This Article 
 Bibliographic References 
 Add to: 
Realistic Haptic Rendering of Interacting Deformable Objects in Virtual Environments
January/February 2006 (vol. 12 no. 1)
pp. 36-47

Abstract—A new computer haptics algorithm to be used in general interactive manipulations of deformable virtual objects is presented. In multimodal interactive simulations, haptic feedback computation often comes from contact forces. Subsequently, the fidelity of haptic rendering depends significantly on contact space modeling. Contact and friction laws between deformable models are often simplified in up to date methods. They do not allow a "realistic” rendering of the subtleties of contact space physical phenomena (such as slip and stick effects due to friction or mechanical coupling between contacts). In this paper, we use Signorini's contact law and Coulomb's friction law as a computer haptics basis. Real-time performance is made possible thanks to a linearization of the behavior in the contact space, formulated as the so-called Delassus operator, and iteratively solved by a Gauss-Seidel type algorithm. Dynamic deformation uses corotational global formulation to obtain the Delassus operator in which the mass and stiffness ratio are dissociated from the simulation time step. This last point is crucial to keep stable haptic feedback. This global approach has been packaged, implemented, and tested. Stable and realistic 6D haptic feedback is demonstrated through a clipping task experiment.

[1] G. Burdea, Force and Touch Feedback for Virtual Reality. New York: John Wiley and Sons, Aug. 1996.
[2] D. James and D.K. Pai, “Pressure Masks for Point-Like Contact with Elastic Models,” Proc. Fifth Phantom User Group Workshop, 2000.
[3] M. Mahvash and V. Hayward, “High-Fidelity Haptic Synthesis of Contact with Deformable Bodies,” IEEE Computer Graphics and Applications, pp. 48-55, Mar. 2004.
[4] A. Gomes de Sa and G. Zachmann, “Virtual Reality as a Tool for Verification of Assembly and Maintenance Processes,” Computers and Graphics, vol. 23, no. 3, pp. 389-403, 1999.
[5] H. Delingette, A. Linney, N. Magnenat-Thalmann, Y. Wu, D. Bartz, M. Hauth, and K. Muller, “Advanced Virtual Medicine: Techniques and Applications for Medicine Oriented Computer Graphics,” Proc. Eurographics 2004, 2004.
[6] Y. Zhuang and J. Canny, “Real-Time Simulation of Physically Realistic Global Deformation,” Proc. IEEE Visualization Conf., 1999.
[7] G. Picinbono, H. Delingette, and N. Ayache, “Non-Linear Anisotropic Elasticity for Real-Time Surgery Simulation,” Graphical Models, vol. 65, no. 5, pp. 305-321, Sept. 2003.
[8] G. Irving, J. Teran, and R. Fedkiw, “Invertible Finite Elements for Robust Simulation of Large Deformation,” Proc. Eurographics/ACM SIGGRAPH Symp. Computer Animation, pp. 131-140, 2004.
[9] C. Duriez, C. Andriot, and A. Kheddar, “A Multi-Threaded Approach for Deformable/Rigid Contacts with Haptic Feedback,” Proc. Haptic Symp. IEEE Virtual Reality, pp. 272-279, 2004.
[10] M. Teschner, S. Kimmerle, B. Heidelberger, G. Zachmann, L. Raghupathi, A. Fuhrmann, M.-P. Cani, F. Faure, N. Magnenat-Thalmann, W. Strasser, and P. Volino, “Collision Detection for Deformable Objects,” Proc. Eurographics, STAR (State of the Art Report), pp. 119-135, 2004.
[11] M.C. Lin and S. Gottschalk, “Collision Detection between Geometric Models: A Survey,” Proc. IMA Conf. Mathematics of Surfaces, pp. 37-56, 1998.
[12] D. Ruspini, K. Kolarov, and O. Khatib, “The Haptic Display of Complex Graphical Environments,” Proc. 24th Ann. Conf. Computer Graphics and Interactive Techniques, pp. 345-352, 1997.
[13] F. Benedetti, “Physical Response to Collision between Deformable Objects,” postgraduate course on graphics visualization and comm., EPFL, VRLab, 2002.
[14] S. Fisher and M.C. Lin, “Deformed Distance Fields for Simulation of Non-Penetrating Flexible Bodies,” Proc. Eurographic Workshop Computer Animation and Simulation, pp. 99-111, 2001.
[15] S. Hasegawa and M. Sato, “Real-Time Rigid Body Simulation for Haptic Interactions Based on Contact Volume of Polygonal Objects,” Computer Graphics Forum, vol. 23, no. 3, pp. 529-538, Sept. 2004.
[16] S. Cotin, H. Delingette, and N. Ayage, “Efficient Linear Elastic Models of Soft Tissues for Real-Time Surgery Simulation,” INRIA technical report, Oct. 1998.
[17] D.L. James and D.K. Pai, “Real Time Simulation of Multizone Elastokinematic Models,” Proc. IEEE Int'l Conf. Robotics and Automation, pp. 927-932, 2002.
[18] J.J. Moreau, “Quadratic Programming in Mechanics: Dynamics of One-Sided Constraints,” SIAM J. Control, 1966.
[19] N. Kikuchi and J.T. Oden, Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods. J. Tinsley Oden, 1988.
[20] C. Duriez, C. Andriot, and A. Kheddar, “Signorini's Contact Model for Deformable Objects in Haptic Simulations,” Proc. IEEE Int'l Conf. Intelligent Robots and Systems (IROS '04), pp. 3232-3237, 2004.
[21] J.-J. Moreau and M. Jean, “Numerical Treatment of Contact and Friction: The Contact Dynamics Method,” Eng. Systems Design and Analysis, vol. 4, pp. 201-208, 1996.
[22] K.G. Murty, Linear Complementarity, Linear and Nonlinear Programming. Internet ed., 1997.
[23] D. Baraff, “Fast Contact Force Computation for Nonpenetrating Rigid Bodies,” SIGGRAPH '94 Conf. Proc., Ann. Conf. Series, pp. 23-34, 1994.
[24] J. Sauer and E. Schömer, “A Constraint-Based Approach to Rigid Body Dynamics for Virtual Reality Applications,” Virtual Reality Software and Technology, pp. 153-162, 1998.
[25] M. Anitescu, F. Potra, and D. Stewart, “Time-Stepping for Three-Dimentional Rigid Body Dynamics,” Computer Methods in Applied Mechanics and Eng., no. 177, pp. 183-197, 1999.
[26] F. Jourdan, P. Alart, and M. Jean, “A Gauss-Seidel Like Algorithm to Solve Frictional Contact Problems,” Computer Methods in Applied Mechanics and Eng., pp. 33-47, 1998.
[27] T. Liu and M.Y. Wang, “Computation of Three-Dimensional Rigid-Body Dynamics of Multiple Contacts Using Time-Stepping and Gauss-Seidel Methods,” IEEE Trans. Automation Science and Eng., vol. 2, no. 1, pp. 19-31, Jan. 2005.
[28] P. Alart and A. Curnier, “A Mixed Formulation for Frictional Contact Problems Prone to Newton Like Solution Methods,” Computer Methods in Applied Mechanics and Eng., vol. 92, pp. 353-375, 1991.
[29] D. Terzopoulos and A. Witkin, “Physically Based Models with Rigid and Deformable Components,” IEEE Computer Graphics and Applications, vol. 8, no. 6, pp. 41-51, 1988.
[30] C.A. Felippa, “A Systematic Approach to the Element-Independent Corotational Dynamics of Finite Elements,” technical report, Center for Aerospace Structures, Jan. 2000.
[31] A.A. Shabana, Computational Dynamics. John Wiley and Sons, 1994.
[32] M. Hauth and W. Strasser, “Corotational Simulation of Deformable Solids,” J. Winter School of Computer Graphics, vol. 12, nos. 1-3, pp. 137-145, Feb. 2003.
[33] M. Pauly, D.K. Pai, and G. Leonidas, “Quasi-Rigid Objects in Contact,” Proc. Eurographics/ACM SIGGRAPH Symp. Computer Animation, pp. 109-119, 2004.
[34] P. Song, J.S. Pang, V. Kumar, “A Semi-Implicit Time-Stepping Model for Frictional Compliant Contact Problems,” Int'l J. Robotics Research, vol. 60, pp. 2231-2261, 2004.
[35] R.J. Adams and B. Hannaford, “Stable Haptic Interaction with Virtual Environments,” IEEE Trans. Robotics and Automation, vol. 15, no. 3, pp. 465-474, 1999.

Index Terms:
Computer hatics, Signorini's law, Coulomb's friction law, corotational deformable objects, Delassus operator,Gauss-Seidel type resolution, real-time simulation.
Christian Duriez, Fr?d?ric Dubois, Abderrahmane Kheddar, Claude Andriot, "Realistic Haptic Rendering of Interacting Deformable Objects in Virtual Environments," IEEE Transactions on Visualization and Computer Graphics, vol. 12, no. 1, pp. 36-47, Jan.-Feb. 2006, doi:10.1109/TVCG.2006.13
Usage of this product signifies your acceptance of the Terms of Use.