Abstract
The investigations presented in this paper are based on our previousstudies where the modeling and control problems of rigid body manipulatorswere treated through the so-called vector-parametrization of the SO(3)group. The nice property of this parametrization, which also displays a Liegroup structure, is that it drastically simplifies some considerations andreduces the computational burden in solving direct kinematic problems,inverse kinematic problems and dynamic modeling by more than 30 hitherto.This statement, which is valid for models built through vector-parameter,becomes stronger in pure vector-parameter considerations. It is provedadditionally that the computational effectiveness of the vector-parameterapproach increases with the increasing number of the revolute degrees offreedom. Here we show that this can be used successfully in the problems ofelastic joint manipulators where, besides the real n links,nfictious links are included and an additional nrevolute degrees of freedom are involved. The present paper also considersthe role of group representations of the rotation motions in the modelingand control of manipulators with elastic joints. Dynamic models‘through’ vector-parameter and in ‘pure’vector-parameter form are developed and the inverse dynamic problem isdiscussed. It is shown that the nonlinear equations of motion are globallylinearizable by smooth invertible coordinate transformation and nonlinear state feedback.
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References
Angeles, J.: Rational Kinematics, Springer, New York, 1988.
Brockett, R. W.: Lie algebras and Lie group in control theory, in: D. Q. Mayne and R. Brockett (eds), Geometrical Methods in System Theory, 1973, pp. 43–82.
Craig, J. J.: Introduction of Robotics: Mechanics and Control, Addison-Wesley, Reading, MA, 1986.
Dahl, O.: Path following for a flexible joint robot, in: I. Troch, K. Desoyer, and P. Kopacek (eds), Robot Control 1991, Pergamon, 1991, pp. 363–368.
Fedorov, F.: The Lorentz Group, Nauka, Moscow (in Russian), 1979.
Jankowski, K. P. and Brussel, H. V.: An approach to discrete inverse dynamic control of flexible-joint robots, IEEE Trans. on Robot. and Automation, 8(5) (1992), 651–658.
Herve, J. M.: Fundamentals of kinematics of rigid body, in: Proc. 3rd Workshop on Advances in Robot Kinematics, Ferrara, Italy, 1992, pp. 19–26.
Isidori, A.: Nonlinear Control Systems: An Introduction, Lecture Notes in Control and Inf. Sciences, Vol. 72, Springer, Berlin, 1985.
Marino, R. W. and Spong, M. W.: Nonlinear control techniques for flexible joint manipulators: A single link case study, in: Proc. IEEE Conf. Robotics Automation, San Francisco, 1986, pp. 1030–1036.
McCarthy, J. M.: An Introduction to Theoretical Kinematics, MIT Press, Cambridge, MA, 1990.
Mladenova, C.: An approach to description of a rigid body motion, Compt. Rend. Bulg. Acad. Sci., 38(1985), 1657–1660.
Mladenova, C.: Reduction of the computational burden in robot manipulator simulation and control, in: Proc. Vth IFAC Symp. on Robot Control-SYROCO’88, Karlsruhe 1988, pp. 96.1–96.5.
Mladenova, C.: A contribution to the modelling and control of manipulators, J. Intell. Robot. Syst., 3(1990), 349–363.
Mladenova, C.: About the topological structure of SO(3) group, Compt. Rend. Bulg. Acad. Sci., 44(1991), 27–29.
Mladenova, C.: Mathematical modelling and control of manipulator systems, Robot. Comput. Integr. Mgf., 8(1991), 233–242.
Mladenova, C.: Group theoretical methods in manipulator kinematics, in: Proc. 3rd Workshop on Advances in Robot Kinematics, Ferrara, Italy, 1992, pp. 187–193.
Murphy, S. H.: Simulation of space manipulators, in: A. Desrochers (ed.), Intelligent Robotic Systems for Space Exploration, Kluwer Academic Publishers, Boston, 1992, pp. 257–295.
Müler, P. C.: Modellvereinfachung nichtlinearer Systeme, VDI Berichte, 925 (1992), 161–188.
Müler, P. C.: Schätzung und Kompensation von Nichtlinearitytäten, VDI Berichte, 1026(1993), 199–208.
Nocosia, S., Tomei, P., and Tornambe, A.: Observer-based control law for a class of non-linear systems, Int. J. Cont., 51(3) (1990), 553–566.
Nijmeijer, H. and Schaft, A.: Nonlinear Dynamical Control Problems, Springer, New York, 1990.
Olver, P.: Applications of Lie Groups to Differential Equations, Springer, New York, 1986.
Spong, M. W.: Modeling and control of elastic joint robots, Trans. ASME, J. Dyn. Syst. Meas. Cont., 109(1987), 310–319.
Spong, M. W. and Vidyasagar, M.: Robot Dynamic and Control, Wiley, New York, 1989.
Su, R.: On the linear equivalents of nonlinear systems, Syst. Cont. Lett., 2(1981).
Vukobratovic, M. and Potkonjak, V.: Dynamics of Manipulation Robots: Theory and Applications, Scientific Fundamentals of Robotics, Springer, Berlin/Heidelberg/New York, 1982, p. 38.
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Mladenova, C.D., Müller, P.C. Dynamics and Control of Elastic Joint Manipulators. Journal of Intelligent and Robotic Systems 20, 23–44 (1997). https://doi.org/10.1023/A:1007900812069
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DOI: https://doi.org/10.1023/A:1007900812069