A unified treatment of elastostatic contact simulation for real time haptics

We describe real-time, physically-based simulation algorithms for haptic interaction with elastic objects. Simulation of contact with elastic objects has been a challenge, due to the complexity of physically accurate simulation and the difficulty of constructing useful approximations suitable for real time interaction. We show that this challenge can be effectively solved for many applications. In particular global deformation of linear elastostatic objects can be efficiently solved with low run-time computational costs, using precomputed Green's functions and fast low-rank updates based on Capacitance Matrix Algorithms. The capacitance matrices constitute exact force response models, allowing contact forces to be computed much faster than global deformation behavior. Vertex pressure masks are introduced to support the convenient abstraction of localized scale-specific point-like contact with an elastic and/or rigid surface approximated by a polyhedral mesh. Finally, we present several examples using the CyberGlove™ and PHANToM™ haptic interfaces.

[1]  J. Z. Zhu,et al.  The finite element method , 1977 .

[2]  Gene H. Golub,et al.  Matrix computations , 1983 .

[3]  S. Mukherjee,et al.  Boundary element techniques: Theory and applications in engineering , 1984 .

[4]  F. Hartmann.  The Mathematical Foundation of Structural Mechanics , 1985 .

[5]  Charles T. Loop,et al.  Smooth Subdivision Surfaces Based on Triangles , 1987 .

[6]  Barry Hilary Valentine Topping,et al.  Static Reanalysis: A Review , 1987 .

[7]  W. Press,et al.  Numerical Recipes: The Art of Scientific Computing , 1987 .

[8]  William W. Hager,et al.  Updating the Inverse of a Matrix , 1989, SIAM Rev..

[9]  William H. Press,et al.  Numerical recipes , 1990 .

[10]  Thomas H. Massie,et al.  The PHANToM Haptic Interface: A Device for Probing Virtual Objects , 1994 .

[11]  John Kenneth Salisbury,et al.  A constraint-based god-object method for haptic display , 1995, Proceedings 1995 IEEE/RSJ International Conference on Intelligent Robots and Systems. Human Robot Interaction and Cooperative Robots.

[12]  Morten Bro-Nielsen,et al.  Surgery Simulation Using fast Finite Elements , 1996, VBC.

[13]  Mandayam A. Srinivasan,et al.  Force Shading for Haptic Shape Perception , 1996, Dynamic Systems and Control.

[14]  Morten Bro-Nielsen,et al.  Real‐time Volumetric Deformable Models for Surgery Simulation using Finite Elements and Condensation , 1996, Comput. Graph. Forum.

[15]  Brian Mirtich,et al.  A Survey of Deformable Modeling in Computer Graphics , 1997 .

[16]  W. Eric L. Grimson,et al.  Volumetric object modeling for surgical simulation , 1998, Medical Image Anal..

[17]  Vincent Hayward,et al.  Multirate haptic simulation achieved by coupling finite element meshes through Norton equivalents , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[18]  Ole Vilhelm Larsen,et al.  Using Region-of-Interest Based Finite Element Modeling for Brain-Surgery Simulation , 1998, MICCAI.

[19]  H Delingette,et al.  Efficient linear elastic models of soft tissues for real-time surgery simulation. , 1999, Studies in health technology and informatics.

[20]  U. Kühnapfel,et al.  3D Modeling for Endoscopic Surgery , 1999 .

[21]  Cagatay Basdogan,et al.  Efficient Point-Based Rendering Techniques for Haptic Display of Virtual Objects , 1999, Presence.

[22]  Dinesh K. Pai,et al.  ArtDefo: accurate real time deformable objects , 1999, SIGGRAPH.

[23]  Mathieu Desbrun,et al.  Interactive multiresolution animation of deformable models , 1999, Computer Animation and Simulation.

[24]  Herve Delingette,et al.  Real-Time Elastic Deformations of Soft Tissues for Surgery Simulation , 1999, IEEE Trans. Vis. Comput. Graph..

[25]  Christian Laugier,et al.  A haptic interface for a virtual exam of the human thigh , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[26]  H. Ehlers.  LECTURERS , 1948, Statistics for Astrophysics.

[27]  Frank Tendick,et al.  Multirate simulation for high fidelity haptic interaction with deformable objects in virtual environments , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[28]  John F. Canny,et al.  Haptic interaction with global deformations , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[29]  Hervé Delingette,et al.  Anisotropic elasticity and force extrapolation to improve realism of surgery simulation , 2000, Proceedings 2000 ICRA. Millennium Conference. IEEE International Conference on Robotics and Automation. Symposia Proceedings (Cat. No.00CH37065).

[30]  Dimitris N. Metaxas,et al.  Dynamic deformable models for enhanced haptic rendering in virtual environments , 2000, Proceedings IEEE Virtual Reality 2000 (Cat. No.00CB37048).

[31]  Doug L. James,et al.  Scanning physical interaction behavior of 3D objects , 2001, SIGGRAPH Courses.