{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T09:52:59Z","timestamp":1777715579311,"version":"3.51.4"},"reference-count":26,"publisher":"SAGE Publications","issue":"9","license":[{"start":{"date-parts":[[2005,9,1]],"date-time":"2005-09-01T00:00:00Z","timestamp":1125532800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The International Journal of Robotics Research"],"published-print":{"date-parts":[[2005,9]]},"abstract":"<jats:p>In this paper we describe a new solution for stable haptic interaction with deformable object simulations featuring low servo rates and computational delays. The solution presented is a combination of the local model and the virtual coupling concepts proposed in the past. By varying the local model impedance depending on the local stiffness of the deformable object, the interaction between local model and simulation can always be made stable independently of low servo rates or computational delays. Moreover, by using more complex local impedances that feature an integral term, we are able to control the steady-state error between the device and the surface of the deformable object. This allows us to maximize the Z -width of the simulation, while obtaining overall stable behavior without using any added damping. The local model is always computed using the current deformable object surface, thus allowing for multi-point contact interaction, i.e., allowing multiple users to feel each other\u2019s influence on the object. The proposed solution is presented and analyzed in a multirate setting. Experimental results employing a Phantom haptic interface are presented.<\/jats:p>","DOI":"10.1177\/0278364905057055","type":"journal-article","created":{"date-parts":[[2005,9,6]],"date-time":"2005-09-06T04:38:03Z","timestamp":1125981483000},"page":"703-715","source":"Crossref","is-referenced-by-count":34,"title":["A Multirate Approach to Haptic Interaction with Deformable Objects Single and                 Multipoint Contacts"],"prefix":"10.1177","volume":"24","author":[{"given":"Federico","family":"Barbagli","sequence":"first","affiliation":[{"name":"Stanford Robotics Laboratory, Stanford University, Stanford, CA, USA and                         Information Engineering Department, University of Siena, Siena, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Domenico","family":"Prattichizzo","sequence":"additional","affiliation":[{"name":"Information Engineering Department, University of Siena, Siena, Italy,"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kenneth","family":"Salisbury","sequence":"additional","affiliation":[{"name":"Stanford Robotics Laboratory, Stanford University, Stanford, CA, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2005,9,1]]},"reference":[{"key":"atypb1","doi-asserted-by":"crossref","unstructured":"Adachi, Y., Kumano, T., and Ogino, K. 1995. Intermediate representation for stiff virtual objects . IEEE Virtual Reality Annual International Symposium, Research Triangle Park, NC, March, pp. 203-210 .","DOI":"10.1109\/VRAIS.1995.512497"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1109\/70.768179"},{"key":"atypb3","doi-asserted-by":"crossref","unstructured":"Astley, O. and Hayward, V. 1998. Multirate haptic simulation achieved by coupling finite element meshes through Norton equivalents . Proceedings of the IEEE International Conference on Robotics and Automation (ICRA98), Leuven, Belgium, pp. 989-994 .","DOI":"10.1109\/ROBOT.1998.677216"},{"key":"atypb4","unstructured":"Balaniuk, R. 1999. Using fast local modeling to buffer haptic data . Proceedings of Fourth Phantom Users Group Workshop (PUG99)."},{"key":"atypb5","doi-asserted-by":"crossref","unstructured":"Barbagli, F., Prattichizzo, D., and Salisbury, J. 2003. Dynamic local models for stable multicontact haptic interaction with deformable objects . Haptics Symposium 2003, Los Angeles, CA, pp. 109-116 .","DOI":"10.1109\/HAPTIC.2003.1191248"},{"key":"atypb6","unstructured":"Brady, K. and Tarn, T. 1998. Internet-based remote teleoperation . Proceedings of the IEEE International Conference on Robotics and Automation, Leuven, Belgium, May."},{"key":"atypb7","doi-asserted-by":"crossref","unstructured":"Cavusoglu, M. and Tendick, F. 2000. Multirate simulation for high fidelity haptic interaction with deformable objects in virtual environments . Proceedings of the IEEE International Conference on Robotics and Automation, San Francisco, CA, April 24-28, pp. 2458-2465 .","DOI":"10.1109\/ROBOT.2000.846397"},{"key":"atypb8","unstructured":"Colgate, E. and Brown, J. 1994. Factors affecting the z-width of a haptic display . Proceedings of the IEEE International Conference on Robotics and Automation, Los Alamitos, CA, pp. 3205-3210 ."},{"key":"atypb9","unstructured":"Colgate, E., Stanley, M., and Brown, J. 1995. Issues in the haptic display of tool use . Proceedings of the International Conference on Intelligent Robots and Systems, Pittsburgh, PA, August."},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1007\/PL00007215"},{"key":"atypb11","unstructured":"de Pascale, M., de Pascale, G., Prattichizzo, D., and Barbagli, F. 2004. A new method for haptic GPU rendering of deformable objects . Proceedings of EuroHaptics 2004, Munich, Germany, June."},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1109\/9.1310"},{"key":"atypb13","doi-asserted-by":"crossref","unstructured":"Gillespie, B. and Cutkosky, M. 1996. Rendering of the virtual wall . Proceedings of the ASME International Mechanical Engineering Conference and Exposition, Atlanta, GA, November, Vol. 58, pp. 397-406 .","DOI":"10.1115\/IMECE1996-0362"},{"key":"atypb14","unstructured":"James, D. and Pai, D. 2001. A unified treatment of elasto-static contact simulation for real time haptics . haptics-e, The Electronic Journal of Haptics Research 2(1)."},{"key":"atypb15","unstructured":"Jury, E. I. 1964. Theory and Applications of the z-Transform Method, Wiley, New York ."},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1985.1103841"},{"key":"atypb17","unstructured":"Mahvash, M. and Hayward, V. 2003. Passivity-based high-fidelity haptic rendering of contact . Proceedings of the 2003 IEEE International Conference on Robotics and Automation (ICRA 2003), Taipei, Taiwan, September 14-19."},{"key":"atypb18","doi-asserted-by":"crossref","unstructured":"Mahvash, M. and Hayward, V. 2004. High fidelity haptic synthesis of contact with deformable bodies . IEEE Computer Graphics and Applications, special issue on haptic rendering, 48-55 .","DOI":"10.1109\/MCG.2004.1274061"},{"key":"atypb19","doi-asserted-by":"crossref","unstructured":"Mark, W., Randolph, S., Finch, M., Verth, J. V., and Taylor, R. 1996. Adding force feedback to graphics systems: issues and solutions . Computer Graphics: Proceedings of SIGGRAPH\u201996, August, pp. 447-452 .","DOI":"10.1145\/237170.237284"},{"key":"atypb20","unstructured":"Massie, T. 1996. Taking the mush out of haptics with infinitely stiff walls . Proceedings of the First Phantom Users Group Workshop, Dedham, MA, September."},{"key":"atypb21","unstructured":"Mazzella, F., Montgomery, K., and Latombe, J. 2002. The force grid: a buffer structure for haptic interaction with virtual elastic objects . Proceedings of the IEEE International Conference on Robotics and Automation (ICRA02), Seoul, Korea, May 21-26."},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1109\/70.897782"},{"key":"atypb23","doi-asserted-by":"crossref","unstructured":"Niemeyer, G. and Slotine, J. 1997. Designing force reflecting teleoperators with large time delays to appear as virtual tools . Proceedings of the IEEE Conference on Robotics and Automation, Albuquerque, NM, pp. 2212-2218 .","DOI":"10.1109\/ROBOT.1997.619290"},{"key":"atypb24","doi-asserted-by":"crossref","unstructured":"Ruspini, D., Kolarov, K., and Khatib, O. 1997. The haptic display of complex graphical environments . Computer Graphics 31: 345-352 .","DOI":"10.1145\/258734.258878"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1115\/1.2801114"},{"key":"atypb26","doi-asserted-by":"crossref","unstructured":"Zilles, C. and Salisbury, J. 1995. A constraint based god-object method for haptic display . Proceedings of the IEE\/RSJ International Conference on Intelligent Robots and Systems, Human Robot Interaction, and Cooperative Robots, Pittsburgh, PA, Vol. 3, pp. 146-151 .","DOI":"10.1109\/IROS.1995.525876"}],"container-title":["The International Journal of Robotics Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/journals.sagepub.com\/doi\/pdf\/10.1177\/0278364905057055","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/journals.sagepub.com\/doi\/pdf\/10.1177\/0278364905057055","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T10:15:34Z","timestamp":1777457734000},"score":1,"resource":{"primary":{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/journals.sagepub.com\/doi\/10.1177\/0278364905057055"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,9]]},"references-count":26,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2005,9]]}},"alternative-id":["10.1177\/0278364905057055"],"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.1177\/0278364905057055","relation":{},"ISSN":["0278-3649","1741-3176"],"issn-type":[{"value":"0278-3649","type":"print"},{"value":"1741-3176","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,9]]}}}