The actual impedance control scheme has been derived by resorting  to an inverse dynamics strategy with contact force and moment measurement, with the adoption of  an  inner loop on end-effector position and orientation aimed at dis- turbance rejection. An  experimental study has been carried out on an  indus- trial robot with open control architecture and forcehorque sensor. The numerical results of a case study have demon- strated the good performance of the robot manipulator when its end effector comes into contact with a compliant surface of unknown location. As well known, impedance control represents an  indirect way of  controlling the interaction force. Future research efforts will thus be  devoted to  apply  the findings of  the present work  to the force control problem, i.e. when  the contact force and moment are required to reach a desired value. Acknowledgments This work was  supported by  Minister0 dell’Universit2  e della Ricerca Scientijka e Tecnologica. References [I] N. Hogan, “Impedance control: An  approach  to ma- nipulation, Parts 1-111,”  ASME J.  of  Dynamic Systems, Measurement, and Control, vol. 107,  pp. 1-24,  1985. [2] J.K. Salisbury, “Active  stiffness control of  a manipu- lator in Cartesian coordinates,” Proc. 19th IEEE Con$ Decision and Control,  Albuquerque, NM, 1980, pp. 95- 100. [3]  0. Khatib, “A  unified approach for motion  and  force control of  robot manipulators: The operational space formulation,” IEEE  J.  of  Robotics and  Automation, [4] L. Sciavicco and B. Siciliano, Modeling and Control of Robot Manipulators, McGraw-Hill, New York, NY, 1996. [5]  P.C.  Hughes,  Spacecraft Attitude  Dynamics, Wiley, New York, NY,  1996. [6]  J.T.-Y. Wen  and  K.  Kreutz-Delgado, “The attitude control problem,” IEEE  Trans. on Automatic Control, [7]  0.  Egeland and J.-M. Godhavn, “Passivity-based adap- tive attitude control of a rigid spacecraft,”  IEEE Trans. on Automatic Control, vol. 39, pp. 842-846,  1994. [8]  J.S.-C. Yuan, “Closed-loop manipulator control using quaternion feedback,”  IEEE J. of  Robotics andAutoma- tion, vol. 4, pp. 434-440, 1988. [9] J. LonEariC, “Normal forms of stiffness and compliance matrices,”  IEEE J. of  Robotics and Automution, vol. 3, [  101 E.D. Fasse, “Simplification  of compliance selection us- ing spatial compliance control,” Proc. ASME Dynamic Systems and Control Division, vol. 57-1, pp. 193-198, 1995. [Ill E.D. Fasse  and  J.F. Broenink,  “A  spatial impedance controller for robotic manipulation,” IEEE Trans. on Robotics and Automation,  to appear, 1997. [12]  J.Y.S. Luh, M.W. Walker, and R.P.C. Paul, “Resolved- acceleration control of mechanical manipulators,”  IEEE Trans.  on Automatic Control, vol.  25, pp.  468-474, 1980. [13] W.-S. Lu  and Q.-H. Meng, “Impedance control with adaptation for robotic manipulators,” IEEE  Trans. on Robotics andAutomation, vol. 7, pp. 408-415, 1991. [  141  J.-J.E. Slotine and W.  Li, Applied Nonlinear Control, Prentice-Hall, Englewoods Cliffs, NJ, 1991. [  151 G. Antonelli, F. Caccavale, and P. Chiacchio, “Experi- mental estimation of dynamic parameters for an indus- trial manipulator,”  Proc. 2nd IMACS Symp. on Mathe- matical Modelling, Vienna, A, 1997, pp. 667-672. vol. 3, pp. 43-53,  1987. vol. 36, pp. 1148-1162,1991. pp. 567-572,1987.
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