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Generalized penetration depth for penalty-based six-degree-of-freedom haptic rendering

Published online by Cambridge University Press:  01 July 2008

Maxim Kolesnikov  and
Miloš Žefran
Maxim Kolesnikov*
Affiliation:
Department of Electrical and Computer Engineering, University of Illinois at Chicago, Chicago, IL 60607-7053. Email: mkoles2@uic.edu, mzefran@uic.edu
Miloš Žefran
Affiliation:
Department of Electrical and Computer Engineering, University of Illinois at Chicago, Chicago, IL 60607-7053. Email: mkoles2@uic.edu, mzefran@uic.edu
*
*Corresponding author: E-mail: mkoles2@uic.edu
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Summary

Existing penalty-based haptic rendering approaches are based on the penetration depth estimation in strictly translational sense and cannot properly take object rotation into account. We propose a new six-degree-of-freedom (6-DOF) haptic rendering algorithm which is based on determining the closest-point projection of the inadmissible configuration onto the set of admissible configurations. Energy is used to define a metric on the configuration space. Once the projection is found the 6-DOF wrench can be computed from the generalized penetration depth. The space is locally represented with exponential coordinates to make the algorithm more efficient. Examples compare the proposed algorithm with the existing approaches and show its advantages.

Keywords

hapticshaptic renderingsix degrees of freedomgeneralized penetration depth
Type
Article
Information
Robotica , Volume 26 , Special Issue 4: Geometry in Robotics: Sensing , July 2008 , pp. 513 - 524
Copyright
Copyright © Cambridge University Press 2008

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References

1.Salisbury, K., Conti, F. and Barbagli, F., “Haptic rendering: Introductory concepts,” IEEE Comput. Graph. Appl. 24 (2), 24–32 (2004).CrossRefGoogle ScholarPubMed
2.Otaduy, M. A. and Lin, M. C., High Fidelity Haptic Rendering, vol. 1 of Synthesis Lectures on Computer Graphics. (Morgan & Claypool Publishers, San Rafael, CA, 2006).CrossRefGoogle Scholar
3.Moore, M. and Wilhelms, J., “Collision Detection and Response for Computer Animation,” Proceedings of the 15th International Conference on Computer Graphics and Interactive Techniques (SIGGRAPH 88), vol. 22, Atlanta, GA (1988) pp. 289–294.Google Scholar
4.Kim, Y. J., Otaduy, M. A., Lin, M. C. and Manocha, D., “Six-degree-of-freedom haptic rendering using localized contact computations,” Presence: Teleop. Virt. 12 (3), 277–295 (2003).CrossRefGoogle Scholar
5.Otaduy, M. A. and Lin, M. C., “Stable and Responsive Six-Degree-of-Freedom Haptic Manipulation using Implicit Integration,” Proceedings of the World Haptics Conference, Pisa, Italy (2005) pp. 247–256.Google Scholar
6.Colgate, J. E., Stanley, M. C. and Brown, J. M., “Issues in the Haptic Display of Tool Use,” Proceedings of IEEE/RSJ International Conference on Intelligent Robots and Systems, Chicago, IL (1994) pp. 295–300.Google Scholar
7.Zilles, C. B. and Salisbury, J. K., “A Constraint-Based God-Object Method for Haptic Display,”Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Pittsburgh, PA (1995) pp. 146–151.Google Scholar
8.Ruspini, D. C., Kolarov, K. and Khatib, O., “The Haptic Display of Complex Graphical Environments,” Proceedings of the 24th International Conference on Computer Graphics and Interactive Techniques (SIGGRAPH 97), Los Angeles, CA (1997) pp. 345–352.Google Scholar
9.Ortega, M., Redon, S. and Coquillart, S., “A Six Degree-of-Freedom God-Object Method for Haptic Display of Rigid Bodies,” Proceedings of the IEEE Virtual Reality, Alexandria, VA (2006) pp. 197–204.Google Scholar
10.Constantinescu, D., Sacludean, S. E. and Croft, E. A., “Haptic rendering of rigid contacts using impulsive and penalty forces,” IEEE Trans. Robot. 21 (3), 309–323 (2005).CrossRefGoogle Scholar
11.Mc Neely, W. A., Puterbaugh, K. D. and Troy, J. J., “Six Degree-of-Freedom Haptic Rendering Using Voxel Sampling,” Proceedings of the 26th International Conference on Computer Graphics and Interactive Techniques (SIGGRAPH '99), New York, NY, USA (1999) pp. 401–408.Google Scholar
12.Otaduy, M. A., Jain, N., Sud, A. and Lin, M. C., “Haptic Display of Interaction Between Textured Models,” Proceedings of IEEE Visualization Conference, Austin, TX (2004) pp. 297–304.Google Scholar
13.Zhang, L., Varadhan, G., Kim, Y. J. and Manocha, D., “Generalized Penetration Depth Computation,” Proceedings of ACM Solid and Physical Modeling Conference (SPM06), Wales, UK (2006) pp. 173–184.Google Scholar
14.Zhang, L., Kim, Y. J. and Manocha, D., “C-Dist: Efficient Distance Computation for Rigid and Articulated Models in Configuration Space,” Proceedings of ACM Solid and Physical Modeling Conference (SPM07), Beijing, China (2007) pp. 159–169.Google Scholar
15.Zhang, L., Kim, Y. J. and Manocha, D., “A Fast and Practical Algorithm for Generalized Penetration Depth Computation,” Proceedings of Robotics: Science and Systems (RSS07), Atlanta, GA (2007).Google Scholar
16.Kane, C., Repetto, E. A., Ortiz, M. and Marsden, J. E., “Finite element analysis of nonsmooth contact,” Comput. Methods Appl. Mech. Engng. 180 (1–2), 1–26 (1999).CrossRefGoogle Scholar
17.Luo, Q. and Xiao, J., “Physically accurate haptic rendering with dynamic effects,” IEEE Comput. Graph. and Appl. 24 (6), 60–69 (2004).CrossRefGoogle ScholarPubMed
18.Murray, R. M., Li, Z. and Sastry, S. S., A Mathematical Introduction to Robotic Manipulation (Boca Raton, FL, CRC Press, 1994).Google Scholar
19.Žpefran, M. and Bullo, F., “Lagrangian Dynamics,” Robotics and Automation Handbook (Kurfess, T. R., ed.), (CRC Press, 2005) pp. 5-1–5-16.Google Scholar
20.Boothby, W. M., An Introduction to Differentiable Manifolds and Riemannian Geometry, 2nd ed. (Academic Press, New York, 1986).Google Scholar
21.Lin, Q. and Burdick, J. W., “Objective and frame-invariant kinematic metric functions for rigid bodies,” Intl J. Robot. Res. 19 (6), 612–625 (2000).CrossRefGoogle Scholar
22.Žefran, M. and Kumar, V., “A geometrical approach to the study of the Cartesian stiffness matrix,” J. Mech. Design 124 (1), 30–38 (2002).CrossRefGoogle Scholar
23.Lin, M. C. and Canny, J. F., “A Fast Algorithm for Incremental Distance Calculation,” IEEE International Conference on Robotics and Automation, Sacramento, CA (1991) pp. 1008–1014.Google Scholar
24.Abramowitz, M. and Stegun, I. A., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, New York, 1972).Google Scholar
25.Booth, S., Angelis, F. De and Schmidt-Tjarksen, T., “The Influence of Changing Haptic Refresh-Rate on Subjective User Experiences – Lessons for Effective Touch-Based Applications,” EuroHaptics 2003 Conference Proceedings, Dublin, Ireland (2003) pp. 374–383.Google Scholar
26.Stoer, J. and Bulirsch, R., Introduction to Numerical Analysis (Springer-Verlag, New York, 1980).CrossRefGoogle Scholar