{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T09:56:42Z","timestamp":1777715802941,"version":"3.51.4"},"reference-count":32,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2001,1,1]],"date-time":"2001-01-01T00:00:00Z","timestamp":978307200000},"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":[[2001,1]]},"abstract":"<jats:p>A singularity-robust trajectory generator is presented that, given a prescribed manipulator path and corresponding kinematic solution, computes a feasible trajectory in the presence of kinematic singularities. The resulting trajectory is close to minimum time, subject to individual bounds on joint velocities and accelerations, and follows the path with precision. The algorithm has complexity O(M log M), where M is the number of robot joints, and works using \u201ccoordinate pivoting,\u201d in which the path timing near singularities is controlled using the fastest changing joint coordinate. This allows the handling of singular situations, including linear self-motions (e.g., wrist singularities), where the speed along the path is zero but some joint velocities are nonzero. To compute the trajectory, knot points are inserted along the path, dividing it into intervals, with the knot density increasing near singularities. An appropriate path velocity is then computed at each knot point, and the resulting knot velocity sequence is integrated to yield the path timing. Examples involving the PUMA manipulator are shown.<\/jats:p>","DOI":"10.1177\/02783640122067264","type":"journal-article","created":{"date-parts":[[2003,7,19]],"date-time":"2003-07-19T02:59:46Z","timestamp":1058583586000},"page":"38-56","source":"Crossref","is-referenced-by-count":34,"title":["Singularity-Robust Trajectory Generation"],"prefix":"10.1177","volume":"20","author":[{"given":"John E.","family":"Lloyd","sequence":"first","affiliation":[{"name":"Computer Science Department, University of British Columbia, 201-2366                         Main Mall, Vancouver, B.C., V6T 1Z4, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vincent","family":"Hayward","sequence":"additional","affiliation":[{"name":"Centre for Intelligent Machines, McGill University, 3480 University                         Street, Montr\u00e9al, P.Q., H3A 2A7, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2001,1,1]]},"reference":[{"key":"atypb1","doi-asserted-by":"crossref","unstructured":"Aboaf, E. W., and Paul, R. P. 1987. Living with the singularity of robot wrists . In Proceedings of the IEEE International Conference on Robotics and Automation, pp. 1713\u20131717 .","DOI":"10.1109\/ROBOT.1987.1087792"},{"key":"atypb2","doi-asserted-by":"crossref","unstructured":"Bobrow, J. E., Dubowsky, S., and Gibson, J. S. 1985. Time-optimal control of robotic manipulators along specified paths . International Journal of Robotics Research 4(3): 3\u201317 .","DOI":"10.1177\/027836498500400301"},{"key":"atypb3","unstructured":"Chang, K. S., and Khatib, O. 1995. Manipulator control at kinematic singularities: A dynamically consistent strategy . In Proceedings of the IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 84\u201388 ."},{"key":"atypb4","doi-asserted-by":"crossref","unstructured":"Chevallereau, C. 1996. Feasible trajectories for a nonredundant robot at a singularity . In Proceedings of the IEEE International Conference on Robotics and Automation, pp. 1871\u20131876 .","DOI":"10.1109\/ROBOT.1996.506984"},{"key":"atypb5","doi-asserted-by":"crossref","unstructured":"Chevallereau, C., and Daya, B. 1994. A new method for robot control in singular configurations with motion in any Cartesian direction . In Proceedings of the IEEE International Conference on Robotics and Automation, vol. 4, pp. 2692\u20132697 .","DOI":"10.1109\/ROBOT.1994.350929"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1017\/S026357470001835X"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1177\/027836499101000409"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1109\/87.294335"},{"key":"atypb9","doi-asserted-by":"crossref","unstructured":"Deo, A. S., and Walker, I. D. 1993. Adaptive non-linear least squares for inverse kinematics . In Proceedings of the IEEE International Conference on Robotics and Automation, vol. 1, pp. 186\u2013193 .","DOI":"10.1109\/ROBOT.1993.291981"},{"key":"atypb10","doi-asserted-by":"crossref","unstructured":"Kieffer, J. 1994. Differential analysis of bifurcations and isolated singularities for robots and mechanisms . IEEE Transactions on Robotics and Automation RA-10(1): 1\u201310 .","DOI":"10.1109\/70.285580"},{"key":"atypb11","doi-asserted-by":"crossref","unstructured":"Kircanski, M. V. 1993. Inverse kinematics problem near singularities for simple manipulators: Symbolical damped least-squares solution . In Proceedings of the IEEE International Conference on Robotics and Automation, vol. 1, pp. 974\u2013979 .","DOI":"10.1109\/ROBOT.1993.292102"},{"key":"atypb12","unstructured":"Lloyd, J. E. 1995. Robot trajectory generation for paths with kinematic singularities. Ph.D. diss., Department of Electrical Engineering, McGill University, Montreal, Canada."},{"key":"atypb13","doi-asserted-by":"crossref","unstructured":"Lloyd, J. E. 1996. Using puiseux series to control nonredundant robots at singularities . In Proceedings of the IEEE International Conference on Robotics and Automation, pp. 1877\u20131882 .","DOI":"10.1109\/ROBOT.1996.506985"},{"key":"atypb14","doi-asserted-by":"crossref","unstructured":"Lloyd, J. E. 1998. Desingularization of non-redundant serial manipulator trajectories using puiseux series . IEEE Transactions on Robotics and Automation RA-14(4): 590\u2013600 .","DOI":"10.1109\/70.704227"},{"key":"atypb15","doi-asserted-by":"crossref","unstructured":"Lloyd, J. E., and Hayward, V. 1996. A discrete algorithm for fixed-path trajectory generation at kinematic singularities . In Proceedings of the IEEE International Conference on Robotics and Automation, pp. 2743\u20132748 .","DOI":"10.1109\/ROBOT.1996.506577"},{"key":"atypb16","doi-asserted-by":"crossref","unstructured":"Lloyd, J. E., and Hayward, V. 1998. Removing the singularities of serial manipulators by transforming the workspace . In International Conference on Robotics and Automation, pp. 2935\u20132940 .","DOI":"10.1109\/ROBOT.1998.680733"},{"key":"atypb17","doi-asserted-by":"crossref","unstructured":"Maciejewski, A. A., and Klein, C. A. 1989. The singular value decomposition: Computation and applications to robotics . International Journal of Robotics Research 8(6): 63\u201379 .","DOI":"10.1177\/027836498900800605"},{"key":"atypb18","unstructured":"Murray, R. W., Li, Z., and Shastry, S. 1994. A Mathematical Introduction to Robotic Manipulation. Boca Raton, FL: CRC Press ."},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1115\/1.3143764"},{"key":"atypb20","doi-asserted-by":"crossref","unstructured":"Nenchev, D. N., Tsumaki, Y., Uchiyama, M., Senft, V., and Hirzinger, G. 1996. Two approaches to singularity-consistent motion of nonredundant robotic mechanisms . In Proceedings of the IEEE International Conference on Robotics and Automation, pp. 1883\u20131890 .","DOI":"10.1109\/ROBOT.1996.506986"},{"key":"atypb21","doi-asserted-by":"crossref","unstructured":"Nielsen, L., de Wit, C. C., and Hagander, P. 1990. Controllability issues of robots near singular configurations . In Advances in Robot Kinematics, 2nd International Workshop, pp. 283\u2013290 .","DOI":"10.1007\/978-3-7091-4433-6_32"},{"key":"atypb22","doi-asserted-by":"crossref","unstructured":"O\u2019Neil, K. A., Cheng, Y. C., and Seng, J. 1997. Removing singularities of resolved motion rate control of mechanisms, including self-motion . IEEE Transactions on Robotics and Automation RA-13(5): 741\u2013751 .","DOI":"10.1109\/70.631235"},{"key":"atypb23","doi-asserted-by":"crossref","unstructured":"Pohl, E. D., and Lipkin, H. 1991. A new method of robotic motion control near singularities . In Fifth International Conference on Advanced Robotics (91 ICAR), pp. 405\u2013410 .","DOI":"10.1109\/ICAR.1991.240619"},{"key":"atypb24","doi-asserted-by":"crossref","unstructured":"Preparata, F. P., and Shamos, M. I. 1985. Computational Geometry: An Introduction. New York: Springer-Verlag .","DOI":"10.1007\/978-1-4612-1098-6"},{"key":"atypb25","doi-asserted-by":"crossref","unstructured":"Senft, V., and Hirzinger, G. 1995. Redundant motions of non-redundant robots: A new approach to singularity treatment . In Proceedings of the IEEE International Conference on Robotics and Automation, pp. 1553\u20131558 .","DOI":"10.1109\/ROBOT.1995.525496"},{"key":"atypb26","doi-asserted-by":"crossref","unstructured":"Shin, K. G., and McKay, N. D. 1985. Minimum-time control of robotic manipulators with geometric path constraints . IEEE Transactions on Automatic Control AC-30(6): 531\u2013541 .","DOI":"10.1109\/TAC.1985.1104009"},{"key":"atypb27","doi-asserted-by":"crossref","unstructured":"Slotine, J.J., and Yang, H. S. 1989. Improving the efficiency of time-optimal path-following algorithms . IEEE Transactions on Robotics and Automation RA-5(1): 118\u2013124 .","DOI":"10.1109\/70.88024"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1147\/rd.234.0424"},{"key":"atypb29","doi-asserted-by":"crossref","unstructured":"Tcho\u0144, Krzysztof, and Muszy\u0144ski, Robert. 1998. Singular inverse kinematic problem for robotic manipulators: A normal form approach . IEEE Transactions on Robotics and Automation RA-14(1): 93\u2013104 .","DOI":"10.1109\/70.660848"},{"key":"atypb30","doi-asserted-by":"crossref","unstructured":"Tumeh, Z. S., and Alford, C. O. 1988. Solving for manipulator joint rates in singular positions . In Proceedings of the IEEE International Conference on Robotics and Automation, pp. 987\u2013992 .","DOI":"10.1109\/ROBOT.1988.12189"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1115\/1.3152644"},{"key":"atypb32","doi-asserted-by":"crossref","unstructured":"Wolovich, W. A., and Elliott, H. 1984. A computational technique for inverse kinematics . In Proceedings of the 23rd IEEE Conference on Decision and Control, pp. 1359\u20131363 .","DOI":"10.1109\/CDC.1984.272258"}],"container-title":["The International Journal of Robotics Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/02783640122067264","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/02783640122067264","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T10:16:28Z","timestamp":1777457788000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/02783640122067264"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,1]]},"references-count":32,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2001,1]]}},"alternative-id":["10.1177\/02783640122067264"],"URL":"https:\/\/doi.org\/10.1177\/02783640122067264","relation":{},"ISSN":["0278-3649","1741-3176"],"issn-type":[{"value":"0278-3649","type":"print"},{"value":"1741-3176","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,1]]}}}