Abstract
Advanced, synthetic haptic virtual environments require textured virtual surfaces. We found that texturing smooth surfaces often reduces the system passivity margin of a haptic simulation. As a result, a smooth virtual surface that can be rendered in a passive manner may loose this property once textured. We propose that any texture algorithm is associated with a characteristic number that expresses the relative change in loop gain. We further found that a passive virtual interaction can have severe unwanted artifacts if the synthesized force field is not conservative. The energy characteristics of seven algorithms are analyzed. Finally a new texture synthesis algorithm, which operates by modulating a friction force during scanning, is shown to have several advantages over previous ones.
Reprinted from Gianni Campion and Vincent Hayward, “On the Synthesis of Haptic Textures.”IEEE Transactions on Robotics, Volume 24, Number 3, 527–536, 2008.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Abbott, J.J., Okamura, A.M.: Effects of position quantization and sampling rate on virtual wall passivity. IEEE Trans. Robot.21(5), 952–964 (2005)
Adams, R.J., Hannaford, B.: Stable haptic interaction with virtual environments. IEEE Trans. Robot. Autom.15(3), 465–474 (1999)
Campion, G., Hayward, V.: Fundamental limits in the rendering of virtual haptic textures. In: Proceedings of the First Joint Eurohaptics Conference and Symposium on Haptic Interfaces for Virtual Environments and Teleoperator Systems, WHC’05, pp. 263–270 (2005)
Campion, G., Hayward, V.: On the synthesis of haptic textures. IEEE Trans. Robot.24(3), 527–536 (2008)
Campion, G., Wang, Q., Hayward, V.: The Pantograph Mk-II: A haptic instrument. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS’05, pp. 723–728 (2005)
Choi, S., Tan, H.Z.: Perceived instability of virtual haptic texture. I. Experimental studies. Presence13(4), 395–415 (2004)
Choi, S., Tan, H.Z.: Perceived instability of virtual haptic texture. II. Effect of collision-detection algorithm. Presence14(4), 463–481 (2005)
Colgate, J.E., Schenkel, G.: Passivity of a class of sampled-data systems: Application to haptic interfaces. In: Proceedings of the American Control Conference, pp. 3236–3240 (1994)
Colgate, J.E., Grafing, P.E., Stanley, M.C., Schenkel, G.: Implementation of stiff virtual walls in force-reflecting interfaces. In: Virtual Reality Annual International Symposium, pp. 202–208 (1993)
Costa, M.A., Cutkosky, M.R.: Roughness perception of haptically displayed fractal surfaces. In: Proceedings ASME IMECE Symposium on Haptic Interfaces for Virtual Environments and Teleoperator Systems, vol. 69-2, pp. 1073–1079 (2000)
Crossan, A., Williamson, J., Murray-Smith, R.: Haptic granular synthesis: Targeting, visualisation and texturing. In: Proceedings of the International Symposium on Non-visual & Multimodal Visualization, pp. 527–532. IEEE Press, New York (2004)
Diolaiti, N., Niemeyer, G., Barbagli, F., Salisbury, J.K.: Stability of haptic rendering: Discretization, quantization, time delay, and coulomb effects. IEEE Trans. Robot.22(2), 256–268 (2006)
Frisoli, A.: Personal communication (2004)
Fritz, J.P., Barner, K.E.: Stochastic models for haptic textures. In: Stein, M.R. (ed.) Telemanipulator and Telepresence Technologies III. Proc. SPIE, vol. 2901, pp. 34–44 (1996)
Goldstein, H.: Classical Mechanics. Addison-Wesley, Reading (1950)
Gosline, A.H., Campion, G., Hayward, V.: On the use of eddy current brakes as tunable, fast turn-on viscous dampers for haptic rendering. In: Proceedings of Eurohaptics, pp. 229–234 (2006)
Hardwick, A., Furner, S., Rush, J.: Tactile display of virtual reality from the world wide web—a potential access method for blind people. Displays18, 153–161 (1998)
Hayward, V.: Haptic synthesis. In: Proceedings of the 8th International IFAC Symposium on Robot Control, SYROCO 2006, pp. 19–24 (2006)
Hayward, V., Armstrong, B.: A new computational model of friction applied to haptic rendering. In: Corke, P., Trevelyan, J. (eds.) Experimental Robotics VI. Lecture Notes in Control and Information Sciences, vol. 250, pp. 403–412 (2000)
Hayward, V., Astley, O.R.: Performance measures for haptic interfaces. In: Giralt, G., Hirzinger, G. (eds.) Robotics Research: The 7th International Symposium, pp. 195–207. Springer, Heidelberg (1996)
Hayward, V., Yi, D.: Change of height: An approach to the haptic display of shape and texture without surface normal. In: Siciliano, B., Dario, P. (eds.) Experimental Robotics VIII. Springer Tracts in Advanced Robotics, pp. 570–579. Springer, Heidelberg (2003)
Hill, D.J., Moylan, P.J.: Dissipative dynamical systems: Basic input-output and state properties. J. Franklin Inst.309(5), 327–357 (1980)
Mahvash, M., Hayward, V.: High fidelity haptic synthesis of contact with deformable bodies. IEEE Comput. Graph. Appl.24(2), 48–55 (2004)
Mahvash, M., Hayward, V.: High fidelity passive force reflecting virtual environments. IEEE Trans. Robot.21(1), 38–46 (2005)
Melder, N., Harwin, W.S.: Force shading and bump mapping using the friction cone algorithm. In: Proceedings of the First Joint Eurohaptics Conference and Symposium on Haptic Interfaces for Virtual Environments and Teleoperator Systems, WHC’05, pp. 573–575 (2005)
Minsky, M., Lederman, S.J.: Simulated haptic textures: Roughness. In: Proceedings of the ASME IMECE Symposium on Haptic Interfaces for Virtual Environments and Teleoperator Systems, vol. DSC-Vol. 58, pp. 421–426 (1996)
Morgenbesser, H.B., Srinivasan, M.A.: Force shading for haptic shape perception. In: Proceedings of the Fifth Symposium on Haptic Interfaces for Virtual Environments and Teleoperators, ASME Dynamic Systems and Control Division, vol. DSC 58, pp. 407–412 (1996)
Otaduy, M.A., Jain, N., Sud, A., Lin, M.C.: Haptic display of interaction between textured models. In: Proceedings of IEEE Visualization, pp. 297–304 (2004)
Otaduy, M.A., Lin, M.C.: A perceptually-inspired force model for haptic texture rendering. In: Proceedings of the 1st Symposium on Applied Perception in Graphics and Visualization, pp. 123–126. ACM Press, New York (2004)
Salisbury, J.K., Conti, F., Barbagli, F.: Haptic rendering: Introductory concepts. IEEE Comput. Graph. Appl.24(2), 24–32 (2004)
Salisbury, K.J., Brock, D., Massie, T., Swarup, N., Zilles, C.: Haptic rendering: Programming touch interaction with virtual objects. In: Proceedings Symposium on Interactive 3D Graphics, pp. 123–130. ACM Press, New York (1995)
Siira, J., Pai, D.K.: Haptic textures—a stochastic approach. In: Proceedings of IEEE International Conference on Robotics and Automation, pp. 557–562 (1996)
Wall, S.A., Harwin, W.S.: Effects of physical bandwidth on perception of virtual gratings. In: Proceedings of the Symposium on Haptic Interfaces for Virtual Environments and Teleoperators, ASME Dynamic Systems and Control Division, pp. 1033–1039 (2000)
Weisenberger, J.M., Kreier, M.J., Rinker, M.A.: Judging the orientation of sinusoidal and square-wave virtual gratings presented via 2-DOF and 3-DOF haptic interfaces. Haptics-e1(4) (2000), online
Zhou, K., Doyle, J.C.: Essentials of Robust Control. Prentice Hall, New York (1997)
Zilles, C.B., Salisbury, J.K.: A constraint-based god object method for haptic display. In: Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS’95, vol. 3, pp. 146–151 (1995)
Acknowledgements
The authors would like to thank Mohsen Mahvash and Andrew H.C. Gosline for insightful comments on earlier drafts of this paper. This research was supported in part by the Institute for Robotics and Intelligent Systems, andnserc, the Natural Sciences and Engineering Research Council of Canada.
Author information
Authors and Affiliations
Corresponding author
Appendices
Appendix 1: Characteristic Number of AlgorithmF
An upper bound for\(q_{\mbox{\scriptsize{\textsf{\textbf{F}}}}}\) \(h(p^{x})=A\sin (2\pi p^{x}/l)\) is
Appendix 2: Jacobian Matrix of AlgorithmD
For the god-object method, the assumptions are:
-
the boundary curveh(p x) is smooth and differentiable.
-
there is just one point\((p^{x}_{h},p^{z}_{h})\) onh that minimizes the distance between the (p x,p z) and the boundary.
-
probe is ‘inside’ the texture.
We know that:
while the linearization around (p x,p z) gives:
The energy function can be described by
Differentiating (5.35) gives
where we used Eq. (5.32), (5.33), and (5.34). The derivation of the force is complete by defining\(\boldsymbol{f}_{\!\mbox{\scriptsize{\textsf{\textbf{D}}}}}(\boldsymbol{s})_{x} = 0 \mbox{ if } h'(p^{x}_{h})=0\).
The same reasoning can be used to derive
and\(\boldsymbol{f}_{\!\mbox{\scriptsize{\textsf{\textbf{D}}}}}(\boldsymbol {s})_{z} = 0 \mbox{ if }1/h'(p^{x}_{h}) =0\). The Jacobian can be easily computed:
hence
Knowing that:
and
we can write
Appendix 3: Erratum to “On the Synthesis of Haptic Textures”
Reprinted from Gianni Campion and Vincent Hayward, Erratum to “On the Synthesis of Haptic Textures.”IEEE Transactions on Robotics, Volume 25, Issue 2, 475, 2008.
In Sect. IV.D.3 of reference [4] (5.5.4 of this book) it is stated that the characteristic number of the first variant of the ‘god-object’ method applied to texture synthesis is 1. However, the assumptions used to simplify the Jacobian matrix neglect the effect of curvature of the height function, hence this statement is not always true. The ‘god-object’ method generates a force field based on minimizing the distance between the interaction point,p=(p x,p z), and a point\(p_{h}=(p_{h}^{x},p_{h}^{z})\) on the texture,z=h(x). In other words, there exists a functionu(x,y) such that\(p_{h}^{u}, p_{h}^{h(u)}\) minimizes ‖p−p h ‖ and such that the vectorp h −p is normal to the curveh at pointu. In a reference frame at located atu (tangent and normal to the curve, coordinatesξ,ν, see Fig. 5.1), the complete expression of the Jacobian matrix of the force field is (the original expression was given in global coordinates)
Upon evaluation of the norm of this matrix, it can be found that the characteristic number is indeed 1 except when the interaction point approaches the center of curvature of the curve describing the height function. Specifically, it is
which has a singularity forν=1/h″(0) and tends to 1 asν→∞. In practice not all centers of curvature represent a problem. For a sine wave\(A \sin(2\pi p^{x} / l)\) there is one singular point per period at (l,1−(l/2π)2). Notice that as the spatial frequency increases the singular points are closer to the surface, becoming less likely to be encountered. Moreover, the increase of stiffness happens only in the convex regions where limit cycles are less likely to occur.
Rights and permissions
Copyright information
© 2008 IEEE
About this chapter
Cite this chapter
Campion, G. (2008). On the Synthesis of Haptic Textures. In: The Synthesis of Three Dimensional Haptic Textures: Geometry, Control, and Psychophysics. Springer Series on Touch and Haptic Systems. Springer, London. https://doi.org/10.1007/978-0-85729-576-7_5
Download citation
DOI: https://doi.org/10.1007/978-0-85729-576-7_5
Publisher Name: Springer, London
Print ISBN: 978-0-85729-575-0
Online ISBN: 978-0-85729-576-7
eBook Packages: Computer ScienceComputer Science (R0)