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Robot motion planning with task specifications via regular languages

  • James McMahon (a1) (a2) and Erion Plaku (a1)

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.

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Corresponding author

*Corresponding author. E-mail: plaku@cua.edu

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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), 13621379 (2007).
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), 6171 (2007).
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).
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.
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.
6. Bhatia, A., Maly, M., Kavraki, L. and Vardi, M., “Motion planning with complex goals,” IEEE Robot. Autom. Mag. 18, 5564 (2011).
7. Camacho, E. F. and Alba, C. B., Model Predictive Control (Springer, London, 2013).
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), 158171 (2012).
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), 488494 (2008).
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.
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).
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, 651666 (2013).
13. Coumans, E., “Bullet physics engine,” (2012). Http://bulletphysics.org/; [accessed on 06/04/2015].
14. Şucan, I. A. and Kavraki, L. E., “A sampling-based tree planner for systems with complex dynamics,” IEEE Trans. Robot. 28 (1), 116131 (2012).
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.
16. Dantam, N. T. and Stilman, M., “The motion grammar: Analysis of a linguistic method for robot control,” IEEE Trans. Robot. 29 (3), 704718 (2013).
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.
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.
19. Ding, X. C., Lazar, M. and Belta, C., “LTL receding horizon control for finite deterministic systems,” Automatica 50 (2), 399408 (2014).
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.
21. Fainekos, G. E., Girard, A., Kress-Gazit, H. and Pappas, G. J., “Temporal logic motion planning for dynamic mobile robots,” Automatica 45 (2), 343352 (2009).
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.
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.
24. Frazzoli, E., Dahleh, M. A. and Feron, E., “Maneuver-based motion planning for nonlinear systems with symmetries,” IEEE Trans. Robot. 21 (6), 10771091 (2005).
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.
26. Hsu, D., Kindel, R., Latombe, J. C. and Rock, S., “Randomized kinodynamic motion planning with moving obstacles,” Int. J. Robot. Res. 21 (3), 233255 (2002).
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.
28. Karaman, S. and Frazzoli, E., “Sampling-based algorithms for optimal motion planning,” Int. J. Robot. Res. 30 (7), 846894 (2011)
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.
30. Keller, H., Numerical Methods for Two-Point Boundary-Value Problems (Dover, New York, NY, 1992).
31. Kloetzer, M. and Belta, C., “Temporal logic planning and control of robotic swarms by hierarchical abstractions,” IEEE Trans. Robot. 23 (2), 320331 (2007).
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), 3038 (2008).
33. Kress-Gazit, H., Fainekos, G. E. and Pappas, G. J., “Temporal logic-based reactive mission and motion planning,” IEEE Trans. Robot. 25 (6), 13701381 (2009).
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), 6574 (2011).
35. Kupferman, O. and Vardi, M., “Model checking of safety properties,” Formal Methods Syst. Des. 19 (3), 291314 (2001).
36. Latvala, T., “Efficient Model Checking of Safety Properties,” Model Checking Software, Lecture Notes in Computer Science, vol. 2648 (2003) pp. 7488.
37. LaValle, S. M., Planning Algorithms (Cambridge University Press, Cambridge, MA, 2006).
38. LaValle, S. M., “Motion planning: The essentials,” IEEE Robot. Autom. Mag. 18 (1), 7989 (2011).
39. LaValle, S. M. and Kuffner, J. J., “Randomized kinodynamic planning,” Int. J. Robot. Res. 20 (5), 378400 (2001).
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.
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.
42. Plaku, E., “Robot Motion Planning with Dynamics as Hybrid Search,” AAAI Conference on Artificial Intelligence, Bellevue, Washington, USA (2013) pp. 1415–1421.
43. Plaku, E., Kavraki, L. and Vardi, M., “Falsification of LTL safety properties in hybrid systems,” Int. J. Softw. Tools Technol. Transfer 15 (4), 305320 (2013).
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.
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), 469482 (2010).
46. Rajamani, R., Vehicle Dynamics and Control (Springer, New York, 2011).
47. Raman, V. and Kress-Gazit, H., “Explaining impossible high-level robot behaviors,” IEEE Trans. Robot. 29 (1), 94104 (2013).
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.
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), 526 (2002).
50. Shewchuk, J. R., “Delaunay refinement algorithms for triangular mesh generation,” Comput. Geom.: Theory Appl. 22 (1–3), 2174 (2002).
51. Sistla, A., “Safety, liveness and fairness in temporal logic,” Form. Asp. Comput. 6, 495511 (1994).
52. Smith, M., “Open dynamics engine,” (2006). www.ode.org; [accessed on 06/04/2015].
53. Ulusoy, A., Wongpiromsarn, T. and Belta, C., “Incremental controller synthesis in probabilistic environments with temporal logic constraints,” Int. J. Robot. Res. 33 (8), 11301144 (2014).
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.
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.

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Robot motion planning with task specifications via regular languages

  • James McMahon (a1) (a2) and Erion Plaku (a1)

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