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Clearance-driven motion planning for mobile robots with differential constraints

Published online by Cambridge University Press:  27 February 2018

Evis Plaku,
Erion Plaku and
Patricio Simari
Evis Plaku
Affiliation:
Department of Electrical Engineering and Computer Science, The Catholic University of America, Washington, DC 20064, USA. E-mails: 74plaku@cua.edu, simari@cua.edu
Erion Plaku*
Affiliation:
Department of Electrical Engineering and Computer Science, The Catholic University of America, Washington, DC 20064, USA. E-mails: 74plaku@cua.edu, simari@cua.edu
Patricio Simari
Affiliation:
Department of Electrical Engineering and Computer Science, The Catholic University of America, Washington, DC 20064, USA. E-mails: 74plaku@cua.edu, simari@cua.edu
*
*Corresponding author. E-mail: plaku@cua.edu
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Summary

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This paper presents an approach that integrates the geometric notion of clearance (distance to the closest obstacle) into sampling-based motion planning to enable a robot to safely navigate in challenging environments. To reach the goal destination, the robot must obey geometric and differential constraints that arise from the underlying motion dynamics and the characteristics of the environment. To produce safe paths, the proposed approach expands a motion tree of collision-free and dynamically feasible motions while maintaining locally maximal clearance. In distinction from related work, rather than explicitly constructing the medial axis, the proposed approach imposes a grid or a triangular tessellation over the free space and uses the clearance information to construct a weighted graph where edges that connect regions with low clearance have high cost. Minimum-cost paths over this graph produce high-clearance routes that tend to follow the medial axis without requiring its explicit construction. A key aspect of the proposed approach is a route-following component which efficiently expands the motion tree to closely follow such high-clearance routes. When expansion along the current route becomes difficult, edges in the tessellation are penalized in order to promote motion-tree expansions along alternative high-clearance routes to the goal. Experiments using vehicle models with second-order dynamics demonstrate that the robot is able to successfully navigate in complex environments. Comparisons to the state-of-the-art show computational speedups of one or more orders of magnitude.

Keywords

Motion PlanningMobile RobotsNavigationPath PlanningRobot Dynamics

Information

Type
Articles
Information
Robotica , Volume 36 , Issue 7 , July 2018, pp. 971 - 993
Copyright
Copyright © Cambridge University Press 2018 

References

1. Amenta, N., Choi, S. and Kolluri, R. K., “The power crust, unions of balls, and the medial axis transform,” Comput. Geom. 19 127–153 (2001).CrossRefGoogle Scholar
2. de Berg, M., Cheong, O., van Kreveld, M. and Overmars, M. H., Computational Geometry: Algorithms and Applications (Springer-Verlag, Santa Clara, CA, 2008).Google Scholar
3. Branicky, M. S., “Universal computation and other capabilities of continuous and hybrid systems,” Theor. Comput. Sci. 138 (1), 67–100 (1995).Google Scholar
4. Brin, S., “Near Neighbor Search in Large Metric Spaces,” Proceedings of the 21th International Conference on Very Large Data Bases, Zurich, Switzerland (1995) pp. 574–584.Google Scholar
5. Chen, Y. F., Liu, S. Y., Liu, M., Miller, J. and How, J. P., “Motion Planning with Diffusion Maps,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Deajeon, South Korea (2016) pp. 1423–1430.Google Scholar
6. 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, Cambridge, MA, 2005).Google Scholar
7. Cohen, J., “A power primer,” Psychol. Bull. 112 (1), 155 (1992).Google Scholar
8. Şucan, I. A. and Kavraki, L.E., “A sampling-based tree planner for systems with complex dynamics,” IEEE Trans. Robot. 28, 116–131 (2012).Google Scholar
9. Şucan, I. A., Moll, M. and Kavraki, L. E., “The open motion planning library,” IEEE Robot. Autom. Mag. 19 (4), 72–82 (2012). Available at: http://ompl.kavrakilab.orgCrossRefGoogle Scholar
10. Culver, T., Keyser, J. and Manocha, D., “Exact computation of the medial axis of a polyhedron,” Comput. Aided Geom. Des. 21 (1), 65–98 (2004).Google Scholar
11. Denny, J., Greco, E., Thomas, S. and Amato, N. M., “MARRT: Medial Axis Biased Rapidly-Exploring Random Trees,” Proceedings of the IEEE International Conference on Robotics and Automation, Hong Kong, China (2014) pp. 90–97.Google Scholar
12. Devaurs, D., Simeon, T. and Cortés, J., “Enhancing the Transition-Based RRT to Deal with Complex Cost Spaces,” Proceedings of the IEEE International Conference on Robotics and Automation, Karlsruhe, Germany (2013) pp. 4120–4125.Google Scholar
13. Dey, T. K. and Zhao, W., “Approximating the medial axis from the voronoi diagram with a convergence guarantee,” Algorithmica 38 (1), 179–200 (2003)CrossRefGoogle Scholar
14. Etzion, M. and Rappoport, A., “Computing the Voronoi Diagram of a 3-d Polyhedron by Separate Computation of its Symbolic and Geometric Parts,” Proceedings of Symposium on Solid Modeling and Applications, New York, NY (1999) pp. 167–178.Google Scholar
15. Guibas, L. J., Holleman, C. and Kavraki, L. E., “A Probabilistic Roadmap Planner for Flexible Objects with a Workspace Medial-Axis-Based Sampling Approach,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Kyongju, South Korea (1999) pp. 254–260.Google Scholar
16. Hampel, F. R., Ronchetti, E. M., Rousseeuw, P. J. and Stahel, W.A., Robust Statistics: The Approach Bon Influence Functions, Vol. 114 (John Wiley & Sons, New York, NY, 2011).Google Scholar
17. Hauer, F. and Tsiotras, P., “Deformable Rapidly-Exploring Random Trees,” Proceedings of the Robotics: Science and Systems Conference, Boston, MA (2017) p. P08.Google Scholar
18. Hoff, K. E. III, Keyser, J., Lin, M., Manocha, D. and Culver, T., “Fast Computation Of Generalized Voronoi Diagrams Using Graphics Hardware,” Proceedings of the Conference on Computer Graphics and Interactive Techniques, New York, NY (1999) pp. 277–286.Google Scholar
19. Holleman, C. and Kavraki, L. E., “A Framework for Using the Workspace Medial Axis in PRM Planners,” Proceedings of the IEEE International Conference on Robotics and Automation, San Francisco, CA (2000) pp. 1408–1413.Google Scholar
20. Huh, J., Lee, B. and Lee, D. D., “Adaptive Motion Planning with High-Dimensional Mixture Models,” Proceedings of the IEEE International Conference on Robotics and Automation, Singapore (2017) pp. 3740–3747.Google Scholar
21. Kallmann, M., “Dynamic and robust local clearance triangulations,” ACM Trans. Graph. 33 (5), 161:1–161:17 (2014).Google Scholar
22. Kiesel, S., Burns, E. and Ruml, W., “Abstraction-Guided Sampling for Motion Planning,” Proceedings of the Symposium on Combinatorial Search Niagara Falls, Canada (2012) pp. 162–163. Also as UNH CS Technical Report 12-01.Google Scholar
23. Kirkpatrick, D. G., “Optimal search in planar subdivisions,” SIAM J. Comput. 12 (1), 28–35 (1983).CrossRefGoogle Scholar
24. Ladd, A. M. and Kavraki, L. E., “Motion Planning in the Presence of Drift, Underactuation and Discrete System Changes,” Proceedings of the Robotics: Science and Systems Conference, Boston, MA (2005) pp. 233–241.Google Scholar
25. Larsen, E., Gottschalk, S., Lin, M. C. and Manocha, D., Fast Proximity Queries with Swept Sphere Volumes. Technical Report (Department of Computer Science, University of North Carolina, Chapel Hill, NC, 1999).Google Scholar
26. LaValle, S. M., Planning Algorithms (Cambridge University Press, Cambridge, MA, 2006).Google Scholar
27. LaValle, S. M., “Motion planning: The essentials,” IEEE Robot. Autom. Mag. 18 (1), 79–89 (2011).CrossRefGoogle Scholar
28. LaValle, S. M. and Kuffner, J. J., “Randomized kinodynamic planning,” Int. J. Robot. Res. 20 (5), 378–400 (2001).CrossRefGoogle Scholar
29. Lien, J. M., Thomas, S. L. and Amato, N. M., “A General Framework for Sampling on the Medial Axis of the Free Space,” Proceedings of the IEEE International Conference on Robotics and Automation, Taipei, Taiwan (2003) pp. 4439–4444.Google Scholar
30. Muja, M. and Lowe, D. G., “Scalable nearest neighbor algorithms for high dimensional data,” IEEE Trans. Pattern Anal. Mach. Intell. 36, 2227–2240 (2014).Google Scholar
31. Mukadam, M., Yan, X. and Boots, B., “Gaussian Process Motion Planning,” Proceedings of the IEEE International Conference on Robotics and Automation, Stockholm, Sweden (2016) pp. 9–15.Google Scholar
32. Palmieri, L., Koenig, S. and Arras, K. O., “RRT-Based Nonholonomic Motion Planning Using Any-Angle Path Biasing,” Proceedings of the IEEE International Conference on Robotics and Automation, Stockholm, Sweden (2016) pp. 2775–2781.Google Scholar
33. Palmieri, L., Kucner, T., Magnusson, M., Lilienthal, A. and Arras, K., “Kinodynamic Motion Planning on Gaussian Mixture Fields,” Proceedings of the IEEE International Conference on Robotics and Automation, Singapore (2017) pp. 6176–6181.Google Scholar
34. Pendleton, S. D., Liu, W., Andersen, H., Eng, Y. H., Frazzoli, E., Rus, D. and Ang, M. H., “Numerical approach to reachability-guided sampling-based motion planning under differential constraints,” IEEE Robot. Autom. Lett. 2 (3), 1232–1239 (2017).CrossRefGoogle Scholar
35. Plaku, E., “Region-guided and sampling-based tree search for motion planning with dynamics,” IEEE Trans. Robot. 31, 723–735 (2015).CrossRefGoogle Scholar
36. 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
37. Reif, J., “Complexity of the Mover's Problem and Generalizations,” Proceedings of the IEEE Symposium on Foundations of Computer Science, San Juan, Puerto Rico (1979) pp. 421–427.Google Scholar
38. Rosenthal, R., Cooper, H. and Hedges, L., “Parametric Measures of Effect Size,” In: The Handbook of Research Synthesis (Cooper, H. and Hedges, L. V., eds.) (Russell Sage Foundation, New York, 1994) pp. 231–244.Google Scholar
39. Shewchuk, J. R., “Triangle: Engineering a 2d Quality Mesh Generator and Delaunay Triangulator,” In: Applied Computational Geometry: Towards Geometric Engineering, Lecture Notes in Computer Science, (Lin, M. C. and Manocha, D., eds.) vol. 1148 (Springer, Berlin, Heidelbergm, 1996) pp. 203–222. Code available at https://www.cs.cmu.edu/~quake/triangle.htmlCrossRefGoogle Scholar
40. Shewchuk, J. R., “Delaunay refinement algorithms for triangular mesh generation,” Comput. Geom.: Theory Appl. 22 21–74 (2002).Google Scholar
41. Tracy, D. J., Buss, S. R. and Woods, B.M., “Efficient Large-Scale Sweep and Prune Methods with AABB Insertion and Removal,” Proceedings of the IEEE Conference on Virtual Reality, Lafayette, LA (2009) pp. 191–198.Google Scholar
42. Vleugels, J. and Overmars, M., “Approximating generalized Voronoi diagrams in any dimension,” Graph. Models Image Process. (Utrecht University, Utrecht, Netherlands, 1995).Google Scholar
43. Wells, A. and Plaku, E., “Adaptive Sampling-Based Motion Planning for Mobile Robots with Differential Constraints,” In: Towards Autonomous Robotic Systems, Lecture Notes in Computer Science, (Dixon, C. and Tuyls, K., eds.) vol. 9287 (Springer, Cham, 2015) pp. 283–295.Google Scholar
44. Wilmarth, S. A., Amato, N. M. and Stiller, P. F., “MAPRM: A Probabilistic Roadmap Planner with Sampling on the Medial Axis of the Free Space,” Proceedings of the IEEE International Conference on Robotics and Automation, Detroit, MI (1999) pp. 1024–1031.Google Scholar
45. Wilmarth, S. A., Amato, N. M. and Stiller, P. F., “Motion Planning for a Rigid Body Using Random Networks on the Medial Axis of the Free Space,” Proceedings of the Symposium on Computational Geometry, New York, NY (1999) pp. 173–180.Google Scholar
46. Yeh, H. C., Denny, J., Lindsey, A., Thomas, S. L. and Amato, N. M., “UMAPRM: Uniformly Sampling the Medial Axis,” Proceedings of the International Conference on Robotics and Automation, Hong Kong, China (2014) pp. 5798–5803.Google Scholar

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