{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T20:13:41Z","timestamp":1770063221805,"version":"3.49.0"},"reference-count":27,"publisher":"SAGE Publications","issue":"7","license":[{"start":{"date-parts":[[2009,10,22]],"date-time":"2009-10-22T00:00:00Z","timestamp":1256169600000},"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":[[2010,6]]},"abstract":"<jats:p> Steerable needles can be used in medical applications to reach targets behind sensitive or impenetrable areas. The kinematics of a steerable needle are non-holonomic and, in two dimensions, equivalent to a Dubins car with constant radius of curvature. In three dimensions, the needle can be interpreted as an airplane with constant speed and pitch rate, zero yaw, and controllable roll angle. We present a constant-time motion planning algorithm for steerable needles based on explicit geometric inverse kinematics similar to the classic Paden\u2014 Kahan subproblems. Reachability and path competitivity are analyzed using analytic comparisons with shortest path solutions for the Dubins car (for two dimensions) and numerical simulations (for three dimensions). We also present an algorithm for local path adaptation using null-space results from redundant manipulator theory. Finally, we discuss several ways to use and extend the inverse kinematics solution to generate needle paths that avoid obstacles. <\/jats:p>","DOI":"10.1177\/0278364909352202","type":"journal-article","created":{"date-parts":[[2009,10,23]],"date-time":"2009-10-23T00:55:34Z","timestamp":1256259334000},"page":"789-800","source":"Crossref","is-referenced-by-count":96,"title":["Three-dimensional Motion Planning Algorithms for Steerable Needles Using Inverse Kinematics"],"prefix":"10.1177","volume":"29","author":[{"given":"Vincent","family":"Duindam","sequence":"first","affiliation":[{"name":"Departments of EECS and IEOR, University of California at Berkeley, Berkeley, CA, USA"}]},{"family":"Jijie Xu","sequence":"additional","affiliation":[{"name":"GCCIS, Rochester Institute of Technology, New York, USA"}]},{"given":"Ron","family":"Alterovitz","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA"}]},{"given":"Shankar","family":"Sastry","sequence":"additional","affiliation":[{"name":"Departments of EECS and IEOR, University of California at Berkeley, Berkeley, CA, USA"}]},{"given":"Ken","family":"Goldberg","sequence":"additional","affiliation":[{"name":"Departments of EECS and IEOR, University of California at Berkeley, Berkeley, CA, USA"}]}],"member":"179","published-online":{"date-parts":[[2009,10,22]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1177\/0278364908097661"},{"key":"atypb2","volume-title":"Motion Planning in Medicine: Optimization and Simulation Algorithms for Image-Guided Procedures (Springer Tracts in Advanced Robotics, Vol. 50)","author":"Alterovitz, R.","year":"2008"},{"key":"atypb3","volume-title":"Proceedings of the IEEE International Conference on Robotics and Automation","author":"Alterovitz, R."},{"key":"atypb4","volume-title":"Proceedings of the IEEE\/RSJ International Conference on Intelligent Robots and 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