{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T11:50:11Z","timestamp":1769860211844,"version":"3.49.0"},"reference-count":17,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2009,3,9]],"date-time":"2009-03-09T00:00:00Z","timestamp":1236556800000},"content-version":"unspecified","delay-in-days":7191,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Robotica"],"published-print":{"date-parts":[[1989,7]]},"abstract":"<jats:title>SUMMARY<\/jats:title><jats:p>An approach for collision\u2013free trajectory planning along designated paths of two robots in a common workspace is presented. Specifically, in order to describe potential collision between the links of two robots along the designated paths, explicit forms of virtual obstacle are adopted, according to which links of one robot are made to grow while the other robot is forced to shrink as a point on the path. Then, a notion of virtual coordination space is introduced to visualize all the collision\u2013free coordinations of two trajectories. Assuming that a collision\u2013free coordination curve between the two robots is given via a virtual coordination space, the minimum time collision\u2013free trajectory pair for the two robots is sought considering dynamic constraints of torque and velocity bounds of actuators of the two robots.<\/jats:p>","DOI":"10.1017\/s0263574700006068","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T13:20:38Z","timestamp":1236691238000},"page":"205-212","source":"Crossref","is-referenced-by-count":31,"title":["Collision\u2013Free Trajectory Planning for Two Robot Arms"],"prefix":"10.1017","volume":"7","author":[{"given":"Youshik","family":"Shin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zeungnam","family":"Bien","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,3,9]]},"reference":[{"key":"S0263574700006068_ref005","unstructured":"5. Freund E. and Hoyer H. , \u201cOn the On\u2013Line Solution of the Findpath Problem in Multi\u2013Robot Systems\u201d In: Proc. 3rd Int. Symp. Robotics Research, Gouvieux, France (MIT Press, Cambridge, MA, Oct., 1985)."},{"key":"S0263574700006068_ref016","doi-asserted-by":"crossref","unstructured":"16. Singh S. and Leu M.C. , \u201cOptimal Trajectory Generation for Robotic Manipulators using Dynamic Programming\u201d Trans. ASME, J. Dynamic Syst., Meas., Contr. 109, 88\u201396 (06, 1987)","DOI":"10.1115\/1.3143842"},{"key":"S0263574700006068_ref014","first-page":"263","article-title":"Structuring Free Space as a Hypergraph for Roving Robot Path Planning and Navigation","volume":"9","author":"Rueb","year":"1987","journal-title":"IEEE Trans."},{"key":"S0263574700006068_ref004","doi-asserted-by":"crossref","unstructured":"4. Red W.E. and Troung\u2013Cao H.V. , \u201cConfiguration Maps for Robot Path Planning in Two\u2013Dimension\u201d ASME J. of Dynamic Systems, Measurement and Control, 292\u2013298 (1987).","DOI":"10.1115\/1.3140739"},{"key":"S0263574700006068_ref003","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1984.1103640"},{"key":"S0263574700006068_ref008","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1177\/027836498600500304","article-title":"Toward Efficient Trajectory Planning: The Path-Velocity Decomposition","volume":"5","author":"Zucker","year":"1986","journal-title":"Int. J. Robotics Res."},{"key":"S0263574700006068_ref012","doi-asserted-by":"publisher","DOI":"10.1145\/359156.359164"},{"key":"S0263574700006068_ref001","first-page":"681","article-title":"Automatic Planning of Manipulator Transfer Movements","volume":"11","author":"Lozano-Perez","year":"1981","journal-title":"IEEE Trans. Syst."},{"key":"S0263574700006068_ref002","doi-asserted-by":"publisher","DOI":"10.1177\/027836498300200402"},{"key":"S0263574700006068_ref017","unstructured":"17. Park W.T. , \u201cState\u2013Space Representations for Coordination of Multiple Manipulators\u201d Proc. 14th Int. Symp. Industrial Robots, Gothenburg, Sweden 397\u2013405 (1984)."},{"key":"S0263574700006068_ref011","doi-asserted-by":"publisher","DOI":"10.1109\/JRA.1987.1087094"},{"key":"S0263574700006068_ref006","doi-asserted-by":"crossref","unstructured":"6. Freund E. and Hoyer H. , \u201cPathfinding in Multi\u2013Robot Systems: Solution and Applications\u201d Proc. IEEE Int. Conf. Robotics and Automation 103\u2013111 (1986).","DOI":"10.1109\/ROBOT.1986.1087653"},{"key":"S0263574700006068_ref009","doi-asserted-by":"crossref","unstructured":"9. Lee B.H. , \u201cWrist Collision Avoidance of Two Robots: A Collision Map and Time Scheduling Approach\u201d Proc. 25th IEEE Conf. Decision and Control, Athens, Greece 429\u2013434 (12, 1986)","DOI":"10.1109\/CDC.1986.267294"},{"key":"S0263574700006068_ref007","doi-asserted-by":"crossref","unstructured":"7. Erdmann M. and Lozano-Perez T. , \u201cOn Multiple Moving Objects\u201d Proc. IEEE Int. Conf. Robotics and Automation 1419\u20131424 (1986).","DOI":"10.21236\/ADA196213"},{"key":"S0263574700006068_ref013","first-page":"190","article-title":"Solving the Find-Path Problem by Good Representation of Free Space","volume":"13","author":"Brooks","year":"1983","journal-title":"IEEE Trans. Syst."},{"key":"S0263574700006068_ref015","unstructured":"15. Singh S. and Leu M.C. , \u201cOptimal Trajectory Planning and Control of Robotic Manipulators\u201d Proc. Japan\u2013U.S.A., Symp. 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