Parallel Collision Detection in Constant Time

We prove that the maximum number of intersecting pairs spheres between two sets of polydisperse sphere packings is linear in the worst case. This observation is the basis for a new collision detection algorithm. Our new approach guarantees a linear worst case running time for arbitrary 3D objects. Additionally, we present a parallelization of our new algorithm that runs in constant time, even in the worst case. Consequently, it is perfectly suited for all time-critical environments that allow only a fixed time budget for finding collision. Our implementation using CUDA shows collision detection at haptic rates for complex objects.

[1]  Gabriel Zachmann,et al.  ProtoSphere: a GPU-assisted prototype guided sphere packing algorithm for arbitrary objects , 2010, SIGGRAPH ASIA.

[2]  George Vanĕček,et al.  Collision Detection and Analysis in a Physically Based Simulation , 1991 .

[3]  Turner Whitted,et al.  Designing a PC Game Engine , 1998, IEEE Computer Graphics and Applications.

[4]  Elmar Schömer,et al.  Subquadratic algorithms for the general collision detection problem , 1995 .

[5]  Sean Quinlan,et al.  Efficient distance computation between non-convex objects , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[6]  Chong-Won Lee,et al.  A collision detection method for real time assembly simulation , 1995, Proceedings. IEEE International Symposium on Assembly and Task Planning.

[7]  Gershon Elber,et al.  Precise global collision detection in multi-axis NC-machining , 2005, Comput. Aided Des..

[8]  Reinhard Klein,et al.  GPU‐based Collision Detection for Deformable Parameterized Surfaces , 2006, Comput. Graph. Forum.

[9]  David G. Kirkpatrick,et al.  A Linear Algorithm for Determining the Separation of Convex Polyhedra , 1985, J. Algorithms.

[10]  Dinesh K. Pai,et al.  CInDeR: Collision and Interference Detection in Real-time using graphics hardware , 2003, Graphics Interface.

[11]  Subhash Suri,et al.  Collision detection in aspect and scale bounded polyhedra , 1998, SODA '98.

[12]  Gabriel Zachmann,et al.  Rapid collision detection by dynamically aligned DOP-trees , 1998, Proceedings. IEEE 1998 Virtual Reality Annual International Symposium (Cat. No.98CB36180).

[13]  Philip M. Hubbard,et al.  Approximating polyhedra with spheres for time-critical collision detection , 1996, TOGS.

[14]  F. Faure,et al.  Volume contact constraints at arbitrary resolution , 2010, ACM Trans. Graph..

[15]  M. Levas.  OBBTree : A Hierarchical Structure for Rapid Interference Detection , .

[16]  Elmar Schömer,et al.  Efficient collision detection for moving polyhedra , 1995, SCG '95.

[17]  Joseph S. B. Mitchell,et al.  Efficient Collision Detection Using Bounding Volume Hierarchies of k-DOPs , 1998, IEEE Trans. Vis. Comput. Graph..

[18]  Anthony Prior,et al.  The use of a proximity agent in a collaborative virtual environment with 6 degrees-of-freedom voxel-based haptic rendering , 2005, First Joint Eurohaptics Conference and Symposium on Haptic Interfaces for Virtual Environment and Teleoperator Systems. World Haptics Conference.

[19]  Dinesh Manocha,et al.  gProximity: Hierarchical GPU‐based Operations for Collision and Distance Queries , 2010, Comput. Graph. Forum.

[20]  James J. Troy,et al.  Six degree-of-freedom haptic rendering using voxel sampling , 1999, SIGGRAPH.

[21]  Greg Turk,et al.  Interactive Collision Detection for Molecular Graphics , 1990 .

[22]  Dinesh Manocha,et al.  GPU-based parallel collision detection for fast motion planning , 2012, Int. J. Robotics Res..

[23]  Ming C. Lin,et al.  Accurate and Fast Proximity Queries Between Polyhedra Using Convex Surface Decomposition , 2001, Comput. Graph. Forum.

[24]  Markus H. Gross,et al.  Detection of Collisions and Self-collisions Using Image-space Techniques , 2004, WSCG.

[25]  Blake Hannaford,et al.  Stable haptic interaction with virtual environments , 1999, IEEE Trans. Robotics Autom..

[26]  Baba C. Vemuri,et al.  Fast Collision Detection Algorithms with Applications to Particle Flow , 1998, Comput. Graph. Forum.

[27]  Ming C. Lin,et al.  Fast penetration depth estimation for elastic bodies using deformed distance fields , 2001, Proceedings 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems. Expanding the Societal Role of Robotics in the the Next Millennium (Cat. No.01CH37180).

[28]  Pietro BelottiLeo Liberti.  The Kissing Number Problem , 2007 .

[29]  Dinesh Manocha,et al.  Incremental algorithms for collision detection between solid models , 1995, Symposium on Solid Modeling and Applications.

[30]  Gabriel Zachmann,et al.  A model for the expected running time of collision detection using AABBs trees , 2006, EGVE'06.

[31]  Stefano Caselli,et al.  Exploiting Advanced Collision Detection Libraries in a Probabilistic Motion Planner , 2002, WSCG.

[32]  Gino van den Bergen.  Efficient Collision Detection of Complex Deformable Models using AABB Trees , 1997, J. Graphics, GPU, & Game Tools.

[33]  Boeing Phantom,et al.  Voxel-Based 6-DOF Haptic Rendering Improvements , 2006 .

[34]  Lixu Gu,et al.  Hierarchical Spatial Hashing for Real-time Collision Detection , 2007, IEEE International Conference on Shape Modeling and Applications 2007 (SMI '07).

[35]  Steven M. LaValle,et al.  Planning algorithms , 2006 .

[36]  Gabriel Zachmann,et al.  Collision Detection Based on Fuzzy Scene Subdivision , 2015 .

[37]  C. Preusche,et al.  A benchmarking suite for 6-DOF real time collision response algorithms , 2010, VRST '10.

[38]  Gabriel Zachmann,et al.  Minimal hierarchical collision detection , 2002, VRST '02.

[39]  Debasish Ghose,et al.  Obstacle avoidance in a dynamic environment: a collision cone approach , 1998, IEEE Trans. Syst. Man Cybern. Part A.

[40]  Xinyu Zhang,et al.  Interactive Collision Detection for Deformable Models Using Streaming AABBs , 2007, IEEE Transactions on Visualization and Computer Graphics.

[41]  Ming C. Lin,et al.  CLODs: Dual Hierarchies for Multiresolution Collision Detection , 2003, Symposium on Geometry Processing.

[42]  Gershon Elber,et al.  Efficient continuous collision detection for bounding boxes under rational motion , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[43]  Jérémie Allard,et al.  Image-based collision detection and response between arbitrary volume objects , 2008, SCA '08.

[44]  Gabriel Zachmann,et al.  Inner sphere trees for proximity and penetration queries , 2009, Robotics: Science and Systems.

[45]  Andreas Kolb,et al.  Hardware-based simulation and collision detection for large particle systems , 2004, Graphics Hardware.

[46]  E. Rosado,et al.  ABSTRACT , 1990 .

[47]  Eigil Samset,et al.  High Performance GPU‐based Proximity Queries using Distance Fields , 2008, Comput. Graph. Forum.

[48]  James J. Troy,et al.  Advances in voxel-based 6-DOF haptic rendering , 2005, SIGGRAPH Courses.

[49]  Dinesh Manocha,et al.  Interactive collision detection between deformable models using chromatic decomposition , 2005, SIGGRAPH 2005.

[50]  Masayuki Inaba,et al.  Self-collision detection and prevention for humanoid robots , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[51]  Ming C. Lin,et al.  Interactive collision detection between deformable models using chromatic decomposition , 2005, ACM Trans. Graph..

[52]  René Weller.  A Benchmarking Suite for Static Collision Detection Algorithms , 2007 .

[53]  van den BergenGino.  Efficient collision detection of complex deformable models using AABB trees , 1998 .