Hostname: page-component-77c89778f8-fv566 Total loading time: 0 Render date: 2024-07-20T18:44:11.576Z Has data issue: false hasContentIssue false
  • English
  • Français

On Stability of Virtual Torsion Sensor for Control of Flexible Robotic Joints with Hysteresis

Published online by Cambridge University Press:  24 September 2019

Michael Ruderman Open the ORCID record for Michael Ruderman [Opens in a new window]
Michael Ruderman*
Affiliation:
Faculty of Engineering and Science, University of Agder, Norway
*
*Corresponding author. E-mail: michael.ruderman@uia.no
Get access Rights & Permissions [Opens in a new window]

Summary

The aim of the virtual torsion sensor (VTS) is to observe the nonlinear deflection in the flexible joints of robotic manipulators and, by its use, improve positioning control of the joint load. This model-based approach utilizes the motor-side sensing only and, therefore, replaces the load-side encoders at nearly zero hardware costs. For being applied in the closed control loop, the stability and robustness of VTS are most crucial. This work extends the previous analysis by a general case of nonlinear joint stiffness with hysteresis and provides straightforward conditions with respect to the system dynamics. The dissipativity and passivity of the torsion-torque hysteresis map are analyzed and discussed in detail. The absolute stability of VTS inclusion into position control loop is shown based on the equivalent loop transformations and Popov criteria, including the sector conditions. Illustrative numerical examples of the control error dynamics and its convergence are provided.

Keywords

Flexible joint robotHysteresisJoint torsionRobot controlVirtual torsion sensorDissipativity
Type
Articles
Information
Robotica , Volume 38 , Issue 7 , July 2020 , pp. 1191 - 1204
Copyright
© Cambridge University Press 2019

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Hung, J., “Control of industrial robots that have transmission elasticity,” IEEE Trans. Ind. Electron. 38(6), 421–427 (1991).CrossRefGoogle Scholar
Jankovic, M., “Observer based control for elastic joint robots,” IEEE Trans. Robot. Autom. 11(4), 618–623 (1995).CrossRefGoogle Scholar
Spong, M., “Modeling and control of elastic joint robots,” J. Dyn. Syst. Meas. Control 109(4), 310–319 (1987).CrossRefGoogle Scholar
Axelsson, P., Karlsson, R. and Norrlöf, M., “Bayesian state estimation of a flexible industrial robot,” Control Eng. Pract . 20(11), 1220–1228 (2012).CrossRefGoogle Scholar
De Luca, A., Schroder, D. and Thummel, M., “An Acceleration-Based State Observer for Robot Manipulators with Elastic Joints,” In: IEEE International Conference on Robotics and Automation, Roma, Italy (2007) pp. 3817–3823.Google Scholar
Keppler, M., Lakatos, D., Ott, C. and Albu-Schäffer, A., “A Passivity-Based Controller for Motion Tracking and Damping Assignment for Compliantly Actuated Robots,” In: IEEE 55th Conference on Decision and Control (CDC 2016), Las Vegas, NV (2016) pp. 1521–1528.Google Scholar
Kelly, R. and Santibánez, V., “Global regulation of elastic joint robots based on energy shaping,” IEEE Trans. Autom. Control 43(10), 1451–1456 (1998).CrossRefGoogle Scholar
Tomei, P., “A simple PD controller for robots with elastic joints,” IEEE Trans. Autom. Cont. 36(10), 1208–1213 (1991).CrossRefGoogle Scholar
De Luca, A., “Feedforward/Feedback Laws for the Control of Flexible Robots,” In: IEEE International Conference on Robotics and Automation (ICRA), San Francisco, CA, vol. 1 (2000) pp. 233–240.Google Scholar
Dhaouadi, R., Ghorbel, F. and Gandhi, P., “A new dynamic model of hysteresis in harmonic drives,” IEEE Trans. Ind. Electron. 50(6), 1165–1171 (2003).CrossRefGoogle Scholar
Kircanski, N., Goldenberg, A. and Jia, S., “An experimental study of nonlinear stiffness, hysteresis, and friction effects in robot joints with harmonic drives and torque sensors,” In: Experimental Robotics III, vol. 200 (Springer, Berlin, Germany, 1994) pp. 326–340.Google Scholar
Taghirad, H. and Belanger, P., “Modeling and parameter identification of harmonic drive systems,” J. Dyn. Syst. Meas. Control 120(4), 439–444 (1998).CrossRefGoogle Scholar
Wolf, S., Grioli, G., Eiberger, O., Friedl, W., Grebenstein, M., Höppner, H., Burdet, E., Caldwell, D. G., Carloni, R., Catalano, M. G. and Lefeber, D., “Variable stiffness actuators: Review on design and components,” IEEE/ASME Trans. Mechatron . 21(5), 2418–2430 (2016).CrossRefGoogle Scholar
Byrnes, C. I., Isidori, A. and Willems, J. C., “Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems,” IEEE Trans. Autom. Control 36(11), 1228–1240 (1991).CrossRefGoogle Scholar
Hill, D. J. and Moylan, P. J., “Stability results for nonlinear feedback systems,” Automatica 13(4), 377–382 (1977).CrossRefGoogle Scholar
Khalil, H. K., Nonlinear Systems (Pearson, Upper Saddle River, 2001).Google Scholar
Barabanov, N. E. and Yakubovich, V. A., “Absolute stability of control systems having one hysteresis-like nonlinearity,” Avtomatika i Telemekhanika (12), 5–12 (1979).Google Scholar
Gorbet, R., Morris, K. and Wang, D. W. L., “Passivity-based stability and control of hysteresis in smart actuators,” IEEE Trans. Control Syst. Technol 9(1), 5–16 (2001).CrossRefGoogle Scholar
Ouyang, R. and Jayawardhana, B., “Absolute stability analysis of linear systems with Duhem hysteresis operator,” Automatica 50(7), 1860–1866 (2014).CrossRefGoogle Scholar
Oh, J. and Bernstein, D., “Semilinear Duhem model for rate-independent and rate-dependent hysteresis,” IEEE Trans. Autom. Control 50(5), 631–645 (2005).Google Scholar
Ruderman, M., “Compensation of nonlinear torsion in flexible joint robots: Comparison of two approaches,” IEEE Trans. Ind. Electron. 63(9), 5744–5751 (2016).CrossRefGoogle Scholar
Ruderman, M., Bertram, T. and Iwasaki, M.. “Modeling, observation, and control of hysteresis torsion in elastic robot joints,” Mechatronics 24(5), 407–415 (2014).CrossRefGoogle Scholar
Ruderman, M. and Iwasaki, M., “On Identification and Sensorless Control of Nonlinear Torsion in Elastic Robotic Joints,” IEEE 40th Annual Conference Industrial Electronics Society, Washington, DC (2014) pp. 2828–2833.Google Scholar
Ruderman, M. and Iwasaki, M., “Sensorless torsion control of elastic joint robots with hysteresis and friction,” IEEE Trans. Ind. Electron. 63(3), 1889–1899 (2015).CrossRefGoogle Scholar
Ruderman, M., “On Stability and Robustness of Virtual Torsion Sensor (VTS) for Flexible Joint Robots,” IEEE 42nd Annual Conference of the Industrial Electronics Society, Florence, Italy (2016) pp. 6984–6899.Google Scholar
Siciliano, B. and Khatib, O., Springer Handbook of Robotics (Springer, Berlin, Germany, 2016).CrossRefGoogle Scholar
Spong, M., Hutchinson, S. and Vidyasagar, M., Robot Modeling and Control (Wiley, Hoboken, NJ, 2006).Google Scholar
Siciliano, B., Sciavicco, L., Villani, L. and Oriolo, G., Robotics: Modelling, Planning and Control (Springer, Berlin, Germany, 2009).CrossRefGoogle Scholar
Ruderman, M. and Iwasaki, M., “On damping characteristics of frictional hysteresis in pre-sliding range,” In: Journal of Physics: Conference Series, vol. 727 (2016) p. 012014.Google Scholar
Ruderman, M. and Rachinskii, D., “Use of Prandtl-Ishlinskii hysteresis operators for coulomb friction modeling with presliding,” In: Journal of Physics: Conference Series, vol. 811 (2017) p. 012013.Google Scholar
De Luca, A. and Mattone, R., “Actuator Failure Detection and Isolation Using Generalized Momenta,” Proceedings of IEEE International Conference on Robotics and Automation (ICRA 2003), Taipei, Taiwan (2003) pp. 634–639.Google Scholar
De Persis, C. and Isidori, A., “A geometric approach to nonlinear fault detection and isolation,” IEEE Trans. Autom. Control 46(6), 853–865 (2001).CrossRefGoogle Scholar
Bertotti, G. and Mayergoyz, I., The Science of Hysteresis, vol. 1–3. (Academic Press, Dordrecht, 2006).Google Scholar
Ortega, R., Perez, J. A. L., Nicklasson, P. J. and Sira-Ramirez, H., Passivity-Based Control of Euler-Lagrange Systems: Mechanical, Electrical and Electromechanical Applications (Springer, Berlin, Germany, 1998).CrossRefGoogle Scholar
Willems, J. C., “Dissipative dynamical systems part I: General theory,” Rational Mech. Anal . 45(5), 321–351 (1972).CrossRefGoogle Scholar
Slotine, J.-J. and Li, W., Applied Nonlinear Control (Prentice Hall, Upper Saddle River, NJ, 1991).Google Scholar