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Collision Detection

  • Young J. Kim
  • Ming C. Lin
  • Dinesh Manocha
Reference work entry

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.

References

  1. 1.
    K. Abdel-Malekl, D. Blackmore, K. Joy, Swept volumes: foundations, perspectives, and applications. Int. J. Shape Model. 87–127 (2002)CrossRefGoogle Scholar
  2. 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)Google Scholar
  3. 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)CrossRefGoogle Scholar
  4. 4.
    D. Baraff, Dynamic simulation of non-penetrating rigid body simulation. PhD thesis, Cornell University, 1992Google Scholar
  5. 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. 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. 102–111Google Scholar
  7. 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. 322–331CrossRefGoogle Scholar
  8. 8.
    S. Cameron, Collision detection by four-dimensional intersection testing, in Proceedings of International Conference on Robotics and Automation, 1990, pp. 291–302CrossRefGoogle Scholar
  9. 9.
    S. Cameron, Enhancing GJK: computing minimum and penetration distance between convex polyhedra, in IEEE International Conference on Robotics and Automation, 1997, pp. 3112–3117Google Scholar
  10. 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. 591–596Google Scholar
  11. 11.
    J.F. Canny, Collision detection for moving polyhedra. IEEE Trans. PAMI 8, 200–209 (1986)CrossRefGoogle Scholar
  12. 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)CrossRefGoogle Scholar
  13. 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. 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. 189–196Google Scholar
  15. 15.
    D. Dobkin, J. Hershberger, D. Kirkpatrick, S. Suri, Computing the intersection-depth of polyhedra. Algorithmica 9, 518–533 (1993)MathSciNetCrossRefGoogle Scholar
  16. 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. 400–413Google Scholar
  17. 17.
    P. Dworkin, D. Zeltzer, A new model for efficient dynamics simulation, in Proceedings Eurographics Workshop on Animation and Simulation, 1993, pp. 175–184Google Scholar
  18. 18.
    H. Edelsbrunner, A new approach to rectangle intersections, Part I. Int. J. Comput. Math. 13, 209–219 (1983)CrossRefGoogle Scholar
  19. 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. 2101–2106Google Scholar
  20. 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)CrossRefGoogle Scholar
  21. 21.
    J. Erickson, L. Guibas, J. Stolfi, L. Zhang. Separation sensitive collision detection for convex objects, in Proceedings of the SODA, 1999Google Scholar
  22. 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. 99–111Google Scholar
  23. 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)Google Scholar
  24. 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. 579–586Google Scholar
  25. 25.
    S. Gottschalk, Collision queries using oriented bounding boxes. PhD thesis, Department of Computer Science, University of North Carolina, 2000Google Scholar
  26. 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. 171–180Google Scholar
  27. 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. 25–32Google Scholar
  28. 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, 1999Google Scholar
  29. 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. 151Google Scholar
  30. 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, 1995Google Scholar
  31. 31.
    B.V. Herzen, A.H. Barr, H.R. Zatz, Geometric collisions for time-dependent parametric surfaces. Comput. Graph. 24(4), 39–48 (1990)Google Scholar
  32. 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. 145–148Google Scholar
  33. 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, 2002Google Scholar
  34. 34.
    C.M. Hoffmann, Geometric and Solid Modeling (Morgan Kaufmann, San Mateo, 1989)Google Scholar
  35. 35.
    J.E. Hopcroft, J.T. Schwartz, M. Sharir, Efficient detection of intersections among spheres. Int. J. Robot. Res. 2(4), 77–80 (1983)CrossRefGoogle Scholar
  36. 36.
    H. Six, D. Wood, Counting and reporting intersections of D-ranges. IEEE Trans. Comput. C-31, 46–55 (1982)Google Scholar
  37. 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. 25–32Google Scholar
  38. 38.
    P.M. Hubbard, Interactive collision detection, in Proceedings of IEEE Symposium on Research Frontiers in Virtual Reality, 1993Google Scholar
  39. 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. 119–125Google Scholar
  40. 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)CrossRefGoogle Scholar
  41. 41.
    B. Kim, J. Rossignac, Collision prediction for polyhedra under screw motions, in ACM Conference on Solid Modeling and Applications, 2003Google Scholar
  42. 42.
    D. Kim, L.J. Guibas, S. Shin, Fast collision detection among multiple moving spheres, in ACM Symposium on Computational Geometry, 1997, pp. 373–375Google Scholar
  43. 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. 921–926Google Scholar
  44. 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. 209–216Google Scholar
  45. 45.
    D. Kirkpatrick, J. Snoeyink, B. Speckman, Kinetic collision detection for simple polygons. Int. J. Comput. Geom. Appl. 12, 3–27 (2002)MathSciNetCrossRefGoogle Scholar
  46. 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)CrossRefGoogle Scholar
  47. 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)CrossRefGoogle Scholar
  48. 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. 122–136Google Scholar
  49. 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, 1999Google Scholar
  50. 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)CrossRefGoogle Scholar
  51. 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), 2012Google Scholar
  52. 52.
    Y. Lee, Y.J. Kim, Simple and parallel proximity algorithms for general polygonal models, in CASA (2010)Google Scholar
  53. 53.
    M. Lin, S. Gottschalk, Collision detection between geometric models: a survey. in Proceedings of the IMA Conference on Mathematics of Surfaces, 1998Google Scholar
  54. 54.
    M. C. Lin, Efficient collision detection for animation and robotics. PhD thesis, University of California, Berkeley, 1993Google Scholar
  55. 55.
    M.C. Lin, J.F. Canny, Efficient algorithms for incremental distance computation, in IEEE Conference on Robotics and Automation, 1991, pp. 1008–1014Google Scholar
  56. 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)CrossRefGoogle Scholar
  57. 57.
    I. Lotan, F. Schwarzer, D. Halperin, J.-C. Latombe, Efficient maintenance and self-collision testing for kinematic chains, in Symposium on Computational Geometry, 2002Google Scholar
  58. 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, 1992Google Scholar
  59. 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. 29–38Google Scholar
  60. 60.
    B.V. Mirtich, Impulse-based dynamic simulation of rigid body systems. PhD thesis, University of California, Berkeley, 1996Google Scholar
  61. 61.
    B. Mirtich, V-Clip: fast and robust polyhedral collision detection. ACM Trans. Graph. 17(3), 177–208 (1998)CrossRefGoogle Scholar
  62. 62.
    M. Shamos, D. Hoey, Geometric intersection problems, in Proceedings of the 17th Annual IEEE Symposium on Foundations of Computer Science, 1976, pp. 208–215Google Scholar
  63. 63.
    G. Nawratil, H. Pottmann, B. Ravani, Generalized penetration depth computation based on kinematical geometry. Comput. Aided Geom. Des. 26, 425–443 (2009)MathSciNetCrossRefGoogle Scholar
  64. 64.
    B. Naylor, J. Amanatides, W. Thibault, Merging BSP trees yield polyhedral modeling results, in Proceedings of the ACM SIGGRAPH, 1990, pp. 115–124Google Scholar
  65. 65.
    M.A. Otaduy, M.C. Lin, Sensation preserving simplification for haptic rendering. ACM Trans. Graph. (Proc. ACM SIGGRAPH) 22, 543–553 (2003)CrossRefGoogle Scholar
  66. 66.
    M.H. Overmars, Point location in fat subdivisions. Inform. Proc. Lett. 44, 261–265 (1992)MathSciNetCrossRefGoogle Scholar
  67. 67.
    J. Pan, X. Zhang, D. Manocha, Efficient penetration computation using active learning. ACM Trans. Graph. 32, 1476–1484 (2013)Google Scholar
  68. 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. 3859–3866Google Scholar
  69. 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)Google Scholar
  70. 70.
    M.J. Pratt, Surface/surface intersection problems, in The Mathematics of Surfaces II, ed. by J.A. Gregory (Claredon Press, Oxford, 1986), pp. 117–142Google Scholar
  71. 71.
    S. Quinlan, Efficient distance computation between non-convex objects, in Proceedings of International Conference on Robotics and Automation, 1994, pp. 3324–3329Google Scholar
  72. 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, 2000Google Scholar
  73. 73.
    S. Redon, A. Kheddar, S. Coquillart, Fast continuous collision detection between rigid bodies. Proc. Eur. (Comput. Graph. Forum) 21(3), 279–287 (2002)CrossRefGoogle Scholar
  74. 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, 2004Google Scholar
  75. 75.
    H. Samet, Foundations of Multidimensional and Metric Data Structures (Morgan Kaufmann Publishers Inc., San Francisco, 2005). ISBN:0123694469Google Scholar
  76. 76.
    F. Schwarzer, M. Saha, J.-C. Latombe, Exact collision checking of robot paths, in Workshop on Algorithmic Foundations of Robotics (WAFR), 2002Google Scholar
  77. 77.
    R. Seidel, Linear programming and convex hulls made easy, in Proceedings of the 6th Annual ACM Conference on Computational Geometry (Berkeley, 1990), pp. 211–215Google Scholar
  78. 78.
    J. Snyder et al., Interval methods for multi-point collisions between time dependent curved surfaces, in Proceedings of ACM Siggraph, 1993, pp. 321–334Google Scholar
  79. 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)MathSciNetCrossRefGoogle Scholar
  80. 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)CrossRefGoogle Scholar
  81. 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, 2009Google Scholar
  82. 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, 2010Google Scholar
  83. 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)CrossRefGoogle Scholar
  84. 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. 63–70Google Scholar
  85. 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)CrossRefGoogle Scholar
  86. 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. 87.
    G. van den Bergen, Proximity queries and penetration depth computation on 3D game objects, in Game Developers Conference, 2001Google Scholar
  88. 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
  89. 89.
    Z. Wang, M. Tang, R. Tong, D. Manocha, Tightccd: efficient and robust continuous collision detection using tight error bounds, in Pacific Graphics, 2015CrossRefGoogle Scholar
  90. 90.
    W. Bouma, G. Vanecek, Collision detection and analysis in a physically based simulation, in Proceedings Eurographics Workshop on Animation and Simulation, 1991, pp. 191–203Google Scholar
  91. 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)CrossRefGoogle Scholar
  92. 92.
    L. Zhang, Y. Kim, D. Manocha, A simple path non-existence algorithm using c-obstacle query, in Proceedings of the WAFR, 2006Google Scholar
  93. 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, 2007Google Scholar
  94. 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, 2007Google Scholar
  95. 95.
    L. Zhang, Y.J. Kim, G. Varadhan, D. Manocha. Generalized penetration depth computation. Comput. Aided Des. 39(8), 625–638 (2007)CrossRefGoogle Scholar
  96. 96.
    X. Zhang, Y. Kim, k-IOS: intersection of spheres for efficient proximity query, in IEEE International Conference on Robotics and Automation (ICRA), 2012Google Scholar
  97. 97.
    X. Zhang, M. Lee, Y.J. Kim, Interactive continuous collision detection for non-convex polyhedra. Vis. Comput. 22, 749–760 (2006)CrossRefGoogle Scholar
  98. 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)CrossRefGoogle Scholar

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringEwha Womans UniversitySeoulSouth Korea
  2. 2.Department of Computer ScienceUniversity of North CarolinaChapel HillUSA

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