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Issue No.01 - January-March (2010 vol.3)
pp: 15-27
Amir Haddadi , Queen's University, Kingston
Keyvan Hashtrudi-Zaad , Queen's University, Kingston
ABSTRACT
Available passivity-based robust stability methods for bilateral teleoperation control systems are generally conservative, as they consider an unbounded range of dynamics for the class of passive operators and environments in the complex plane. In this paper, we introduce a powerful 3D geometrical robust stability analysis method based on the notions of wave variables and scattering parameters. The methodology, which was originally a 2D graphical method used in microwave systems for single-frequency analysis [1], is further developed in this paper for teleoperation and haptic systems. The proposed method provides both mathematical and visual aids to determine bounds or regions on the complex frequency response of the passive environment impedance parameters for which a potentially unstable system connected to any passive operator is stable, and vice-versa. Furthermore, the method allows for the design of bilateral controllers when such bounds are known, or can even be utilized when the environment dynamics are active. The geometrical test can also be replaced by an equivalent mathematical condition, which can easily be checked via a new stability parameter. The proposed method results in less conservative guaranteed stability conditions compared to the Llewellyn's criterion; thus, promising a better compromise between stability and performance. The new method is numerically evaluated for two bilateral control architectures.
INDEX TERMS
Bilateral control, teleoperation, robust stability, passivity, absolute stability, impedance, scattering parameters.
CITATION
Amir Haddadi, Keyvan Hashtrudi-Zaad, "Bounded-Impedance Absolute Stability of Bilateral Teleoperation Control Systems", IEEE Transactions on Haptics, vol.3, no. 1, pp. 15-27, January-March 2010, doi:10.1109/TOH.2009.48
REFERENCES
[1] M.L. Edwards and J.H. Sinsky, "A New Criterion for Linear 2-Port Stability Using a Single Geometrically Derived Parameter," IEEE Trans. Microwave Theory and Techniques, vol. 40, no. 12, pp. 2303-2311, Dec. 1992.
[2] D.A. Lawrence, "Stability and Transparency in Bilateral Teleoperation," IEEE Trans. Robotics and Automation, vol. 9, no. 5, pp. 624-637, Oct. 1993.
[3] K. Hashtrudi-Zaad and S.E. Salcudean, "Transparency in Time-Delayed Systems and the Effect of Local Force Feedback for Transparent Teleoperation," IEEE Trans. Robotics and Automation, vol. 18, no. 1, pp. 108-114, Feb. 2002.
[4] L.F. Penin, K. Matsumoto, and S. Wakabayashi, "Force Reflection for Ground Control of Space Robots," IEEE Robotics and Automation Magazine, vol. 7, no. 4, pp. 50-63, Dec. 2000.
[5] R.H. Taylor and D. Stoianovici, "Medical Robotics in Computer-Integrated Surgery," IEEE Trans. Robotics and Automation, vol. 19, no. 5, pp. 765-781, Oct. 2003.
[6] N. Hogan, "Controlling Impedance at the Man/Machine Interface," Proc. IEEE Int'l Conf. Robotics and Automation, pp. 1626-1631, May 1989.
[7] F. Mobasser and K. Hashtrudi-Zaad, "A Method for Online Estimation of Human Arm Dynamics," Proc. IEEE Int'l Conf. Eng. in Medicine and Biology Soc., pp. 2412-2416, 2006.
[8] J. Colgate and N. Hogan, "Robust Control of Dynamically Interacting Systems," Int'l J. Control, vol. 48, no. 1, pp. 65-88, 1988.
[9] J. Yan and S.E. Salcudean, "Teleoperation Controller Design Using $\cal {H_{\infty }}$ -Optimization with Application to Motion-Scaling," IEEE Trans. Control Systems Technology, vol. 4, no. 3, pp. 244-258, May 1996.
[10] K. Hashtrudi-Zaad and S.E. Salcudean, "Analysis of Control Architectures for Teleoperation Systems with Impedance/Admittance Master and Slave Manipulators," Int'l J. Robotics Research, vol. 20, no. 6, pp. 419-445, 2001.
[11] S.I. Niculescu, D. Taoutaou, and R. Lozano, "On the Closed-Loop Stability of a Teleoperation Control Scheme Subject to Communication Time-Delays," Proc. IEEE Conf. Decision and Control, vol. 2, pp. 1790-1795, Dec. 2002.
[12] P. Arcara and C. Melchiorri, "Control Schemes for Teleoperation with Time Delay: A Comparative Study," Robotics and Autonomous Systems, vol. 38, no. 16, pp. 49-64, Jan. 2002.
[13] P.F. Hokayem and M.W. Spong, "Bilateral Teleoperation: An Historical Survey," Proc. IEEE Conf. Decision and Control, vol. 42, no. 12, pp. 2035-2057, Dec. 2006.
[14] R.J. Anderson and M.W. Spong, "Bilateral Control of Teleoperators with Time Delay," IEEE Trans. Automatic Control, vol. 34, no. 5, pp. 494-501, May 1989.
[15] D. Lee and M.W. Spong, "Passive Bilateral Teleoperation with Constant Time Delay," IEEE Trans. Robotics, vol. 22, no. 2, pp. 269-281, Apr. 2006.
[16] J.-H. Ryu, D.-S. Kwon, and B. Hannaford, "Stable Teleoperation with Time-Domain Passivity Control," IEEE Trans. Robotics and Automation, vol. 20, no. 2, pp. 365-373, Apr. 2004.
[17] J.E. Colgate, "Robust Impedance Shaping Telemanipulation," IEEE Trans. Robotics and Automation, vol. 9, no. 4, pp. 374-384, Aug. 1993.
[18] R.J. Adams and B. Hannaford, "Control Law Design for Haptic Interfaces to Virtual Reality," IEEE Trans. Control Systems Technology, vol. 10, no. 1, pp. 3-13, Jan. 2002.
[19] H. Cho and J. Park, "Impedance Control with Variable Damping for Bilateral Teleoperation under Time Delay," JSME Int'l J. Series C, vol. 48, no. 4, pp. 695-703, 2005.
[20] S. Buerger and N. Hogan, "Complementary Stability and Loop Shaping for Improved Human-Robot Interaction," IEEE Trans. Robotics, vol. 23, no. 2, pp. 232-244, Apr. 2007.
[21] G.M.H. Leung, B.A. Francis, and J. Apkarian, "Bilateral Controller for Teleoperators with Time Delay via $\mu$ -Synthesis," IEEE Trans. Robotics and Automation, vol. 11, no. 1, pp. 105-116, Feb. 1995.
[22] S.J. Orfanidis, Electromagnetic Waves and Antennas, http://www.ece.rutgers.edu/orfanidiewa/, 2008.
[23] S.S. Haykin, Active Network Theory. Addison-Wesley, 1970.
[24] H. Khalil, Nonlinear Systems, third ed. Prentice Hall, 2002.
[25] D.M. Pozar, Microwave Engineering, third ed. John Wiley and Sons, 2005.
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