Multivariable Stability of Force-Reflecting Teleoperation: Structures of Finite and Infinite Zeros

Abstract

This paper presents a stability analysis of force-position teleoperation under general end-effector contact. The analysis is based on the finite and infinite zero structure of the multivariable root-locus resulting from modulation of the environment stiffness. The starting point is an analysis of the stability of robot force control, motivated by the observation that the human-operator in a force reflection loop acts as a “force servo,” generating position commands in response to reflected force. Asymptotic root loci properties are used to establish passivity conditions on force feedback to give root locus interpretations of the well-known results that (1) feedback via the inverse joint Jacobian can lead to (kinematic) instability and that (2) passivity is preserved by kinematically proper force feedback through the transpose of the joint angle Jacobian. It is demonstrated that a fully constrained force-position teleoperation loop has an identical infinite zero structure to that of a slave manipulator under kinematically proper force control and that the dominant vibration modes of a force-position loop are fully described by a multivariable analogue of the single-input single-output pseudo-system investigated in a study by Daniel and McAree. Extension of the analysis to cover partial end-effector constraint provides a design tool for teleoperation control and serves to aid selection of teleoperation slave-arms. The paper concludes by giving a passivity condition for multiple-input multiple-output force-position teleoperation for stable contact against all environments.

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References

An, C. H., and Hollerbach, J. M. 1989. The role of dynamic models in Cartesian force control of manipulators . Int. J. Robotics Research. 8(4): 51–72 .

Anderson, R. J., and Spong, M. W. 1992. Asymptotic stability for force reflecting teleoperators with time delay . Int. J. Robotics Research 11: 135–149 .

Armstrong, B., Khatib, O., and Burdick, J. 1986. Explicit dynamic model and inertial parameters of the PUMA 560 arm . Proc. IEEE Int. Conf. Robotics and Automation, San Francisco, CA, pp. 510–518 .

Brooks, T. L. 1990. Telerobot response requirements. A position paper on control requirements for the FTS telerobot. Rep. No. STC/ROB/90-93. Lanham, MD: STX .

Colgate, J. E. 1991. Power and impedance scaling in bilateral manipulation . Proc. IEEE Int. Conf. Robotics and Automation, Sacramento, CA, pp. 2292–2297 .

Daniel, R. W., and McAree, P. R. 1998a. Fundamental limits of performance for force reflecting teleoperation . Int. J. Robotics Research. 17(8): 811–830 .

Daniel, R. W., and McAree, P. R. 1998b. Testing a visual phase advance hypothesis for telerobotics. In Robotics Research: The Eighth International Symposium, ed. Y. Shrirai and S. Hirose, 290–295. Shonan, Japan: Springer-Verlag .

Doulgeri, Z., Fahantidis, N., and Paul, R. P. 1998. Nonlinear stability of hybrid control . Int. J. Robotics Research 17(7): 792–806 .

Eppinger, S. D., and Seering, W. P. 1992. Three dynamic problems in robot force control . IEEE Trans. Robotics and Automation 8(6): 751–758 .

10.

Fischer, P. J. 1993. A novel input device for force control of robots. D.Phil. thesis, Department of Engineering Science, University of Oxford, UK.

11.

Fisher, W. D., and Mujtaba, M. S. 1992. Hybrid position force control: A correct formulation . Int. J. Robotics Research 11(4): 299–311 .

12.

Gibson, C. G., and Hunt, K. H. 1990. Geometry of screw systems 2: Classification of screw systems . Mechanism and Machine Theory 25(1): 11–27 .

13.

Hannaford, B. 1989. Stability and performance tradeoffs in bilateral manipulation . Proc. IEEE Int. Conf. Robotics and Automation, Scotsdale, AZ.

14.

Kouvaritakis, B., and Edmunds, J. M. 1979. Multivariable root locus: A unified approach to finite and infinite zeros . Int. J. Control 29(3): 393–428 .

15.

Kouvaritakis, B., and McFarlane, A.G.J. 1976. Geometric approach to analysis and synthesis of system zeros . Int. J. Control 23(2): 149–166 .

16.

Lawrence, D. A. 1993. Stability and transparency in bilateral teleoperation . IEEE Trans. Robotics and Automation 9(5): 624–637 .

17.

Maciejowski, J. M. 1989. Multivariable Feedback Design. Electronic Systems Engineering Series. Wokingham, UK: Addison-Wesley .

18.

McAree, P. R., and Daniel, R. W. 1998. Stabilizing impacts in force reflecting teleoperation using distance-to-impact estimates . Submitted to Int. J. Robotics Research.

19.

McFarlane, A.G.J., ed. 1980. Complex Variable Methods for Linear Multivariable Feedback Systems. London: Taylor and Francis .

20.

Narendra, K. S., and Annaswamy, A. M. 1989. Stable Adaptive Systems. Information and System Sciences Series. Englewood Cliffs, Prentice-Hall .

21.

Niemeyer, G., and Slotine, J.-J.E. 1991. Stable adaptive teleoperation . IEEE J. Oceanic Engineering 16(1): 152–162 .

22.

Ontañón-Ruiz, J., McAree, P. R., and Daniel, R. W. 1998. Frequency domain consequences of low velocity friction: The non-minimum phase behaviour of geared transmissions . Int. J. Robotics Research 17(12): 1310–1324 .

23.

Owens, D. H. 1978. Feedback and multivariable systems. IEE Control Engineering Series. London: Peter Peregrinus .

24.

Raju, G., Verghese, G., and Sheridan, T. 1989. Design issues in 2-port network models of bilateral remote manipulation . Proc. IEEE Int. Conf. Robotics and Automation, Scotsdale, AZ, pp. 1316–1321 .

25.

Rosenbrock, H. H. 1970. State Space and Multivariable Theory. London: Nelson .

26.

Slotine, J.-J.E., and Li, W. 1991. Applied Nonlinear Control. London: Prentice-Hall International .

27.

Yabuta, T. 1992. Nonlinear basic stability concept of the hybrid position force control scheme for robot manipulators . IEEE Trans. Robotics and Automation 8(5): 663–667 .

28.

Yonghong, B., Daniel, R. W., and McAree, P. R. 1996. Stability analysis of force reflecting telerobotic systems . Proc. IEEE Conf. Intelligent Robots and Systems, Osaka, Japan, pp. 1374–1379 .