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The use of the Adams\u2010Moulton predictorcorrector scheme leads to a fourth\u2010order trajectory following in the joint space. The implementation of a strict descent feature for the trajectory error at the end\u2010effector level contributes to the robustness of the algorithm near singularities. The execution of this algorithm is about 2.7 times faster than that of Gupta and Kazerounian,<jats:sup>16<\/jats:sup>with much of the speed up coming from the use of software optimizations. Several issues related to the accuracy, convergence, speed, real\u2010time computation, and portability of this algorithm are discussed.<\/jats:p>","DOI":"10.1002\/rob.4620080203","type":"journal-article","created":{"date-parts":[[2007,7,6]],"date-time":"2007-07-06T10:59:46Z","timestamp":1183719586000},"page":"159-175","source":"Crossref","is-referenced-by-count":17,"title":["A study of robot inverse kinematics based upon the solution of differential equations"],"prefix":"10.1002","volume":"8","author":[{"given":"H.","family":"Cheng","sequence":"first","affiliation":[]},{"given":"K. C.","family":"Gupta","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2007,3,13]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1980.1102367"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1177\/027836498200100104"},{"key":"e_1_2_1_4_2","unstructured":"D. L.Pieper \u201cThe kinematics of manipulators under computer control \u201d PhD Dissertation Stanford University 1969."},{"key":"e_1_2_1_5_2","first-page":"47","volume-title":"Resolved motion rate control of manipulators and human prosthesis","author":"Whitney D. E.","year":"1969"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1002\/rob.4620010303"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1177\/027836498300200203"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1177\/027836498300200404"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1115\/1.3629602"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1177\/027836498300200302"},{"key":"e_1_2_1_11_2","doi-asserted-by":"crossref","unstructured":"V. K.SinghandK. C.Gupta \u201cA manipulator Jacobian based modified Newton\u2010Raphson algorithm (JMNR) for robot inverse kinematics \u201d Proc. 1989 ASME Design Automation Conf. Montreal September 1989 Vol. 3 pp.327\u2013332.","DOI":"10.1115\/DETC1989-0142"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1177\/027836498500400203"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1115\/1.3140699"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1109\/TSMC.1986.289285"},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.1115\/1.3258791"},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1115\/1.3258708"},{"key":"e_1_2_1_17_2","doi-asserted-by":"crossref","unstructured":"K. C.GuptaandS. M. K.Kazerounian \u201cImproved numerical solutions of inverse kinematics of robots \u201d in International Conf. on Robotics and Automation March 25\u201327 1985 St. Louis MO. pp.743\u2013748.","DOI":"10.1109\/ROBOT.1985.1087237"},{"key":"e_1_2_1_18_2","doi-asserted-by":"publisher","DOI":"10.1002\/rob.4620040403"},{"key":"e_1_2_1_19_2","unstructured":"Y. T.Tsai \u201cA strictly convergent real\u2010time solution for inverse kinematics for robot manipulators \u201d PhD Dissertation The Ohio State University Columbus Ohio 1986."},{"key":"e_1_2_1_20_2","doi-asserted-by":"crossref","unstructured":"K. C.GuptaandV. K.Singh \u201cA numerical algorithm for solving robot inverse kinematics \u201d in 7th IFToMM World Congress Spain Sept.1987 Vol. 2 pp.1203\u20131206;","DOI":"10.1017\/S0263574700005476"},{"key":"e_1_2_1_21_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0263574700005476"},{"key":"e_1_2_1_22_2","unstructured":"K. C.Gupta \u201cA note on position analysis of manipulators \u201d in Proc. 7th Applied Mechanisms Conf. Kansas City 1981;"},{"key":"e_1_2_1_23_2","doi-asserted-by":"publisher","DOI":"10.1016\/0094-114X(84)90003-X"},{"key":"e_1_2_1_24_2","doi-asserted-by":"publisher","DOI":"10.1115\/1.3176034"},{"key":"e_1_2_1_25_2","volume-title":"Applied Numerical Analysis","author":"Gerald C. 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