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Collision Detection

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Abstract

In robotics, a collision or proximity query reports geometric information about the relative configuration or placement of two objects. Some common examples of such queries include checking whether two objects overlap in space, testing if their boundaries intersect, or computing the minimum Euclidean separation distance between their boundaries. Hundreds of papers have been published on different aspects of these queries in robotics and related areas such as computer-aided design and manufacturing, computational geometry, computer graphics, and virtual environments. These queries arise in different robotic applications, including robot motion planning, collision avoidance, grasping, manipulation, control, dynamic simulation, human-robot interaction, haptic rendering, and more. For example, in motion planning for a humanoid robot, it is critical that the planned motion should not result in any collisions between the robot and the surrounding obstacles. At the same time, there should be no self-collisions between different links of the robot (see Fig. 1). The robot’s linkages should not pass through each other, and objects in the environment should move as expected when pushed, pulled, or grasped by the robot. Such actions require fast and accurate collision detection between the geometric representations of both the robot(s) and objects in the scene. Another example is multiple-robot interaction, where the proximity relationships between all possible pairs of robot bodies need to be measured and maintained to realize plausible interaction among the robots. In Fig. 2, the motion of each Nao robot is tracked so as to maintain the safety distance between the two robots to generate physically plausible robotic interactions.

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References

  1. K. Abdel-Malekl, D. Blackmore, K. Joy, Swept volumes: foundations, perspectives, and applications. Int. J. Shape Model. 87–127 (2002)

    Google Scholar 

  2. P. Agarwal, L. Guibas, S. Har-Peled, A. Rabinovitch, M. Sharir, Penetration depth of two convex polytopes in 3D. Nord. J. Comput. 7, 227–240 (2000)

    MathSciNet  MATH  Google Scholar 

  3. P.K. Agarwal, J. Basch, L.J. Guibas, J. Hershberger, L. Zhang, Deformable free space tiling for kinetic collision detection. Int. J. Robot. Res. 21(3), 179–197 (2002)

    Article  MATH  Google Scholar 

  4. D. Baraff, Dynamic simulation of non-penetrating rigid body simulation. PhD thesis, Cornell University, 1992

    Google Scholar 

  5. G. Barequet, B. Chazelle, L. Guibas, J. Mitchell, A. Tal, Boxtree: a hierarchical representation of surfaces in 3D, in Proceedings of Eurographics’96 (1996)

    Google Scholar 

  6. J. Basch, J. Erickson, L. Guibas, J. Hershberger, L. Zhang, Kinetic collision detection between two simple polygons, in Proceedings of the Tenth Annual ACM-SIAM Symposium on Discrete Algorithms, 1999, pp. 102–111

    Google Scholar 

  7. N. Beckmann, H. Kriegel, R. Schneider, B. Seeger, The r*-tree: an efficient and robust access method for points and rectangles, in Proceedings of the SIGMOD Conference on Management of Data, 1990, pp. 322–331

    Google Scholar 

  8. S. Cameron, Collision detection by four-dimensional intersection testing, in Proceedings of International Conference on Robotics and Automation, 1990, pp. 291–302

    Google Scholar 

  9. S. Cameron, Enhancing GJK: computing minimum and penetration distance between convex polyhedra, in IEEE International Conference on Robotics and Automation, 1997, pp. 3112–3117

    Google Scholar 

  10. S. Cameron, R.K. Culley, Determining the minimum translational distance between two convex polyhedra, in Proceedings of International Conference on Robotics and Automation, 1986, pp. 591–596

    Google Scholar 

  11. J.F. Canny, Collision detection for moving polyhedra. IEEE Trans. PAMI 8, 200–209 (1986)

    Article  Google Scholar 

  12. Y.-K. Choi, W. Wang, Y. Liu, M.-S. Kim, Continuous collision detection for elliptic disks. IEEE Trans. Robot. 22(2), 213–224 (2006)

    Article  Google Scholar 

  13. K. Chung, W. Wang, Quick collision detection of polytopes in virtual environments, in Proceedings of ACM Symposium on Virtual Reality Software and Technology (1996)

    Google Scholar 

  14. J. Cohen, M. Lin, D. Manocha, M. Ponamgi, I-COLLIDE: an interactive and exact collision detection system for large-scale environments, in Proceedings of the ACM Interactive 3D Graphics Conference, 1995, pp. 189–196

    Google Scholar 

  15. D. Dobkin, J. Hershberger, D. Kirkpatrick, S. Suri, Computing the intersection-depth of polyhedra. Algorithmica 9, 518–533 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  16. D.P. Dobkin, D.G. Kirkpatrick, Determining the separation of preprocessed polyhedra – a unified approach, in Proceedings of the 17th International Colloquium on Automata, Languages and Programming. Lecture Notes in Computer Science, vol. 443 (Springer, 1990), pp. 400–413

    Google Scholar 

  17. P. Dworkin, D. Zeltzer, A new model for efficient dynamics simulation, in Proceedings Eurographics Workshop on Animation and Simulation, 1993, pp. 175–184

    Google Scholar 

  18. H. Edelsbrunner, A new approach to rectangle intersections, Part I. Int. J. Comput. Math. 13, 209–219 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  19. S. Ehmann, M.C. Lin, Accelerated proximity queries between convex polyhedra using multi-level Voronoi marching, in Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, 2000, pp. 2101–2106

    Google Scholar 

  20. S. Ehmann, M.C. Lin, Accurate and fast proximity queries between polyhedra using convex surface decomposition. Comput. Graphics Forum (Proceedings of Eurographics’2001) 20(3), 500–510 (2001)

    Google Scholar 

  21. J. Erickson, L. Guibas, J. Stolfi, L. Zhang. Separation sensitive collision detection for convex objects, in Proceedings of the SODA, 1999

    Google Scholar 

  22. S. Fisher, M.C. Lin, Deformed distance fields for simulation of non-penetrating flexible bodies, in Proceedings of the EG Workshop on Computer Animation and Simulation, 2001, pp. 99–111

    Google Scholar 

  23. E.G. Gilbert, D.W. Johnson, S.S. Keerthi, A fast procedure for computing the distance between objects in three-dimensional space. IEEE J. Robot. Autom. RA-4, 193–203 (1988)

    Article  Google Scholar 

  24. E.G. Gilbert, C.J. Ong, New distances for the separation and penetration of objects, in Proceedings of International Conference on Robotics and Automation, 1994, pp. 579–586

    Google Scholar 

  25. S. Gottschalk, Collision queries using oriented bounding boxes. PhD thesis, Department of Computer Science, University of North Carolina, 2000

    Google Scholar 

  26. S. Gottschalk, M. Lin, D. Manocha, OBB-Tree: a hierarchical structure for rapid interference detection, in Proceedings of the ACM Siggraph’96, 1996, pp. 171–180

    Google Scholar 

  27. N. Govindaraju, S. Redon, M. Lin, D. Manocha, CULLIDE: interactive collision detection between complex models in large environments using graphics hardware, in Proceedings of the ACM SIGGRAPH/EG Workshop on Graphics Hardware, 2003, pp. 25–32

    Google Scholar 

  28. L. Guibas, D. Hsu, L. Zhang, H-Walk: hierarchical distance computation for moving convex bodies, in Proceedings of the ACM Symposium on Computational Geometry, 1999

    Google Scholar 

  29. M. Held, J. Klosowski, J.S.B. Mitchell, Real-time collision detection for motion simulation within complex environments, in Proceedings of the ACM SIGGRAPH’96 Visual Proceedings, 1996, p. 151

    Google Scholar 

  30. M. Held, J.T. Klosowski, J.S.B. Mitchell, Evaluation of collision detection methods for virtual reality fly-throughs, in Canadian Conference on Computational Geometry, 1995

    Google Scholar 

  31. B.V. Herzen, A.H. Barr, H.R. Zatz, Geometric collisions for time-dependent parametric surfaces. Comput. Graph. 24(4), 39–48 (1990)

    Article  Google Scholar 

  32. K. Hoff, A. Zaferakis, M. Lin, D. Manocha, Fast and simple 2D geometric proximity queries using graphics hardware, in Proceedings of the ACM Symposium on Interactive 3D Graphics, 2001, pp. 145–148

    Google Scholar 

  33. K. Hoff, A. Zaferakis, M. Lin, D. Manocha, Fast 3D geometric proximity queries between rigid and deformable models using graphics hardware acceleration. Technical Report TR02-004, Department of Computer Science, University of North Carolina, 2002

    Google Scholar 

  34. C.M. Hoffmann, Geometric and Solid Modeling (Morgan Kaufmann, San Mateo, 1989)

    Google Scholar 

  35. J.E. Hopcroft, J.T. Schwartz, M. Sharir, Efficient detection of intersections among spheres. Int. J. Robot. Res. 2(4), 77–80 (1983)

    Article  Google Scholar 

  36. H. Six, D. Wood, Counting and reporting intersections of D-ranges. IEEE Trans. Comput. C-31, 46–55 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  37. D. Hsu, L. Kavraki, J. Latombe, R. Motwani, S. Sorkin, On finding narrow passages with probabilistic roadmap planners, in Proceedings of the 3rd Workshop on Algorithmic Foundations of Robotics, 1998, pp. 25–32

    Google Scholar 

  38. P.M. Hubbard, Interactive collision detection, in Proceedings of IEEE Symposium on Research Frontiers in Virtual Reality, 1993

    Google Scholar 

  39. T. Hudson, M. Lin, J. Cohen, S. Gottschalk, D. Manocha, V-COLLIDE: accelerated collision detection for VRML, in Proceedings of the VRML Conference, 1997, pp. 119–125

    Google Scholar 

  40. C. Je, M. Tang, Y. Lee, M. Lee, Y. Kim, PolyDepth: real-time penetration depth computation using iterative contact-space projection. ACM Trans. Graph. 31, 5:1–5:14 (2012)

    Google Scholar 

  41. B. Kim, J. Rossignac, Collision prediction for polyhedra under screw motions, in ACM Conference on Solid Modeling and Applications, 2003

    Google Scholar 

  42. D. Kim, L.J. Guibas, S. Shin, Fast collision detection among multiple moving spheres, in ACM Symposium on Computational Geometry, 1997, pp. 373–375

    Google Scholar 

  43. Y.J. Kim, M.C. Lin, D. Manocha, DEEP: an incremental algorithm for penetration depth computation between convex polytopes, in Proceedings of the IEEE Conference on Robotics and Automation, 2002, pp. 921–926

    Google Scholar 

  44. Y.J. Kim, M.A. Otaduy, M.C. Lin, D. Manocha, 6-DOF haptic display using localized contact computations, in Proceedings of the Haptics Symposium, 2002, pp. 209–216

    Google Scholar 

  45. D. Kirkpatrick, J. Snoeyink, B. Speckman, Kinetic collision detection for simple polygons. Int. J. Comput. Geom. Appl. 12, 3–27 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  46. J. Klosowski, M. Held, J.S.B. Mitchell, H. Sowizral, K. Zikan, Efficient collision detection using bounding volume hierarchies of k-DOPs. IEEE Trans. Vis. Comput. Graph. 4(1), 21–37 (1998)

    Article  Google Scholar 

  47. S. Krishnan, M. Gopi, M. Lin, D. Manocha, A. Pattekar, Rapid and accurate contact determination between spline models using shelltrees. Comput. Graph. Forum, Proc. Eur. 17(3), C315–C326 (1998)

    Google Scholar 

  48. S. Krishnan, A. Pattekar, M. Lin, D. Manocha, Spherical shell: a higher order bounding volume for fast proximity queries, in Proceedings of the Third International Workshop on Algorithmic Foundations of Robotics, 1998, pp. 122–136

    Google Scholar 

  49. E. Larsen, S. Gottschalk, M. Lin, D. Manocha, Fast proximity queries with swept sphere volumes. Technical Report TR99-018, Department of Computer Science, University of North Carolina, 1999

    Google Scholar 

  50. C. Lauterbach, Q. Mo, D. Manocha, gProximity: hierarchical GPU-based operations for collision and distance queries. Comput. Graph. Forum 29(2), 419–428 (2010)

    Article  Google Scholar 

  51. Y. Lee, S. Lengagne, A. Kheddar, Y. Kim, Accurate evaluation of a distance function for optimization-based motion planning, in IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2012

    Google Scholar 

  52. Y. Lee, Y.J. Kim, Simple and parallel proximity algorithms for general polygonal models, in CASA (2010)

    Google Scholar 

  53. M. Lin, S. Gottschalk, Collision detection between geometric models: a survey. in Proceedings of the IMA Conference on Mathematics of Surfaces, 1998

    Google Scholar 

  54. M. C. Lin, Efficient collision detection for animation and robotics. PhD thesis, University of California, Berkeley, 1993

    Google Scholar 

  55. M.C. Lin, J.F. Canny, Efficient algorithms for incremental distance computation, in IEEE Conference on Robotics and Automation, 1991, pp. 1008–1014

    Google Scholar 

  56. F. Liu, T. Harada, Y. Lee, Y.J. Kim, Real-time collision culling of a million bodies on graphics processing units. ACM Trans. Graph. 29(6), 154:1–154:8 (2010)

    Google Scholar 

  57. I. Lotan, F. Schwarzer, D. Halperin, J.-C. Latombe, Efficient maintenance and self-collision testing for kinematic chains, in Symposium on Computational Geometry, 2002

    Google Scholar 

  58. D. Manocha, Algebraic and numeric techniques for modeling and robotics. PhD thesis, Computer Science Division, Department of Electrical Engineering and Computer Science, University of California, Berkeley, 1992

    Google Scholar 

  59. M. McKenna, D. Zeltzer, Dynamic simulation of autonomous legged locomotion, in Computer Graphics (SIGGRAPH ’90 Proceedings), vol. 24, ed. by F. Baskett, 1990, pp. 29–38

    Google Scholar 

  60. B.V. Mirtich, Impulse-based dynamic simulation of rigid body systems. PhD thesis, University of California, Berkeley, 1996

    Google Scholar 

  61. B. Mirtich, V-Clip: fast and robust polyhedral collision detection. ACM Trans. Graph. 17(3), 177–208 (1998)

    Article  Google Scholar 

  62. M. Shamos, D. Hoey, Geometric intersection problems, in Proceedings of the 17th Annual IEEE Symposium on Foundations of Computer Science, 1976, pp. 208–215

    Google Scholar 

  63. G. Nawratil, H. Pottmann, B. Ravani, Generalized penetration depth computation based on kinematical geometry. Comput. Aided Geom. Des. 26, 425–443 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  64. B. Naylor, J. Amanatides, W. Thibault, Merging BSP trees yield polyhedral modeling results, in Proceedings of the ACM SIGGRAPH, 1990, pp. 115–124

    Google Scholar 

  65. M.A. Otaduy, M.C. Lin, Sensation preserving simplification for haptic rendering. ACM Trans. Graph. (Proc. ACM SIGGRAPH) 22, 543–553 (2003)

    Article  Google Scholar 

  66. M.H. Overmars, Point location in fat subdivisions. Inform. Proc. Lett. 44, 261–265 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  67. J. Pan, X. Zhang, D. Manocha, Efficient penetration computation using active learning. ACM Trans. Graph. 32, 1476–1484 (2013)

    Google Scholar 

  68. J. Pan, S. Chitta, D. Manocha, Fcl: a general purpose library for collision and proximity queries, in IEEE International Conference on Robotics and Automation, 2012, pp. 3859–3866

    Google Scholar 

  69. M. Ponamgi, D. Manocha, M. Lin, Incremental algorithms for collision detection between solid models. IEEE Trans. Vis. Comput. Graph. 3(1), 51–67 (1997)

    Article  Google Scholar 

  70. M.J. Pratt, Surface/surface intersection problems, in The Mathematics of Surfaces II, ed. by J.A. Gregory (Claredon Press, Oxford, 1986), pp. 117–142

    Google Scholar 

  71. S. Quinlan, Efficient distance computation between non-convex objects, in Proceedings of International Conference on Robotics and Automation, 1994, pp. 3324–3329

    Google Scholar 

  72. S. Redon, A. Kheddar, S. Coquillart, An algebraic solution to the problem of collision detection for rigid polyhedral objects, in Proceedings of the IEEE Conference on Robotics and Automation, 2000

    Google Scholar 

  73. S. Redon, A. Kheddar, S. Coquillart, Fast continuous collision detection between rigid bodies. Proc. Eur. (Comput. Graph. Forum) 21(3), 279–287 (2002)

    Google Scholar 

  74. S. Redon, Y.J. Kim, M.C. Lin, D. Manocha, Fast continuous collision detection for articulated models, in Proceedings of ACM Symposium on Solid Modeling and Applications, 2004

    Google Scholar 

  75. H. Samet, Foundations of Multidimensional and Metric Data Structures (Morgan Kaufmann Publishers Inc., San Francisco, 2005). ISBN:0123694469

    MATH  Google Scholar 

  76. F. Schwarzer, M. Saha, J.-C. Latombe, Exact collision checking of robot paths, in Workshop on Algorithmic Foundations of Robotics (WAFR), 2002

    Google Scholar 

  77. R. Seidel, Linear programming and convex hulls made easy, in Proceedings of the 6th Annual ACM Conference on Computational Geometry (Berkeley, 1990), pp. 211–215

    Google Scholar 

  78. J. Snyder et al., Interval methods for multi-point collisions between time dependent curved surfaces, in Proceedings of ACM Siggraph, 1993, pp. 321–334

    Google Scholar 

  79. D.E. Stewart, J.C. Trinkle, An implicit time-stepping scheme for rigid body dynamics with inelastic collisions and coulomb friction. Int. J. Numer. Methods Eng. 39, 2673–2691 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  80. M. Tang, Y.J. Kim, Interactive generalized penetration depth computation for rigid and articulated models using object norm. ACM Trans. Graph. 33(1), 1:1–1:15 (2014)

    Google Scholar 

  81. M. Tang, Y.J. Kim, D. Manocha, C2A: controlled conservative advancement for continuous collision detection of polygonal models, in Proceedings of the International Conference on Robotics and Automation, 2009

    Google Scholar 

  82. M. Tang, Y.J. Kim, D. Manocha, Continuous collision detection for non-rigid contact computations using local advancement, in Proceedings of International Conference on Robotics and Automation, 2010

    Google Scholar 

  83. M. Tang, D. Manocha, Y.J. Kim, Hierarchical and controlled advancement for continuous collision detection of rigid and articulated models. IEEE Trans. Vis. Comput. Graph. 20(5), 755–766 (2014)

    Article  Google Scholar 

  84. M. Tang, D. Manocha, J. Lin, R. Tong, Collision-streams: fast GPU-based collision detection for deformable models, in I3D ’11: Proceedings of the 2011 ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games, 2011, pp. 63–70

    Google Scholar 

  85. M. Tang, D. Manocha, R. Tong, MCCD: multi-core collision detection between deformable models using front-based decomposition. Graph. Model. 72(2), 7–23 (2010)

    Article  Google Scholar 

  86. M. Tang, R. Tong, Z. Wang, D. Manocha, Fast and exact continuous collision detection with Bernstein sign classification. ACM Trans. Graph. 33, 186:1–186:8 (2014)

    Google Scholar 

  87. G. van den Bergen, Proximity queries and penetration depth computation on 3D game objects, in Game Developers Conference, 2001

    Google Scholar 

  88. G. van den Bergen, Ray casting against general convex objects with application to continuous collision detection. J. Graph. Tools (2004). http://dtecta.com/papers/jgt04raycast.pdf

    Google Scholar 

  89. Z. Wang, M. Tang, R. Tong, D. Manocha, Tightccd: efficient and robust continuous collision detection using tight error bounds, in Pacific Graphics, 2015

    Google Scholar 

  90. W. Bouma, G. Vanecek, Collision detection and analysis in a physically based simulation, in Proceedings Eurographics Workshop on Animation and Simulation, 1991, pp. 191–203

    Google Scholar 

  91. A. Wilson, E. Larsen, D. Manocha, M.C. Lin, Partitioning and handling massive models for interactive collision detection. Comput. Graph. Forum (Proc. Eur.) 18(3), 319–329 (1999)

    Google Scholar 

  92. L. Zhang, Y. Kim, D. Manocha, A simple path non-existence algorithm using c-obstacle query, in Proceedings of the WAFR, 2006

    Google Scholar 

  93. L. Zhang, Y. Kim, D. Manocha, A fast and practical algorithm for generalized penetration depth computation, in Proceedings of Robotics: Science and Systems, Atlanta, 2007

    Google Scholar 

  94. L. Zhang, Y.J. Kim, D. Manocha, C-DIST: efficient distance computation for rigid and articulated models in configuration space, in ACM Solid and Physical Modeling Conference (SPM07), Beijing, 2007

    Google Scholar 

  95. L. Zhang, Y.J. Kim, G. Varadhan, D. Manocha. Generalized penetration depth computation. Comput. Aided Des. 39(8), 625–638 (2007)

    Article  Google Scholar 

  96. X. Zhang, Y. Kim, k-IOS: intersection of spheres for efficient proximity query, in IEEE International Conference on Robotics and Automation (ICRA), 2012

    Google Scholar 

  97. X. Zhang, M. Lee, Y.J. Kim, Interactive continuous collision detection for non-convex polyhedra. Vis. Comput. 22, 749–760 (2006)

    Article  Google Scholar 

  98. X. Zhang, S. Redon, M. Lee, Y.J. Kim, Continuous collision detection for articulated models using Taylor models and temporal culling. ACM Trans. Graph. (Proc. SIGGRAPH 2007) 26(3), 15 (2007)

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Ewha Womans University, 03760, 52, Ewhayeodae-gil, Seodaemun-gu, Seoul, Korea

    Young J. Kim

  2. Department of Computer Science, University of North Carolina, 27599-3175, 254 Brooks Building, CB#3175, Chapel Hill, NC, USA

    Ming C. Lin & Dinesh Manocha

Authors
  1. Young J. Kim
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  2. Ming C. Lin
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  3. Dinesh Manocha
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Correspondence to Young J. Kim .

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Editors and Affiliations

  1. Intuitive Surgical , Sunnyvale, California, USA

    Ambarish Goswami

  2. Singapore, Singapur, Singapore

    Prahlad Vadakkepat

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Kim, Y.J., Lin, M.C., Manocha, D. (2017). Collision Detection. In: Goswami, A., Vadakkepat, P. (eds) Humanoid Robotics: A Reference. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7194-9_26-1

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