segment flexible soft robots actuated by electroactive polymers. IEEE Robot Autom Lett. 2016;1(1):391–8.
Xiao X, Dufek J, Murphy RR. Robot risk-awareness by formal risk reasoning and planning. IEEE Robot Autom Lett. 2020;5(2):2856–63.
Zucker M, Ratliff N, Dragan AD, Pivtoraiko M, Klingensmith M, Dellin CM, Bagnell JA, Srinivasa SS. Chomp: covariant Hamiltonian optimization for motion planning. Int J Robot Res. 2013;32(9–10):1164–93.
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Dai, S., Hofmann, A. & Williams, B. Fast-Reactive Probabilistic Motion Planning for High-Dimensional Robots. SN COMPUT. SCI. 2, 484 (2021). https://doi.org/10.1007/s42979-021-00878-0
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DOI: https://doi.org/10.1007/s42979-021-00878-0