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Simplification of manipulator dynamic formulations utilizing a dimensionless method

Published online by Cambridge University Press:  09 March 2009

Yueh-Jaw Lin  and
Hai-Yan Zhang
Yueh-Jaw Lin
Affiliation:
Department of Mechanical Engineering; The University of Akron, Akron, OH 44325 (U.S.A.)
Hai-Yan Zhang
Affiliation:
Department of Mechanical Engineering; The University of Akron, Akron, OH 44325 (U.S.A.)
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Summary

This paper presents a new approach for simplifying dynamic equations of motion of robot manipulators by using a nondimensionalization scheme. With this approach the dynamic analysis is done in a nondimensional space. That is, it is required to establish a dimensionless coordinate system in which the dynamic equations of motion of manipulators are formulated. The characteristic parameters of the manipulators are then defined by choosing proper physical quantities as basic units for nondimensionalization. Within the nondimensional space the Lagrange method is applied to the manipulator to obtain a set of general dimensionless equations of motion. This dimensionless dynamic formulation of manipulators leads to an easier way to simplify the dynamic formulation by neglecting insignificant terms using the order of magnitude comparison. The dimensionless dynamic model and its simplified version of PUMA 560 robot are implemented using the proposed approach. It is found that the simplified dynamic model greatly reduces the computation burden of the inverse dynamics. Simulation results also show that the simplified model is extremely accurate. This implies that the proposed nondimensional simplification emethod is reliable.

Keywords

Dimensionless methodRobot motionDynamic formulationSimplified model
Type
Research Article
Information
Robotica , Volume 11 , Issue 2 , March 1993 , pp. 139 - 147
Copyright
Copyright © Cambridge University Press 1993

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References

Goertz, R.C. and Bevilacqua, F., “A Force-Reflecting Positional Servomechanism” Nucleonics 10, 43–55 (11, 1952).Google Scholar
Vukobratović, M., “How to Control Artificial Anthropo-morphic Systems” IEEE Trans, on Systems, Man and Cybernetics. SMC-3 No. 5, 497–507 (1973).Google Scholar
Vukobratović, M., Stokić, D.Gluhajić, N. and Hristić, D.“One Method of Control for Large-scale Humanoid Systems” Mathematical Biosciences 36, No. 3-4, 175–198 (1977).CrossRefGoogle Scholar
Stokifć, D. and Vukobratovifć, M., “Dynamic Stabilization of Biped Posture” Mathematical Biosciences 44, No. 2, 79–98 (1979).Google Scholar
Vukobratović, M., and Stokić, D., “Significance of Force-Feedback in Controlling Artificial Locomotion Manipulation Systems” IEEE Trans, on Biomedical Engineering BME-27, No. 12, 705–713 (1980).CrossRefGoogle Scholar
Vukobratović, M., and Stokić, D., “Contribution to the Decoupled Control of Large-Scale Mechanical Systems” Automatica Vol. 16, No. 1 9–22 (1980).CrossRefGoogle Scholar
Vukobratović, M. and Stokić, D., Control of Manipulation Robots: Theory and Practice Monograph (Springer-Verlag, Berlin, 1982).CrossRefGoogle Scholar
Vukobratović, M. and Stokić, D., “Is Dynamic Control Needed in Robotics Systems, and if so, to what Extent?” Int. J. Robotics Research 2, No. 2, 18–24 (1983).CrossRefGoogle Scholar
Whitney, D.E., “Historical Perspectives and State of the Art in Robot Force Control” Int. J. Robotics Research 6, No. 1, 3–14 (1987).CrossRefGoogle Scholar
Luh, J., Fisher, W. and Paul, R., “Joint Torque Control by a Direct Feedback for Industrial Robots” IEEE Trans, on Automatic Control AC-28, No. 2, 153–161 (1983).CrossRefGoogle Scholar
Tanie, K., Yokoi, K. and Kaneko, M., “A Position Sensor Based Torque Control Method for a DC Motor with Reduction Gears” Proc. of the IEEE Conference on Robotics and Automation 1867-1870(1988).Google Scholar
Hashimoto, M., “Robot Motion Control Based on Joint Torque Sensing” Proceedings of the IEEE International Conference on Robotics and Automation, Scottsdale, Arizona 1,256-261(1989).Google Scholar
Pfeffer, L., Khatib, O. and Hake, J., “Joint Torque Sensory Feedback in the Control of a Puma Manipulator” IEEE Trans, on Robotics and Automation 5, No. 4, 418–425 (1989).Google Scholar
Vukobratović, M., and Stokić, D., Applied Control of Manipulation Robots: Analysis, Synthesis, and Exercises, Textbook (Springer-Verlag, Berlin, 1989).Google Scholar
Paul, R.P., Robot Manipulators: Mathematics, Program- ming and Control, (The MIT Press, Cambridge, Mass, 1981).Google Scholar
Asada, H., Youcef-Toumi, K. and Lim, S.K., “Joint Torque Measurement of A Direct-drive Arm” Proc. of 23rd IEEE Conference on Decision and Control 1332-1337(1984).CrossRefGoogle Scholar
Vukobratović, M., Stokić, D. and Kirćanski, N., Non-adaptive and Adaptive Control of Manipulation Robots, Monograph (Springer-Verlag, Berlin, 1985).Google Scholar
Stokić, D. and Vukobratović, M., “Robustness of Decentralized Robot Controller to Payload Variation” J. Robotic System 5, No. 5, 471–495 (1988).Google Scholar
Timćenko, A., Kirćanski, N. and Vukobratović, M., “A Two-Step Algorithm for Generating Efficient Manipulator Models in Symbolic Form” Proc. of the IEEE Conference on Robotics and Automation, Sacramento 1887-1892(1991).Google Scholar
Wu, C. and Paul, R., “Manipulator Compliance Based on Joint Torque Control” Proc. of the 19th IEEE Conf. on Decision and Control, Albuquerque, NM 1,88-94(1980).Google Scholar
Kosuge, K., Takeuchi, H. and Furuta, K., “Motion Control of a Robot Arm Using Joint Torque Sensors” IEEE Trans. On Robotics and Automation 6, No. 2, 258–263 (1990).Google Scholar
Timofeev, A.V. and Ekalo, Yu. V., “Stability and Stabilization of Programmed Motion of Robot Manipulators” (in Russian), Automatika and Telemechanika No. 10., 148–156 (1976).Google Scholar
Hewit, R.J. and Burdess, S.J., “Fast Dynamic Decoupled Control for Robotics, Using Active Force Control” Mechanism and Machine Theory 16, No.5, 535–542(1981).CrossRefGoogle Scholar
McInroy, J.E. and Saridis, G.N., “Acceleration and Torque Feedback for Robotic Control: Experimental Results” J. Robotic Systems 7, No. 6, 813–832 (1990).Google Scholar
Kaneko, M., Yokoi, K. and Tanie, K., “On a New Torque Sensor for Tendon Drive Fingers” IEEE Trans, on Robotics and Automation 6, No. 4, 501–507 (1990).Google Scholar
Salisbury, J.K. and Craig, J.J., “Articulated hands: Force control and Kinematic Issues” J. Robotics Research 1, No. 1, 4–17 (1982).Google Scholar
Kaneko, M., Patsch, W., Kegel, G. and Tolle, H., “Input-dependent Stability on Joint Torque Control of Robot Hand”, Proc. IEEE Int. Conf. on Robotics and Automation, Cincinatta 1057-1062(1990).Google Scholar
Mason, M.T., “Compliance and Force Control for Computer Controlled Manipulators” IEEE Transaction on Systems, Man and Cybernetics SMC-11, No. 6, 418–432 (1981).CrossRefGoogle Scholar
Raibert, M.H. and Craig, J.J., “Hybrid Position/Force Control of Manipulators” ASME J. Dynamic Systems, Measurement, and Control 102, 126–133 (06, 1981).Google Scholar
Drake, H., “The Use of Compliance in a Robot Assembly System” IFAC Symposium on Information and Control Problems in Manufacturing Technology, Tokyo, 412–416 (1977).Google Scholar
De Schutter, J., “Compliant Robot Motion: Task Formulation and Control” Ph. Thesis (Katholieke Universitiet, Leuven, 1986).Google Scholar
Hogan, N., “Impedance Control: An Approach to Manipulation: Part I Theory, Part II-Implementation, Part III-Applications”. Trans. ASME J. Dynamic Systems, Measurement, and Control 107, 1–24 (1985).Google Scholar
Stokić, D.M., Vukobratovi“, M.K. “Implementation of Force Feedback in Manipulation Robots”, Int. J. Robotic Research No. 1, 66–76 (1986).CrossRefGoogle Scholar
Nevins, J. and Whitney, D.E., “The Force Vector Assembler Concept” Proc. of the First International Conference on Robots and Manipulators, Udine,Italy 273-288(1973).Google Scholar
Vukobratović, M. and Vujić, D., “Contribution to Solving Dynamic Robot Control in A Machining Process” Mechanism and Machine Theory 22, No. 5, 421-429 (1987).Google Scholar
Stokić, D., Vukobratović, M., Vujić, D., Rodić, A. and Surdilović, D., “Dynamic Models in Simulation and Synthesis of Position/Force Control of Robots” Proc. of the 8th CISM-IFToMM Symposium on Theory and Practice of Robots and Manipulators, Cracow 193-200(1990).Google Scholar
An, C.H., Atkeson, C.G. and Hollerbach, J.M., Model- Based Control of a Robot Manipulator (Cambridge, Mass, MIT Press, 1988).Google Scholar
An, C.H. and Hollerbach, J.M., “The Role of Dynamic Models in Cartesian Force Control of Manipulators” Int. J. Robotics Research 8, No. 4, 51–72 (1989).Google Scholar
Stokić, D.M., “Constrained motion control of robots-A Contribution” Robotica 9, Part 2, 157–163 (1990).Google Scholar
Khatib, O., “A Unified Approach for Motion and Force Control of Robot Manipulators: The Operational Space Formulation” IEEE Trans, on Robotics and Automation 3, No. 1, 43–53 (1987).Google Scholar
Elosegui, P., Daniel, R.W. and Sharkey, P.M., “Joint Servoing for Robust Manipulator Force Control” Proc. of the IEEE International Conference on Robotics and Automation, Cincinnati,Ohio246-251(1990).Google Scholar