{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T07:42:26Z","timestamp":1758267746978,"version":"3.38.0"},"reference-count":34,"publisher":"SAGE Publications","issue":"9","license":[{"start":{"date-parts":[[2002,9,1]],"date-time":"2002-09-01T00:00:00Z","timestamp":1030838400000},"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":[[2002,9]]},"abstract":"<jats:p> We study the path planning problem, without obstacles, for closed kinematic chains with n links connected by spherical joints in space or revolute joints in the plane. The configuration space of such systems is a real algebraic variety whose structure is fully determined using techniques from algebraic geometry and differential topology. This structure is then exploited to design a complete path planning algorithm that produces a sequence of compliant moves, each of which monotonically increases the number of links in their goal configurations. The average running time of this algorithm is proportional to n<jats:sup>3<\/jats:sup> . While less efficient than the O (n ) algorithm of Lenhart and Whitesides, our algorithm produces paths that are considerably smoother. More importantly, our analysis serves as a demonstration of how to apply advanced mathematical techniques to path planning problems. <\/jats:p><jats:p> Theoretically, our results can be extended to produce collision-free paths, paths avoiding both link\u2014obstacle and link\u2014link collisions. An approach to such an extension is sketched in Section 4.5, but the details are beyond the scope of this paper. Practically, link\u2014 obstacle collision avoidance will impact the complexity of our algorithm, forcing us to allow only small numbers of obstacles with \u201cnice\u201d geometry, such as spheres. Link\u2014link collision avoidance appears to be considerably more complex. Despite these concerns, the global structural information obtained in this paper is fundamental to closed kinematic chains with spherical joints and can easily be incorporated into probabilistic planning algorithms that plan collision-free motions. This is also described in Section 4.5. <\/jats:p>","DOI":"10.1177\/0278364902021009119","type":"journal-article","created":{"date-parts":[[2003,4,28]],"date-time":"2003-04-28T10:25:30Z","timestamp":1051525530000},"page":"773-789","source":"Crossref","is-referenced-by-count":47,"title":["Complete Path Planning for Closed Kinematic Chains with Spherical Joints"],"prefix":"10.1177","volume":"21","author":[{"given":"J.C.","family":"Trinkle","sequence":"first","affiliation":[{"name":"Department of Computer Science Rensselaer Polytechnic Institute Troy, NY 12180, USA,"}]},{"given":"R. James","family":"Milgram","sequence":"additional","affiliation":[{"name":"Department of Mathematics Stanford University Stanford, CA 94305, USA,"}]}],"member":"179","published-online":{"date-parts":[[2002,9,1]]},"reference":[{"doi-asserted-by":"publisher","key":"atypb1","DOI":"10.1016\/0094-114X(85)90001-1"},{"doi-asserted-by":"publisher","key":"atypb2","DOI":"10.1016\/0094-114X(78)90057-5"},{"volume-title":"The Complexity of Robot Motion Planning","year":"1988","author":"Canny, J.F.","key":"atypb3"},{"volume-title":"Personal communication","year":"2002","author":"Canny, J.F.","key":"atypb4"},{"doi-asserted-by":"publisher","key":"atypb5","DOI":"10.1177\/027836402760475360"},{"doi-asserted-by":"publisher","key":"atypb6","DOI":"10.1109\/70.795789"},{"doi-asserted-by":"publisher","key":"atypb7","DOI":"10.1016\/0094-114X(81)90040-9"},{"doi-asserted-by":"publisher","key":"atypb8","DOI":"10.1177\/027836402760475351"},{"doi-asserted-by":"publisher","key":"atypb9","DOI":"10.1109\/70.406937"},{"volume-title":"Differential Topology","year":"1974","author":"Guillemin, V.","key":"atypb10"},{"volume-title":"Proc. Workshop on Algorithmic Foundations of Robotics","author":"Han, L.","key":"atypb11"},{"volume-title":"Three-dimensional graphics tool for motion design","year":"1994","author":"Iarocci, M.","key":"atypb12"},{"doi-asserted-by":"publisher","key":"atypb13","DOI":"10.4310\/jdg\/1214457034"},{"doi-asserted-by":"publisher","key":"atypb14","DOI":"10.4310\/jdg\/1214459218"},{"volume-title":"Proceedings, Workshop on Algorithmic Foundations of Robotics","author":"Kavraki, L.E.","key":"atypb15"},{"volume-title":"Proc. IEEE International Conference on Robotics and Automation, Vol. 3","author":"Kavraki, L.E.","key":"atypb16"},{"doi-asserted-by":"publisher","key":"atypb17","DOI":"10.1109\/70.508439"},{"doi-asserted-by":"publisher","key":"atypb18","DOI":"10.1007\/978-1-4615-4022-9"},{"doi-asserted-by":"publisher","key":"atypb19","DOI":"10.1177\/02783640122067453"},{"volume-title":"Proc. IEEE International Conference on Robotics and Automation","author":"LaValle, S.M.","key":"atypb20"},{"year":"1994","author":"Lenhart, W.J.","journal-title":"Discrete and Computational Geometry","key":"atypb21"},{"year":"2002","author":"Milgram, R.J.","journal-title":"Homology, Homotopy, and Applications","key":"atypb22"},{"volume-title":"Singular Points of Complex Hypersurfaces (Annals of Mathematics Studies No","year":"1967","author":"Milnor, J.","key":"atypb23"},{"volume-title":"Proc. Workshop on Algorithmic Foundations of Robotics. A. K. Peters","author":"Overmars, M.","key":"atypb24"},{"volume-title":"Planning, Geometry, and Complexity of Robot Motion","year":"1987","author":"Schwartz, J.","key":"atypb25"},{"volume-title":"Dexterous manipulation planning for a planar whole-arm manipulator","year":"1996","author":"Son, W.","key":"atypb26"},{"doi-asserted-by":"publisher","key":"atypb27","DOI":"10.1016\/0094-114X(82)90042-8"},{"doi-asserted-by":"publisher","key":"atypb28","DOI":"10.1115\/1.3259029"},{"doi-asserted-by":"publisher","key":"atypb29","DOI":"10.1115\/1.2912747"},{"doi-asserted-by":"publisher","key":"atypb30","DOI":"10.1109\/70.406939"},{"volume-title":"Proc. IEEE International Conference on Robotics and Automation","author":"Trinkle, J.C.","key":"atypb31"},{"volume-title":"Proc. IEEE International Conference on Intelligent Robots and Systems","author":"Trinkle, J.C.","key":"atypb32"},{"volume-title":"Proc. IEEE International Conference on Robotics and Automation, Vol. 2","author":"Trinkle, J.C.","key":"atypb33"},{"volume-title":"Transactions of Mathematics Monographs, Vol. 98","author":"Vassiliev, V.A.","key":"atypb34"}],"container-title":["The International Journal of Robotics Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0278364902021009119","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0278364902021009119","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,3]],"date-time":"2025-03-03T00:34:57Z","timestamp":1740962097000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/0278364902021009119"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,9]]},"references-count":34,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2002,9]]}},"alternative-id":["10.1177\/0278364902021009119"],"URL":"https:\/\/doi.org\/10.1177\/0278364902021009119","relation":{},"ISSN":["0278-3649","1741-3176"],"issn-type":[{"type":"print","value":"0278-3649"},{"type":"electronic","value":"1741-3176"}],"subject":[],"published":{"date-parts":[[2002,9]]}}}