Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-25T16:11:29.850Z Has data issue: false hasContentIssue false
  • English
  • Français

Robot motion planning with task specifications via regular languages

Published online by Cambridge University Press:  17 June 2015

James McMahon  and
Erion Plaku
James McMahon
Affiliation:
Department of Electrical Engineering and Computer Science, The Catholic University of America, Washington, DC 20064 U.S. Naval Research Laboratory, Code 7130, Washington, DC 20375
Erion Plaku*
Affiliation:
Department of Electrical Engineering and Computer Science, The Catholic University of America, Washington, DC 20064
*
*Corresponding author. E-mail: plaku@cua.edu
Get access Rights & Permissions [Opens in a new window]

Summary

This paper presents an efficient approach for planning collision-free and dynamically feasible trajectories that enable a mobile robot to carry out tasks specified as regular languages over workspace regions. A sampling-based tree search is conducted over the feasible motions and over an abstraction obtained by combining the automaton representing the regular language with a workspace decomposition. The abstraction is used to partition the motion tree into equivalence classes and estimate the feasibility of reaching accepting automaton states from these equivalence classes. The partition is continually refined to discover new ways to expand the search. Comparisons to related work show significant speedups.

Keywords

Motion planningMobile robotsRobot dynamicsRegular languages
Type
Articles
Information
Robotica , Volume 35 , Issue 1 , January 2017 , pp. 26 - 49
Copyright
Copyright © Cambridge University Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Aguiar, A. P. and Hespanha, J. P., “Trajectory-tracking and path-following of underactuated autonomous vehicles with parametric modeling uncertainty,” IEEE Trans. Autom. Control 52 (8), 1362–1379 (2007).CrossRefGoogle Scholar
2. Belta, C., Bicchi, A., Egerstedt, M., Frazzoli, E., Klavins, E. and Pappas, G. J., “Symbolic planning and control of robot motion,” IEEE Robot. Autom. Mag. 14 (1), 61–71 (2007).CrossRefGoogle Scholar
3. de Berg, M., Cheong, O., van Kreveld, M. and Overmars, M. H., Computational Geometry: Algorithms and Applications, 3 ed. (Springer-Verlag, Berlin Heidelberg, 2008).Google Scholar
4. Bhatia, A., Kavraki, L. E. and Vardi, M. Y., “Motion Planning with Hybrid Dynamics and Temporal Goals,” IEEE Conference on Decision and Control, Atlanta, Georgia, USA (2010) pp. 1108–1115.Google Scholar
5. Bhatia, A., Kavraki, L. E. and Vardi, M. Y., “Sampling-Based Motion Planning with Temporal Goals,” IEEE International Conference on Robotics and Automation, Anchorage, Alaska, USA (2010) pp. 2689–2696.Google Scholar
6. Bhatia, A., Maly, M., Kavraki, L. and Vardi, M., “Motion planning with complex goals,” IEEE Robot. Autom. Mag. 18, 55–64 (2011).Google Scholar
7. Camacho, E. F. and Alba, C. B., Model Predictive Control (Springer, London, 2013).Google Scholar
8. Chen, Y., Ding, D., Stefanescu, A. and Belta, C., “A formal approach to the deployment of distributed robotic teams,” IEEE Trans. Robot. 28 (1), 158–171 (2012).Google Scholar
9. Cheng, P., Frazzoli, E. and LaValle, S., “Improving the performance of sampling-based motion planning with symmetry-based gap reduction,” IEEE Trans. Robot. 24 (2), 488–494 (2008).Google Scholar
10. Cheng, P., Pappas, G. and Kumar, V., “Decidability of Motion Planning with Differential Constraints,” IEEE International Conference on Robotics and Automation, Rome, Italy (2007) pp. 1826–1831.Google Scholar
11. Choset, H., Lynch, K. M., Hutchinson, S., Kantor, G., Burgard, W., Kavraki, L. E. and Thrun, S., Principles of Robot Motion: Theory, Algorithms, and Implementations (MIT Press, 2005).Google Scholar
12. Chuy, O., Collins, E., Dunlap, D. and Sharma, A., “Sampling-based direct trajectory generation using the minimum time cost function,” Experimental Robotics, Springer Tracts in Advanced Robotics 88, 651–666 (2013).Google Scholar
13. Coumans, E., “Bullet physics engine,” (2012). Http://bulletphysics.org/; [accessed on 06/04/2015].Google Scholar
14. Şucan, I. A. and Kavraki, L. E., “A sampling-based tree planner for systems with complex dynamics,” IEEE Trans. Robot. 28 (1), 116–131 (2012).CrossRefGoogle Scholar
15. Dalibard, S. and Laumond, J. P., “Control of probabilistic diffusion in motion planning,” International Workshop on Algorithmic Foundations of Robotics, Springer Tracts in Advanced Robotics, vol. 57 (2009) pp. 467–481.Google Scholar
16. Dantam, N. T. and Stilman, M., “The motion grammar: Analysis of a linguistic method for robot control,” IEEE Trans. Robot. 29 (3), 704–718 (2013).CrossRefGoogle Scholar
17. DeCastro, J. A. and Kress-Gazit, H., “Guaranteeing Reactive High-Level Behaviors for Robots with Complex Dynamics,” IEEE/RSJ International Conference on Intelligent Robots and Systems, Tokyo, Japan (2013) pp. 749–756.Google Scholar
18. Devaurs, D., Simeon, T. and Cortés, J., “Enhancing the Transition-Based RRT to Deal with Complex Cost Spaces,” IEEE International Conference on Robotics and Automation, Tokyo, Japan (2013) pp. 4120–4125.Google Scholar
19. Ding, X. C., Lazar, M. and Belta, C., “LTL receding horizon control for finite deterministic systems,” Automatica 50 (2), 399–408 (2014).Google Scholar
20. Dunlap, D. D., Caldwell, C. V. and Collins, E. G. Jr, “Nonlinear Model Predictive Control using Sampling and Goal-Directed Optimization,” IEEE International Conference on Control Applications, Yokohama, Japan (2010) pp. 1349–1356.Google Scholar
21. Fainekos, G. E., Girard, A., Kress-Gazit, H. and Pappas, G. J., “Temporal logic motion planning for dynamic mobile robots,” Automatica 45 (2), 343–352 (2009).Google Scholar
22. Filippidis, I., Dimarogonas, D. V. and Kyriakopoulos, K. J., “Decentralized Multi-Agent Control from Local LTL Specifications,” IEEE Conference on Decision and Control, Maui, Hawaii, USA (2012) pp. 6235–6240.Google Scholar
23. Frazzoli, E., Dahleh, M. A. and Feron, E., “Trajectory Tracking Control Design for Autonomous Helicopters using a Backstepping Algorithm,” American Control Conference, vol. 6, Chicago, Illinois, USA (2000) pp. 4102–4107.Google Scholar
24. Frazzoli, E., Dahleh, M. A. and Feron, E., “Maneuver-based motion planning for nonlinear systems with symmetries,” IEEE Trans. Robot. 21 (6), 1077–1091 (2005).CrossRefGoogle Scholar
25. Gipson, B., Moll, M. and Kavraki, L.E., “Resolution Independent Density Estimation for Motion Planning in High-Dimensional Spaces,” IEEE International Conference on Robotics and Automation, Karlsruhe, Germany (2013) pp. 2437–2443.Google Scholar
26. Hsu, D., Kindel, R., Latombe, J. C. and Rock, S., “Randomized kinodynamic motion planning with moving obstacles,” Int. J. Robot. Res. 21 (3), 233–255 (2002).Google Scholar
27. Kanjanawanishkul, K. and Zell, A., “Path Following for an Omnidirectional Mobile Robot Based on Model Predictive Control,” IEEE International Conference on Robotics and Automation, Kobe, Japan (2009) pp. 3341–3346.Google Scholar
28. Karaman, S. and Frazzoli, E., “Sampling-based algorithms for optimal motion planning,” Int. J. Robot. Res. 30 (7), 846–894 (2011)Google Scholar
29. Karaman, S. and Frazzoli, E., “Sampling-Based Algorithms for Optimal Motion Planning with Deterministic μ-Calculus Specifications,” American Control Conference, Montreal, Canada (2012) pp. 735–742.Google Scholar
30. Keller, H., Numerical Methods for Two-Point Boundary-Value Problems (Dover, New York, NY, 1992).Google Scholar
31. Kloetzer, M. and Belta, C., “Temporal logic planning and control of robotic swarms by hierarchical abstractions,” IEEE Trans. Robot. 23 (2), 320–331 (2007).CrossRefGoogle Scholar
32. Kress-Gazit, H., Conner, D. C., Choset, H., Rizzi, A. and Pappas, G. J., “Courteous cars: Decentralized multi-agent traffic coordination,” IEEE Robot. Autom. Mag. 15 (1), 30–38 (2008).Google Scholar
33. Kress-Gazit, H., Fainekos, G. E. and Pappas, G. J., “Temporal logic-based reactive mission and motion planning,” IEEE Trans. Robot. 25 (6), 1370–1381 (2009).Google Scholar
34. Kress-Gazit, H., Wongpiromsarn, T. and Topcu, U., “Correct, reactive robot control from abstraction and temporal logic specifications,” IEEE Robot. Autom. Mag. 18 (3), 65–74 (2011).Google Scholar
35. Kupferman, O. and Vardi, M., “Model checking of safety properties,” Formal Methods Syst. Des. 19 (3), 291–314 (2001).CrossRefGoogle Scholar
36. Latvala, T., “Efficient Model Checking of Safety Properties,” Model Checking Software, Lecture Notes in Computer Science, vol. 2648 (2003) pp. 74–88.Google Scholar
37. LaValle, S. M., Planning Algorithms (Cambridge University Press, Cambridge, MA, 2006).Google Scholar
38. LaValle, S. M., “Motion planning: The essentials,” IEEE Robot. Autom. Mag. 18 (1), 79–89 (2011).Google Scholar
39. LaValle, S. M. and Kuffner, J. J., “Randomized kinodynamic planning,” Int. J. Robot. Res. 20 (5), 378–400 (2001).Google Scholar
40. McMahon, J. and Plaku, E., “Sampling-Based Tree Search with Discrete Abstractions for Motion Planning with Dynamics and Temporal Logic,” IEEE/RSJ International Conference on Intelligent Robots and Systems, Chicago, Illinois, USA (2014) pp. 3726–3733.Google Scholar
41. Ordonez, C., Gupta, N., Yu, W., Chuy, O. and Collins, E. G., “Modeling of Skid-Steered Wheeled Robotic Vehicles on Sloped Terrains,” ASME Dynamic Systems and Control Conference, Fort Lauderdale, Florida, USA (2012) pp. 91–99.Google Scholar
42. Plaku, E., “Robot Motion Planning with Dynamics as Hybrid Search,” AAAI Conference on Artificial Intelligence, Bellevue, Washington, USA (2013) pp. 1415–1421.Google Scholar
43. Plaku, E., Kavraki, L. and Vardi, M., “Falsification of LTL safety properties in hybrid systems,” Int. J. Softw. Tools Technol. Transfer 15 (4), 305–320 (2013).CrossRefGoogle Scholar
44. Plaku, E., Kavraki, L. E. and Vardi, M. Y., “Falsification of LTL Safety Properties in Hybrid Systems,” Lecture Notes in Computer Science, vol. 5505 (2009) pp. 368–382.Google Scholar
45. Plaku, E., Kavraki, L. E. and Vardi, M. Y., “Motion planning with dynamics by a synergistic combination of layers of planning,” IEEE Trans. Robot. 26 (3), 469–482 (2010).Google Scholar
46. Rajamani, R., Vehicle Dynamics and Control (Springer, New York, 2011).Google Scholar
47. Raman, V. and Kress-Gazit, H., “Explaining impossible high-level robot behaviors,” IEEE Trans. Robot. 29 (1), 94–104 (2013).Google Scholar
48. Rodriguez, S., Tang, X., Lien, J. M. and Amato, N. M., “An Obstacle-Based Rapidly-Exploring Random Tree,” IEEE International Conference on Robotics and Automation, Orlando, Florida, USA (2006) pp. 895–900.Google Scholar
49. Sánchez, G. and Latombe, J. C., “On delaying collision checking in PRM planning: Application to multi-robot coordination,” Int. J. Robot. Res. 21 (1), 5–26 (2002).CrossRefGoogle Scholar
50. Shewchuk, J. R., “Delaunay refinement algorithms for triangular mesh generation,” Comput. Geom.: Theory Appl. 22 (1–3), 21–74 (2002).CrossRefGoogle Scholar
51. Sistla, A., “Safety, liveness and fairness in temporal logic,” Form. Asp. Comput. 6, 495–511 (1994).Google Scholar
52. Smith, M., “Open dynamics engine,” (2006). www.ode.org; [accessed on 06/04/2015].Google Scholar
53. Ulusoy, A., Wongpiromsarn, T. and Belta, C., “Incremental controller synthesis in probabilistic environments with temporal logic constraints,” Int. J. Robot. Res. 33 (8), 1130–1144 (2014).Google Scholar
54. Vasile, C. I. and Belta, C., “Sampling-Based Temporal Logic Path Planning,” IEEE/RSJ International Conference on Intelligent Robots and Systems, Tokyo, Japan (2013) pp. 4817–4822.Google Scholar
55. Vasile, C. I. and Belta, C., “Reactive Sampling-Based Temporal Logic Path Planning,” IEEE International Conference on Robotics and Automation, Hong Kong, China (2014) pp. 4310–4315.Google Scholar

McMahon supplementary material

McMahon supplementary material 1

Download McMahon supplementary material(Video)
Video 16.2 MB