{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,1,18]],"date-time":"2025-01-18T08:10:40Z","timestamp":1737187840439,"version":"3.33.0"},"reference-count":29,"publisher":"Wiley","issue":"7","license":[{"start":{"date-parts":[[2007,3,13]],"date-time":"2007-03-13T00:00:00Z","timestamp":1173744000000},"content-version":"vor","delay-in-days":5276,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Robotic Syst."],"published-print":{"date-parts":[[1992,10]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The effect of robotic manipulator structural compliance on system stability and trajectory tracking performance and the compensation of this structural compliance has been the subject of a number of publications for the case of robotic manipulator noncontact task execution. The subject of this article is the examination of dynamics and stability issues of a robotic manipulator modeled with link structural flexibility during execution of a task that requires the robot tip to contact fixed rigid objects in the work environment. The dynamic behavior of a general<jats:italic>n<\/jats:italic>degree of freedom flexible link manipulator is investigated with a previously proposed nonlinear computed torque constrained motion control applied, computed based on the rigid link equations of motion. Through the use of techniques from the theory of singular perturbations, the analysis of the system stability is investigated by examining the stability of the \u201cslow\u201d and \u201cfast\u201d subsystem dynamics. The conditions under which the fast subsystem dynamics exhibit a stable response are examined. It is shown that if certain conditions are satisfied a control based on only the rigid link equations of motion will lead to asymptotic trajectory tracking of the desired generalized position and force trajectories during constrained motion. Experiments reported here have been carried out to investigate the performance of the nonlinear computed torque control law during constrained motion of the manipulator. While based only on the rigid link equations of motion, experimental results confirm that high\u2010frequency structural link modes, exhibited in the response of the robot, are asymptotically stable and do not destabilize the slow subsystem dynamics, leading to asymptotic trajectory tracking of the overall system. \u00a9 1992 John Wiley &amp; Sons, Inc.<\/jats:p>","DOI":"10.1002\/rob.4620090705","type":"journal-article","created":{"date-parts":[[2007,7,6]],"date-time":"2007-07-06T13:13:48Z","timestamp":1183727628000},"page":"933-953","source":"Crossref","is-referenced-by-count":31,"title":["Stability and control aspects of flexible link robot manipulators during constrained motion tasks"],"prefix":"10.1002","volume":"9","author":[{"given":"James K.","family":"Mills","sequence":"first","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\/9.1220"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1177\/027836498400300305"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1177\/027836498800700404"},{"key":"e_1_2_1_5_2","doi-asserted-by":"crossref","unstructured":"G.Vukovich andJ. K.Mills \u201cModelling stability and control issues of elastic joint manipulators during contact with a stiff environment \u201d Proc. IEEE Conf. on Decision and Control Honolulu HI 1990 pp.2524\u20132529.","DOI":"10.1109\/CDC.1990.203521"},{"key":"e_1_2_1_6_2","unstructured":"W. J.Book \u201cModelling Design and Control of Flexible Manipulator Arms\u201d Ph.D. thesis Massachusetts Institute of technology Cambridge MA 1974."},{"volume-title":"Dynamics of flexible manipulator arm for the space shuttle","year":"1977","author":"Hughes P. C.","key":"e_1_2_1_7_2"},{"key":"e_1_2_1_8_2","unstructured":"X.Ding T. J.Tarn andA. K.Bejczy \u201cA novel approach to the modelling and control of flexible robot arms \u201d Proc. of IEEE Conf. on Decision and Control Tampa FL 1988 pp.1678\u20131683."},{"key":"e_1_2_1_9_2","unstructured":"G.CesareoandR.Marino \u201cOn the controllability properties of elastic robots \u201d Proc. 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Boston MA 1985 pp.1386\u20131391."},{"key":"e_1_2_1_14_2","doi-asserted-by":"crossref","unstructured":"G. G.Hastings andW. J.Book \u201cA linear dynamic model for flexible robotic manipulators \u201d IEEE Control System Mag. February (1987)61\u201364.","DOI":"10.1109\/MCS.1987.1105233"},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.1177\/027836498400300303"},{"key":"e_1_2_1_16_2","unstructured":"C. H.An andJ. M.Hollerbach \u201cDynamic stability issues in force control of manipulators \u201d Proc. of IEEE International Conf. on Robotics and Automation Rawleigh NC 1987 pp.821\u2013827."},{"key":"e_1_2_1_17_2","doi-asserted-by":"crossref","unstructured":"S. D.Eppinger andW. P.Seering \u201cOn dynamic models of robot force control\u201d Proc. IEEE International Conf. on Robotics and Automation San Francisco CA 1986 pp.29\u201334.","DOI":"10.1109\/ROBOT.1986.1087723"},{"key":"e_1_2_1_18_2","doi-asserted-by":"crossref","unstructured":"N. H.McClamroch \u201cA singular perturbation approach to modelling and control of manipulators constrained by a stiff environment \u201d Proc. of IEEE Conf. on Decision and Control Tampa FL 1989 pp.2407\u20132411.","DOI":"10.1109\/CDC.1989.70609"},{"key":"e_1_2_1_19_2","doi-asserted-by":"crossref","unstructured":"J. K.Mills \u201cControl of robotic manipulators with flexible joints during constrained motion task execution \u201d Proc. of IEEE Conf. on Decision and Control Tampa FL 1989 pp.1676\u20131681.","DOI":"10.1109\/CDC.1989.70433"},{"key":"e_1_2_1_20_2","doi-asserted-by":"crossref","unstructured":"S. D.Eppinger andW. P.Seering \u201cModelling robot flexibility for end\u2010point force control \u201d Proc. of IEEE International Conf. on Robotics and Automation Philadelphia PA 1988 pp.165\u2013170.","DOI":"10.1109\/ROBOT.1988.12042"},{"volume-title":"Control of flexible joint robots: A survey","year":"1990","author":"Spong M. 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K.Mills \u201cImplementation of a discontinuous control law on a robot during collision with a stiff environment \u201d Proc. of IEEE International Conf. on Robotics and Automation Cincinnatti OH 1990 pp.55\u201361."},{"key":"e_1_2_1_28_2","unstructured":"D. M.Lokhorst J. K.Mills andP.Kuzan \u201cA facility for experiments in robot contact task control \u201d Proc. of CSME Mechanical Engineering Forum Toronto 1990 pp.149\u2013153."},{"key":"e_1_2_1_29_2","unstructured":"D. M.Lokhorst \u201cAn Approach to Force and Position Control of Robots: Theory and Experiment \u201d M.A.Sc. thesis University of Toronto Toronto Ontario Canada 1990."},{"key":"e_1_2_1_30_2","unstructured":"J. K.Mills andD. 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