Hostname: page-component-76fb5796d-45l2p Total loading time: 0 Render date: 2024-04-25T17:10:11.469Z Has data issue: false hasContentIssue false
  • English
  • Français

An efficient algorithm for real time collision detection involving a continuum manipulator with multiple uniform-curvature sections

Published online by Cambridge University Press:  15 October 2014

Jinglin Li  and
Jing Xiao
Jinglin Li*
Affiliation:
Department of Computer Science, University of North Carolina at Charlotte, NC 28223USA E-mail: xiao@uncc.edu
Jing Xiao
Affiliation:
Department of Computer Science, University of North Carolina at Charlotte, NC 28223USA E-mail: xiao@uncc.edu
*
*Corresponding author. E-mail: jli41@uncc.edu
Get access Rights & Permissions [Opens in a new window]

Summary

A continuum manipulator, such as a multisection trunk/tentacle robot, performs manipulation tasks by continuously deforming into different concave shapes. While such a robot is promising for manipulating a wide range of objects in less-structured and cluttered environments, it poses a greater challenge to collision detection than conventional, articulated manipulators. Existing collision detection algorithms are built upon intersection checking between convex primitives, such as between two convex polygons or polyhedra, with the assumption that both the manipulator and the objects in the environment are modeled in terms of those primitives, for example, as polygonal meshes. However, to approximate a continuum manipulator with a polygonal mesh requires a fine mesh because of its concavity, and each time the manipulator changes its configuration by deforming its shape, the mesh has to be updated for the new configuration. This makes mesh-based collision detection involving such a robot much more computationally expensive than that involving an articulated manipulator with rigid links.

Hence, we introduce an efficient algorithm for Collision Detection between a Continuum Manipulator (CD-CoM) and its environment based on analytical intersection checking with nonconvex primitives. Our algorithm applies to the exact model of any continuum manipulator consisting of multiple uniform-curvature sections of toroidal and (sometimes) cylindrical shapes as well as more general continuum manipulators whose sections can be approximated by toroidal and cylindrical primitives. Our test results show that using this algorithm is both more accurate and efficient in time and space to detect collisions than approximating a continuum manipulator as a polygonal mesh. Moreover, the CD-CoM algorithm also provides the minimum distance information between the continuum manipulator and objects when there is no collision. Such an efficient algorithm is essential for path/trajectory planning of continuum manipulators in real-time.

Keywords

Biomimetic RobotsMotion PlanningPath PlanningRedundant ManipulatorsSurgical Robots
Type
Articles
Information
Robotica , Volume 34 , Issue 7 , July 2016 , pp. 1566 - 1586
Copyright
Copyright © Cambridge University Press 2014 

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.Robinson, G. and Davies, J. B. C., “Continuum Robots – A State of the Art,” Proceedings CDEN Design Conference (1999) pp. 2849–2854.Google Scholar
2.McMahan, W., Jones, B. A., Walker, I. D., Chitrakaran, V., Seshadri, A. and Dawson, D., “Robotic Manipulators Inspired by Cephalopod Limbs,” Proceedings CDEN Design Conference, Montreal, Canada (Jul. 2004) pp. 1–10.Google Scholar
3.Cieslak, R. and Moreck, A., “Elephant trunk type elastic manipulator a tool for bulk and liquid type materials transportation,” Robotica 17, 11–16 (1999).CrossRefGoogle Scholar
4.Trivedi, D., Rahn, C. D., Kier, W. M. and Walker, I. D., “Soft robotics: biological inspiration, state of the art, and future research,” Appl. Bionics Biomech. 5 (3), 99–117 (2008).CrossRefGoogle Scholar
5.Webster, R. J., Romano, J. M. and Cowan, N. J., “Mechanics of precurved-tube continuum robots,” IEEE Trans. Robot. 25 (1), (2009).CrossRefGoogle Scholar
6.Furusho, J., Katsuragi, T., Kikuchi, T., Suzuki, T., Tanaka, H., Chiba, Y. and Horio, H., “Curved multi-tube systems for fetal blood sampling and treatments of organs like brain and breast,” J. Comput. Assist. Radiol. Surg. 1, 223–226 (2006).Google Scholar
7.Mahvash, M. and Dupont, P., “Stiffness control of surgical continuum manipulators,” IEEE Trans. Robot. 27, 334–345 (2011).CrossRefGoogle ScholarPubMed
8.Simaan, N., Zhang, J., Roland, J. T. and Manolidis, S., “Steerable continuum robot design for cochlear implant surgery,” IEEE International Conference on Robotics and Auto. Workshop on Snakes, Worms and Catheters: Continuum and Serpentine Robots for Minimally Invasive Surgery, Anchorage, Alaska, USA (May 2010) pp. 36–38.Google Scholar
9.Rucker, D. C., Jones, B. A. and Webster, R. J., “A geometrically exact model for externally loaded concentric-tube continuum robots,” IEEE Trans. Robot. 26, 769–780 (2010).CrossRefGoogle ScholarPubMed
10.Latombe, J. C., Robot Motion Planning (Kluwer, Norwell, Massachusetts, USA, 1991).CrossRefGoogle Scholar
11.van den Bergen, G., “Eficient collision detection of complex deformable models using aabb trees,” J. Graph. Tools 2 (4), 1–13 (1998).CrossRefGoogle Scholar
12.Gottschalk, S., Lin, M. C., and Manocha, D., “Obb-Tree: A Hierarchical Structure for Rapid Interference Detection,” Proceedings of ACM SIGGRAPH, New Orleans, Louisiana, USA (Aug. 1996) pp. 171–180.CrossRefGoogle Scholar
13.Lin, M. C. and Gottschalk, S., “Collision Detection Between Geometric Models: A Survey,” Proceedings of IMA Conference on Mathematics of Surfaces, Birmingham, UK (Aug. 1998) pp. 37–56.Google Scholar
14.Jimnez, P., Thomas, F. and Torras, C., “3d collision detection: a survey,” Comput. Graph. 25, 269–285 (2000).CrossRefGoogle Scholar
15.Gilbert, E. G., Johnson, D. W. and Keerthi, S. S., “A fast procedure for computing the distance between complex objects in three-dimensional space,” Robot. Autom. 4, 193–203 (1988).Google Scholar
16.Lin, M. and Canny, J., “Efficient Collision Detection for Animation,” 3rd Eurographics Worshop on Animation and Simulation (1992).Google Scholar
17.Palmer, I. J. and Grimsdale, R. L., “Collision detection for animation using sphere-trees,” Comput. Graph. Forum 14, 105–116 (1995).CrossRefGoogle Scholar
18.Chazelle, B., “Convex partition of polyhedral: a low bound and a worst-case optimal algorithm,” SIAM J. Comput. 13, 488–507 (1988).CrossRefGoogle Scholar
19.O'Rourke, J., Computational Geometry in C, 2nd ed. (Cambridge University Press, Cambridge, UK, 1991).Google Scholar
20.Schweikard, A., “Polynomial time collision detection for manipulator paths specified by joint motions,” IEEE Trans. Robot. Auto. 7, 865–870 (1991).CrossRefGoogle Scholar
21.Schwarzer, F., Saha, M. and Latombe, J., “Adaptive dynamic collision checking for single and multiple articulated robots in complex environments,” IEEE Trans. Robot. 21, 338–353 (2005).CrossRefGoogle Scholar
22.Cameron, S., “Collision detection by four-dimensional intersection testing,” IEEE Trans. Robot. Auto. 6, 291–302 (1990).CrossRefGoogle Scholar
23.Foisy, A. and Hayward, V., “A Safe Swept Volume Method for Collision Detection,” The 6th International Symposium of Robotics Research, Pittsburgh (Oct. 1993) pp. 61–68.Google Scholar
24.Baginski, B., “Efficient dynamic collision detection using expanded geometry models,” IEEE/RSJ International Conference on Intelligent Robots and Systems, Grenoble, France (Sep. 1997) pp. 1714–1719.Google Scholar
25.Vatcha, R. and Xiao, J., “Perceiving Guaranteed Continuously Collision-free Robot Trajectories in an Unknown and Unpredictable Environment,” IEEE/RSJ International Conference on Intelligent Robots and Systems, St. Louis, MO, USA (Oct. 2009) pp. 1433–1438.CrossRefGoogle Scholar
26.Larsson, T. and Akenine-Möller, T., “A Dynamic Bounding Volume Hierarchy for Generalized Collision Detection,” Workshop on Virtual Reality Interaction and Physical Simulation (2005).CrossRefGoogle Scholar
27.Lauterbach, C., Yoon, S. and Manocha, D., “Rt-Deform: Interactive Ray Tracing of Dynamic Scenes Using BVHS,” Proceedings of the 2006 IEEE Symposium on Interactive Ray Tracing, Salt Lake City, USA (Sep. 2006) pp. 39–45.CrossRefGoogle Scholar
28.Zachmann, G. and Weller, R., “Kinetic Bounding Volume Hierarchies for Deforming Objects,” ACM International Conference on Virtual Reality Continuum and its Applications, Hong Kong (Jun. 2006) pp. 189–196.CrossRefGoogle Scholar
29.Volino, P. and Thalmann, N. M., “Efficient self-collision detection on smoothly discretized surface animations using geometrical shape regularity,” Comput. Graphs. Forum (EuroGraphics Proc.) 13, 155–166 (1994).CrossRefGoogle Scholar
30.Tang, M., Curtis, S., Yoon, S. and Manocha, D., “Interactive Continuous Collision Detection Between Deformable Models Using Connectivity-Based Culling,” SPM'08: Proceedings of the 2008 ACM Symposium on Solid and Physical Modeling, New York, NY, USA: ACM (2008) pp. 25–36.Google Scholar
31.Klein, J. and Zachmann, G., “Point cloud collision detection,” Computer Graphics Forum 23 (3), 567–576 (Sep. 2004).CrossRefGoogle Scholar
32.Pan, J., Chitta, S. and Manocha, D., “Probabilistic Collision Detection Between Noisy Point Clouds Using Robust Classification,” International Symposium on Robotics Research (ISRR) (2011).Google Scholar
33.Brown, J., Latombe, J. and Montgomery, K., “Real-time knot-tying simulation,” Vis. Comput. Int. J. Comput. (2004).CrossRefGoogle Scholar
34.Phillips, J., Ladd, A. and Kavraki, L. E., “Simulated knot tying,” IEEE International Conference on Robotics and Automation, Washington, DC, USA (May 2002) pp. 841–846.Google Scholar
35.Wang, F., Burdet, E., Vuillemin, R. and Bleuler, H., “Knot-Tying with Visual and Force Feedback for VR Laparoscopic Training,” Proceedings of IEEE Engineering in Medicine and Biology, Shanghai, China (Sep. 2005) pp. 5778–5781.CrossRefGoogle Scholar
36.Eberly, D., “Distance between line and circle or disk in 3d,” (1999), http://www.geometrictools.com/.Google Scholar
37.Li, J. and Xiao, J., “Exact and Efficient Collision Detection for a Multi-section Continuum Manipulator,” IEEE International Conference on Robotics and Automation, St. Paul, MN, USA (May 2012) pp. 4340–4346.CrossRefGoogle Scholar
38.Jones, B. A. and Walker, I. D., “Kinematics for multisection continuum robots,” IEEE Trans. Robot. 22, 43–55 (2006).CrossRefGoogle Scholar
39.Turk, G. and Levoy, M., “Zippered polygon meshes from range images,” SIGGRAPH (1994) pp. 311–318.Google Scholar
40.CGAL, “Cgal, Computational Geometry Algorithms Library,” 2013, http://www.cgal.org.Google Scholar
41.Eberly, D., “Distance between two line segments in 3d,” 1999, http://www.geometrictools.com/.Google Scholar
42.Abramowitz, M. and Stegun, I. A., “Solutions of Quartic Equations,” In: Hand-book of Mathematical Functions with Formulas, Graphs and Mathematical Tables, (Dover, Mineola, New York, USA, 1972) pp. 17–18.Google Scholar
43.Jones, M. W., “3d distance from a point to a triangle,” Technical Report CSR-5-95, Department of Computer Science, University of Wales Swansea (1995).Google Scholar
44.Terdiman, P., “Opcode: Optimized collision detection,” 2003, www.codercorner.com/OPCODE.htm.Google Scholar
45.van den Bergen, G., “A fast and robust gjk implementation for collision detection of convex objects,” J. Graph. Tools 4 (2)7–25 (1999).CrossRefGoogle Scholar
46.Lewis, H. and Papadimitriou, C., Elements of the Theory of Computation, (Prentice-Hall, New Jersey, USA, 1981).Google Scholar
47.Li, J. and Xiao, J., “Progressive, continuum grasping in cluttered space,” IEEE/RSJ International Conference on Intelligent Robots and Systems, Tokyo (Nov. 2013) pp. 4563–4568.Google Scholar
48.Li, J. and Xiao, J., “Task-Constrained Continuum Manipulation in Cluttered Space,” IEEE International Conference on Robotics and Automation, Hong Kong (May 2014) pp. 2183–2188.CrossRefGoogle Scholar
49.Vannoy, J. and Xiao, J., “Real-time adaptive motion planning (RAMP) of mobile manipulators in dynamic environments with unforeseen changes,” IEEE Trans. Robot. 24 1199–1212 (2008).CrossRefGoogle Scholar
50.Laplante, P. and Ovaska, S., Real-Time Systems Design and Analysis: Tools for the Practitioner, 4th ed. (IEEE Press, Wiley, Hoboken, NJ, USA, 2011).CrossRefGoogle Scholar