{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T09:55:45Z","timestamp":1777715745987,"version":"3.51.4"},"reference-count":12,"publisher":"SAGE Publications","issue":"4","license":[{"start":{"date-parts":[[2000,4,1]],"date-time":"2000-04-01T00:00:00Z","timestamp":954547200000},"content-version":"tdm","delay-in-days":0,"URL":"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":[[2000,4]]},"abstract":"<jats:p>In this paper, we continue our investigations into robotic air hockey by studying the problem of controlling the trajectory of a puck subject to impacts. Impacts are modeled using the Routh two-dimensional impact model, which incorporates the effects of spin and friction. Using this model, we derive an explicit mapping between preimpact and postimpact velocities of the puck as a function of the velocities of the impacting objects and the coefficients of restitution and friction. We will see that this mapping depends fundamentally on whether or not relative sliding between the objects occurs throughout the duration of the impact event, or terminates during the impact. We then present results on planning of puck trajectories and control of the puck through impacts with a mallet or striker, which is essentially the problem of inverting the mapping between preimpact and postimpact velocities. Our results confirm the intuitive notion that a large coefficient of friction between the mallet and puck, and between the puck and table walls, enhances the ability to control puck motion through impacts.<\/jats:p>","DOI":"10.1177\/02783640022066897","type":"journal-article","created":{"date-parts":[[2003,7,19]],"date-time":"2003-07-19T02:59:46Z","timestamp":1058583586000},"page":"336-348","source":"Crossref","is-referenced-by-count":36,"title":["Control of Planar Rigid Body Sliding with Impacts and Friction"],"prefix":"10.1177","volume":"19","author":[{"given":"Chad B.","family":"Partridge","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mark W.","family":"Spong","sequence":"additional","affiliation":[{"name":"Coordinated Science Laboratory, University of Illinois at                         Urbana\u2013Champaign, Urbana, Illinois 61801, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2000,4,1]]},"reference":[{"key":"atypb1","unstructured":"Bishop, B. E. 1997.\n                      Intelligent Visual Servo Control of an Air Hockey Playing Robot\n                      . Ph.D. thesis, University of Illinois at Urbana-Champaign."},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1109\/37.768537"},{"key":"atypb3","unstructured":"Black, C. K., and Lynch, K. M. 1998. Planning and control for planar batting and hopping . Proceedings of the 36th Annual Allerton Conference on Communications, Control, and Computing, Monticello, IL, pp. 724\u2013733 ."},{"key":"atypb4","unstructured":"Lynch, K. M., and Mason, M. T. 1997. Dynamic manipulation with a one joint robot . Proceedings of the 1997 IEEE International Conference on Robotics and Automation, Albequerque, NM, pp. 356\u2013366 ."},{"key":"atypb5","doi-asserted-by":"crossref","unstructured":"M\u2019Closkey, R. T., and Burdick, J. W. 1993. Periodic motion of a hopping robot with vertical and forward motion . International Journal of Robotic Research 12(3): 97\u2013218 .","DOI":"10.1177\/027836499301200301"},{"key":"atypb6","unstructured":"Partridge, C. B. 1999. Vision-based prediction of planar rigid body sliding with impacts and friction. M.S. thesis, University of Illinois at Urbana-Champaign."},{"key":"atypb7","doi-asserted-by":"crossref","unstructured":"Rizzi, A. A., and Koditschek, D. E. 1992. Progress in spatial robot juggling . Proceedings of the 1992 IEEE International Conference on Robotics and Automation, Nice, France, pp. 775\u2013780 .","DOI":"10.1109\/ROBOT.1992.220275"},{"key":"atypb8","unstructured":"Routh, E. J. 1960. Dynamics of a System of Rigid Bodies. 7th ed. New York: Dover ."},{"key":"atypb9","unstructured":"Serway, R. A. 1992. Physics. 3d ed. Philadelphia, PA: Saunders College Publishing ."},{"key":"atypb10","doi-asserted-by":"crossref","unstructured":"Voyenli, K., and Eriksen, E. 1985. On the motion of an ice hockey puck . Am. J. Physics 12: 1149\u20131153 .","DOI":"10.1119\/1.14071"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1115\/1.2893771"},{"key":"atypb12","doi-asserted-by":"crossref","unstructured":"Warren, J.W.H., Young, D. S., and Lee, D. N. 1986. Visual control of step length during running over irregular terrain . Journal of Experimental Psychology 12(3): 259\u2013266 .","DOI":"10.1037\/\/0096-1523.12.3.259"}],"container-title":["The International Journal of Robotics Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/02783640022066897","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/02783640022066897","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T10:16:08Z","timestamp":1777457768000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/02783640022066897"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,4]]},"references-count":12,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2000,4]]}},"alternative-id":["10.1177\/02783640022066897"],"URL":"https:\/\/doi.org\/10.1177\/02783640022066897","relation":{},"ISSN":["0278-3649","1741-3176"],"issn-type":[{"value":"0278-3649","type":"print"},{"value":"1741-3176","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,4]]}}}