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A nonlinear coordinate transformation that takes into account the complete dynamics with nonholonomic constraints is used in order to obtain a linear system in space coordinates. An input-output feedback linearization inner loop is subsequently designed to transform this system into a linear-point mass system in the coordinates corresponding to the control objectives. A rigorous yet simple approach to motion planning through optimization techniques is presented for these mobile vehicles. The resulting Cartesian trajectory generated from the motion planning algorithm is employed as the reference trajectory in the outer loop, which is designed based on a Lyapunov function candidate. The net result is a base motion controller that gives capabilities to these mobile vehicles not only for tracking a Cartesian trajectory but also to achieve a desired final orientation (docking angle).<\/jats:p>","DOI":"10.1017\/s0263574700016878","type":"journal-article","created":{"date-parts":[[2009,3,10]],"date-time":"2009-03-10T13:13:39Z","timestamp":1236690819000},"page":"529-539","source":"Crossref","is-referenced-by-count":17,"title":["Path planning and control of a mobile base with nonholonomic constraints"],"prefix":"10.1017","volume":"12","author":[{"given":"S.","family":"Jagannathan","sequence":"first","affiliation":[]},{"given":"S. Q.","family":"Zhu","sequence":"additional","affiliation":[]},{"given":"F. L.","family":"Lewis","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2009,3,9]]},"reference":[{"volume-title":"Optimal Control","year":"1986","author":"Lewis","key":"S0263574700016878_ref021"},{"volume-title":"Explicit Representation of the Motion and Robust Path Tracking for Mobile Robot Nonholonomic Systems","year":"1994","author":"Zhu","key":"S0263574700016878_ref019"},{"volume-title":"Control of Robot Manipulators","year":"1993","author":"Lewis","key":"S0263574700016878_ref018"},{"unstructured":"14. Canudas De Wit C. and Samson C. , \u201cPath Following of a 2-DOF Wheeled Mobile Robot Under Kinematic Constraints\u201d Proceedings of the European Control Conference, France (July, 1991) pp. 2084\u20132088.","key":"S0263574700016878_ref014"},{"doi-asserted-by":"crossref","unstructured":"13. Sastry S. and Li Z. , \u201cRobot Motion Planning with Nonholomic Constraints\u201d Proceedings of the 28th Conference on Decision and Control (December, 1989) pp. 211\u2013216.","key":"S0263574700016878_ref013","DOI":"10.1109\/CDC.1989.70105"},{"unstructured":"12. Rouchon P. , Fliess M. , Levine J. and Martin P. , \u201cFlatness and Motion Planning: the Car with n Trailers\u201d Proc. of the 2nd European Control Conference, Groningen (July, 1993).","key":"S0263574700016878_ref012"},{"doi-asserted-by":"publisher","key":"S0263574700016878_ref011","DOI":"10.1109\/9.277235"},{"doi-asserted-by":"crossref","unstructured":"9. Sarkar N. , Yun X. and Kumar V. , \u201cDynamic Path Following: A New Control Algorithm for Mobile Robots\u201d Proc. of the IEEE Conference on Decision and Control (Dec, 1993) pp. 2670\u20132675.","key":"S0263574700016878_ref009","DOI":"10.1109\/CDC.1993.325681"},{"unstructured":"6. Jagannathan S. , Lewis F.L. and Liu K. , \u201cMotion Control and Obstacle Avoidance of a Mobile Robot with an Onboard Manipulator\u201d J. Intelligent Manufacturing Systems (to appear in 94).","key":"S0263574700016878_ref006"},{"doi-asserted-by":"publisher","key":"S0263574700016878_ref015","DOI":"10.1177\/027836498600500106"},{"doi-asserted-by":"publisher","key":"S0263574700016878_ref002","DOI":"10.1109\/9.28014"},{"volume-title":"Applied Non-Linear Control","year":"1991","author":"Slotine","key":"S0263574700016878_ref016"},{"key":"S0263574700016878_ref010","first-page":"11","volume-title":"Control Theory and Singular Riemannian Geometry: New Directions in Applied Mathematics","author":"Brockett","year":"1982"},{"doi-asserted-by":"publisher","key":"S0263574700016878_ref008","DOI":"10.1177\/027836499301200104"},{"doi-asserted-by":"crossref","unstructured":"7. Samson C. and Ait-Abderrahim K. , \u201cFeedback Control of a Nonholonomic Wheeled Cart in Cartesian Space\u201d Proceedings of the 1991 IEEE International Conference on Robotics and Automation (April, 1991) pp. 1136\u20131141.","key":"S0263574700016878_ref007","DOI":"10.1109\/ROBOT.1991.131748"},{"volume-title":"Robot Dynamics and Control","year":"1989","author":"Spong","key":"S0263574700016878_ref017"},{"doi-asserted-by":"crossref","unstructured":"1. De Luca A. and Di Benedetto M.D. , \u201cSome Structural Aspects in the Control of Non-holonomic Systems via Dynamic Compensation\u201d 2nd IFAC Workshop On Systems, Structure and Control (September, 1992) pp. 240\u2013243.","key":"S0263574700016878_ref001","DOI":"10.1016\/B978-0-08-042057-8.50062-8"},{"doi-asserted-by":"crossref","unstructured":"3. Bloch A.M. and McCIamroch N.H. , \u201cControl of Mechanical Systems with Classical Nonholonomic Constraints\u201d Proceedings of the 28th Conference on Decision and Control (December, 1989) pp. 201\u2013205.","key":"S0263574700016878_ref003","DOI":"10.1109\/CDC.1989.70103"},{"volume-title":"An Introduction to the Calculus of Variations","year":"1962","author":"Pars","key":"S0263574700016878_ref020"},{"doi-asserted-by":"crossref","unstructured":"4. Bloch A.M. , Reyhanoglu M. and McCIamroch N.N. , \u201cControl and stabilization of Nonholonomic Caplygin Dynamic Systems\u201d Proceedings of the 30th Conference on Decision and Control (December, 1991) pp. 1127\u20131132.","key":"S0263574700016878_ref004","DOI":"10.1109\/CDC.1991.261519"},{"doi-asserted-by":"crossref","unstructured":"5. d'Andrea-Novel B. , Bastin G. and Campion G. , \u201cModelling and Control of Nonholonomic Wheeled Mobile Robots\u201d Proceedings of the 1991 IEEE International Conference on Robotics and Automation (April 1991) pp. 1130\u20131135.","key":"S0263574700016878_ref005","DOI":"10.1109\/ROBOT.1991.131747"}],"container-title":["Robotica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0263574700016878","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,8]],"date-time":"2025-02-08T04:54:50Z","timestamp":1738990490000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0263574700016878\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,11]]},"references-count":21,"journal-issue":{"issue":"6","published-print":{"date-parts":[[1994,11]]}},"alternative-id":["S0263574700016878"],"URL":"https:\/\/doi.org\/10.1017\/s0263574700016878","relation":{},"ISSN":["0263-5747","1469-8668"],"issn-type":[{"type":"print","value":"0263-5747"},{"type":"electronic","value":"1469-8668"}],"subject":[],"published":{"date-parts":[[1994,11]]}}}