{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T09:51:52Z","timestamp":1777715512490,"version":"3.51.4"},"reference-count":17,"publisher":"SAGE Publications","issue":"9","license":[{"start":{"date-parts":[[2015,10,6]],"date-time":"2015-10-06T00:00:00Z","timestamp":1444089600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["The International Journal of Robotics Research"],"published-print":{"date-parts":[[2016,8]]},"abstract":"<jats:p>The stable, quantization-error noise-free, rendering of high-stiffness dynamics can be challenging using impedance-type haptic displays. In this paper we examine a canonical, one degree of freedom, haptic display rendering a virtual spring and damper, including the effects of the device and human dynamics, sampling, position quantization, time delay, and the low-pass filter operating on the device velocity estimate. We construct various stability and quantization-error regions as a function of the system parameters and show the necessary trade-offs that occur between them. Although we apply the quantization-error analysis to virtual spring and damper rendering, it applies to a general virtual environment. We present sufficiency for quantization-error passivity, necessity for no malicious-touch limit cycles, and necessity for no uncoupled-touch limit cycles. Using these results, aided by the presented supplementary code, we find control parameters to render the largest, renderable, virtual stiffness for a given haptic display. The analytical results are experimentally verified using a Phantom Premium 1.5 haptic device.<\/jats:p>","DOI":"10.1177\/0278364915596234","type":"journal-article","created":{"date-parts":[[2015,10,7]],"date-time":"2015-10-07T21:27:51Z","timestamp":1444253271000},"page":"1103-1120","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":37,"title":["Stability and quantization-error analysis of haptic rendering of virtual stiffness and damping"],"prefix":"10.1177","volume":"35","author":[{"given":"Nick","family":"Colonnese","sequence":"first","affiliation":[{"name":"Mechanical Engineering Department, Stanford University, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Allison","family":"Okamura","sequence":"additional","affiliation":[{"name":"Mechanical Engineering Department, Stanford University, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2015,10,6]]},"reference":[{"key":"bibr1-0278364915596234","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2005.851377"},{"key":"bibr2-0278364915596234","doi-asserted-by":"publisher","DOI":"10.1115\/1.4028526"},{"key":"bibr3-0278364915596234","doi-asserted-by":"publisher","DOI":"10.1016\/0016-0032(92)90044-H"},{"key":"bibr4-0278364915596234","doi-asserted-by":"publisher","DOI":"10.1109\/ROBOT.1994.351077"},{"key":"bibr5-0278364915596234","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-4563(199701)14:1<37::AID-ROB4>3.0.CO;2-V"},{"key":"bibr6-0278364915596234","doi-asserted-by":"publisher","DOI":"10.1109\/HAPTICS.2014.6775439"},{"key":"bibr7-0278364915596234","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2009.2037254"},{"key":"bibr8-0278364915596234","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2005.862487"},{"key":"bibr9-0278364915596234","volume-title":"Feedback Control of Dynamic Systems","author":"Franklin GF","year":"2001","edition":"4"},{"key":"bibr10-0278364915596234","volume-title":"Digital Control of Dynamic Systems","author":"Franklin GF","year":"1997","edition":"3"},{"key":"bibr11-0278364915596234","doi-asserted-by":"publisher","DOI":"10.1115\/1.3074283"},{"key":"bibr12-0278364915596234","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2008.924256"},{"key":"bibr13-0278364915596234","doi-asserted-by":"publisher","DOI":"10.1109\/TRO.2010.2088751"},{"key":"bibr14-0278364915596234","doi-asserted-by":"publisher","DOI":"10.1109\/IROS.2008.4650697"},{"key":"bibr15-0278364915596234","volume-title":"Nonlinear Systems","author":"Khalil HK","year":"2001","edition":"3"},{"key":"bibr16-0278364915596234","volume-title":"Applied Nonlinear Control","author":"Slotine JE","year":"1991"},{"key":"bibr17-0278364915596234","volume-title":"Robust and Optimal Control","author":"Zhou K","year":"1996"}],"container-title":["The International Journal of Robotics Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0278364915596234","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1177\/0278364915596234","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0278364915596234","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T10:15:22Z","timestamp":1777457722000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/0278364915596234"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,10,6]]},"references-count":17,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2016,8]]}},"alternative-id":["10.1177\/0278364915596234"],"URL":"https:\/\/doi.org\/10.1177\/0278364915596234","relation":{},"ISSN":["0278-3649","1741-3176"],"issn-type":[{"value":"0278-3649","type":"print"},{"value":"1741-3176","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,10,6]]}}}