×
Niculescu, S.-I.; Brogliato, B.

Force measurement time-delays and contact instability phenomenon. (English) Zbl 0936.93031

Eur. J. Control 5, No. 2-4, 279-289 (1999).
The paper starts with some models in robot mechanics and control. The main mathematical problem is to guarantee stability of the neutral functional differential equation in the form \[ \dot x(t)+ (\lambda_1-1)\dot x(t-\tau)= -\lambda_2x_2(t- \tau). \] The resolution is then computed in steps and some estimates are given.
Reviewer: Vladimir Răsvan (Craiova)

Cited in 15 Documents

MSC:

93C23 Control/observation systems governed by functional-differential equations
93D15 Stabilization of systems by feedback
93C85 Automated systems (robots, etc.) in control theory
34K35 Control problems for functional-differential equations

Keywords:

delay-induced instability; feedback stabilization; robot; neutral functional differential equation
Cite Review PDF
Full Text: DOI

References:

[2] An, C. H.; Hollerbach, J. M., The role of dynamic models in cartesian force control of manipulators, Int J Robotic Res, 8, 51-72 (1989)
[3] Anderson, R. J.; Spong, M. W., Bilaterial control of teleoperators with time delay, (Proceedings of IEEE international conference on systems, man and cybernetics. Proceedings of IEEE international conference on systems, man and cybernetics, Beijing, China (1988)), 131-136, vol 1
[4] Boese, F. G., Stability in a special class of retarded difference-differential equations with interval-valued parameters, J Math Anal Appl, 181, 367-368 (1994) · Zbl 0804.34067
[5] Brogliato, B., Nonsmooth mechanics: models, dynamics, control (1999), CCES, Springer: CCES, Springer London · Zbl 0917.73002
[6] Brogliato, B.; Niculescu, S. I.; Orhant, P., On the control of finite-dimensional mechanical systems with unilateral contraints, IEEE Trans Autom Control, 42, 2, 200-215 (1997) · Zbl 0872.70019
[7] Castelan, W. B.; Infante, E. F., A Lyapunov functional for a matrix neutral difference-differential equation with one delay, J. Diff Eq, 71, 105-130 (1979) · Zbl 0415.34058
[8] Chiaverini, S.; Sciavicco, L., The parallel approach to force-position control of robotic manipulators, IEEE Trans Robotics Autom, 9, 361-373 (1993)
[9] Chiu, D.; Lee, S., Robust optimal impact controller for manipulators, (Proceedings of IEEE. RSJ international conference on intelligent robot systems. Proceedings of IEEE. RSJ international conference on intelligent robot systems, Pittsburgh, PA (August 1995)), 299-304
[10] Colgate, E.; Hogan, N., An analysis of contact instability in terms of passive physical equivalents, (IEEE international conference on robotics and automation. IEEE international conference on robotics and automation, Scottdale (1989)), 404-409
[11] Cruz, M. A.; Hale, J. K., Stability of functional differential equations of neutral type, J. Diff Eq, 7, 334-355 (1970) · Zbl 0191.38901
[12] De Luca, A.; Manes, C., Hybrid force-position control for robots in contact with dynamic environments, (3rd IFAC SYROCO. 3rd IFAC SYROCO, Wien (September 1991)), 16-18
[13] Duffy, J., The fallacy of modem hybrid control theory that is based on’orthogonal complements’ of twist and wrench, J Robotic Syst, 7, 139-144 (1990)
[14] Eppinger, S. D.; Seering, W. P., Three dynamic problems in robot force control, IEEE Trans Robotics Autom, 6, 751-758 (1992)
[15] Fiala, J.; Lumia, R., The effect of time delay and discrete control on the contact stability of simple position controllers, IEEE Trans Autom Control, 39, 870-873 (1994) · Zbl 0800.93843
[16] Fisher, W. D.; Shahid Mujtaba, M., Hybrid position/force control: a correct formulation, Int J Robotics Res, 11, 299-311 (1992)
[17] Gopalsamy, K., A simple stability criterion for linear neutral differential systems, Funkcialaj Ekvacioj, 28, 33-38 (1985) · Zbl 0641.34069
[18] Hale, J. K.; Verduyn Lunel, S. M., Introduction to functional differential equations, Applied Mathematics and Sciences, 99 (1991), Springer: Springer New York
[19] Kazerooni, H., Robust nonlinear impedance control for robot manipulators, (IEEE international conference on robotics and automation. IEEE international conference on robotics and automation, Raleigh, NC, USA (1987)), 741-750
[20] Kolmanovskii, V. B.; Nosov, V. R., On the stability of first order nonlinear equations of neutral type, Prikl Math Mech, 34, 587-594 (1970) · Zbl 0231.34064
[21] Kolmanovskii, V. B.; Nosov, V. R., Stability of functional differential equations. (1986), Academic Press: Academic Press New York · Zbl 0593.34070
[22] Lozano, R.; Brogliato, B., Adaptive hybrid force-position control for redundant manipulators, IEEE Trans Autom Control, 1501-1505 (1992), AC-37 · Zbl 0770.93059
[23] MacClamroch, N. H.; Wang, D., Feedback stabilization and tracking of constrained robots, IEEE Trans Autom Control, 419-426 (1988), AC-33 · Zbl 0648.93045
[24] Melvin, W. R., Lyapunov’s direct method applied to neutral functional differential equations, J Math Anal Appl, 49, 47-58 (1975) · Zbl 0317.34062
[25] Mills, J. K., Stability of robotic manipulators during transition to and from compliant motion, Automatica, 26, 861-874 (1990) · Zbl 0712.70007
[26] Mills, J. K., Stability and control of elastic-joint manipulators during constrained motion tasks, IEEE Trans Robotics Autom, 8, 119-126 (1992)
[27] Mills, J. K.; Lokhorst, D. M., Control of robotic manipulators during general task execution: a discontinuous control approach, Int J Robotics Res, 12, 146-163 (1993)
[28] Niculescu SL, Time-delay systems: qualitative aspects on the stability and stabilization (in French) (1997), ’Nouveaux Essais’ Series, Diderot: ’Nouveaux Essais’ Series, Diderot Paris · Zbl 0912.93001
[29] Niemeyer, G.; Slotine, J. J.E., Stable adaptive teleoperation, IEEE J Ocean Eng, 16, 152-162 (1991)
[30] Raibert, M. H.; Craig, J. J., Hibrid position/force control of manipulators, Trans ASME J Dynam Syst Meas Control, 102, 126-133 (1981)
[31] Sinha, P. R.; Goldenberg, A. A., A unified theory for hybrid control of manipulators, (IEEE international conference on robotics and automation. IEEE international conference on robotics and automation, Atlanta, GE, USA (1993)), 343-34832
[32] Slemrod, M.; Infante, E. F., Asymptotic stability criteria for linear systems of difference-differential equations of neutral type and their discrete analogues, J Math Anal Appl, 38, 399-415 (1972) · Zbl 0202.10301
[33] Visher, D.; Khatib, O., Performance evaluation of force/torque feedback control methodologies, (Proceedings of Robotics and Manipulation Systems’90. Proceedings of Robotics and Manipulation Systems’90, Cracow, Poland (1990))
[34] Volpe, R.; Khosla, P., A theoretical and experimental investigation of impact control for manipulators, Int J Robotics Res, 12, 351-365 (1993)
[35] Volpe, R.; Khosla, P., A theoretical and experimental investigation of explicit torque control strategies for manipulators, IEEE Trans Autom Control, 1634-1649 (1993), AC38
[36] Wang, Y., Dynamic modeling and stability analysis of mechanical sytems with time-varying topologies, ASME J Mech Design, 115, 808-816 (1993)
[37] Wen, J. T.; Murphy, S., Stability analysis of position and force control for robot arms, IEEE Trans Autom Control, 365-371 (1991), AC-36 · Zbl 0737.93053
[38] Wilfinger, L. S.; Wen, J. T.; Murphy, S. H., Integral force control with robustness enhancement, IEEE Control Syst, 14, 31-40 (1994)
[39] Yoshikawa, T., Dynamic hybrid position/force control of robot manipulation: description of hand constraints and calculation of joint driving force, IEEE J Robotics Autom, 3, 386-392 (1987)
[40] Yoshikawa, T.; Surgie, T.; Tanaka, M., Dynamic hybrid position/force control of robot manipulators: controller design and experiment, IEEE J Robotics Autom, 4, 699-705 (1988)
[41] Yun, X., Dynamic state feedback control of constrained robot manipulators, (27th conference on decision and control. 27th conference on decision and control, Austin, TX (1988)), 622-626
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.