Skip to main content
×
×
Home

Clearance-driven motion planning for mobile robots with differential constraints

  • Evis Plaku (a1), Erion Plaku (a1) and Patricio Simari (a1)
Summary

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.

Copyright
Corresponding author
*Corresponding author. E-mail: plaku@cua.edu
References
Hide All
1. Amenta, N., Choi, S. and Kolluri, R. K., “The power crust, unions of balls, and the medial axis transform,” Comput. Geom. 19 127153 (2001).
2. de Berg, M., Cheong, O., van Kreveld, M. and Overmars, M. H., Computational Geometry: Algorithms and Applications (Springer-Verlag, Santa Clara, CA, 2008).
3. Branicky, M. S., “Universal computation and other capabilities of continuous and hybrid systems,” Theor. Comput. Sci. 138 (1), 67100 (1995).
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.
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.
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).
7. Cohen, J., “A power primer,” Psychol. Bull. 112 (1), 155 (1992).
8. Şucan, I. A. and Kavraki, L.E., “A sampling-based tree planner for systems with complex dynamics,” IEEE Trans. Robot. 28, 116131 (2012).
9. Şucan, I. A., Moll, M. and Kavraki, L. E., “The open motion planning library,” IEEE Robot. Autom. Mag. 19 (4), 7282 (2012). Available at: http://ompl.kavrakilab.org
10. Culver, T., Keyser, J. and Manocha, D., “Exact computation of the medial axis of a polyhedron,” Comput. Aided Geom. Des. 21 (1), 6598 (2004).
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.
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.
13. Dey, T. K. and Zhao, W., “Approximating the medial axis from the voronoi diagram with a convergence guarantee,” Algorithmica 38 (1), 179200 (2003)
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.
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.
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).
17. Hauer, F. and Tsiotras, P., “Deformable Rapidly-Exploring Random Trees,” Proceedings of the Robotics: Science and Systems Conference, Boston, MA (2017) p. P08.
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.
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.
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.
21. Kallmann, M., “Dynamic and robust local clearance triangulations,” ACM Trans. Graph. 33 (5), 161:1161:17 (2014).
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.
23. Kirkpatrick, D. G., “Optimal search in planar subdivisions,” SIAM J. Comput. 12 (1), 2835 (1983).
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.
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).
26. LaValle, S. M., Planning Algorithms (Cambridge University Press, Cambridge, MA, 2006).
27. LaValle, S. M., “Motion planning: The essentials,” IEEE Robot. Autom. Mag. 18 (1), 7989 (2011).
28. LaValle, S. M. and Kuffner, J. J., “Randomized kinodynamic planning,” Int. J. Robot. Res. 20 (5), 378400 (2001).
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.
30. Muja, M. and Lowe, D. G., “Scalable nearest neighbor algorithms for high dimensional data,” IEEE Trans. Pattern Anal. Mach. Intell. 36, 22272240 (2014).
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.
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.
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.
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), 12321239 (2017).
35. Plaku, E., “Region-guided and sampling-based tree search for motion planning with dynamics,” IEEE Trans. Robot. 31, 723735 (2015).
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), 469482 (2010).
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.
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. 231244.
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. 203222. Code available at https://www.cs.cmu.edu/~quake/triangle.html
40. Shewchuk, J. R., “Delaunay refinement algorithms for triangular mesh generation,” Comput. Geom.: Theory Appl. 22 2174 (2002).
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.
42. Vleugels, J. and Overmars, M., “Approximating generalized Voronoi diagrams in any dimension,” Graph. Models Image Process. (Utrecht University, Utrecht, Netherlands, 1995).
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. 283295.
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.
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.
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.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Robotica
  • ISSN: 0263-5747
  • EISSN: 1469-8668
  • URL: /core/journals/robotica
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords

Type Description Title
VIDEO
Supplementary materials

Plaku et al. supplementary material 4
Supplementary Movie

 Video (61.5 MB)
61.5 MB
VIDEO
Supplementary materials

Plaku et al. supplementary material 1
Supplementary Movie

 Video (87.6 MB)
87.6 MB
UNKNOWN
Supplementary materials

Plaku et al. supplementary material 5
Plaku et al. supplementary material

 Unknown (539 bytes)
539 bytes
VIDEO
Supplementary materials

Plaku et al. supplementary material 2
Supplementary Movie

 Video (71.1 MB)
71.1 MB
VIDEO
Supplementary materials

Plaku et al. supplementary material 3
Supplementary Movie

 Video (55.2 MB)
55.2 MB

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 61 *
Loading metrics...

Abstract views

Total abstract views: 244 *
Loading metrics...

* Views captured on Cambridge Core between 27th February 2018 - 16th August 2018. This data will be updated every 24 hours.