Hostname: page-component-74656f9884-8r8nv Total loading time: 0 Render date: 2026-11-07T12:58:15.223Z Has data issue: false hasContentIssue false
  • English
  • Français

Addressing Control Implementation Issues in Robotic Systems Using Adaptive Control

Published online by Cambridge University Press:  14 May 2019

Rameez Hayat Open the ORCID record for Rameez Hayat [Opens in a new window] ,
Marion Leibold  and
Martin Buss
Rameez Hayat*
Affiliation:
Chair of Automatic Control Engineering, Department of Electrical and Computer Engineering, Technical University of Munich, Theresienstr. 90, 80333, Munich, Germany E-mail: marion.leibold@tum.de TUM Institute of Advanced Study, Technical University of Munich, Lichtenbergstrasse 2a, 85748 Garching, Germany E-mail: mb@tum.de
Marion Leibold
Affiliation:
Chair of Automatic Control Engineering, Department of Electrical and Computer Engineering, Technical University of Munich, Theresienstr. 90, 80333, Munich, Germany E-mail: marion.leibold@tum.de
Martin Buss
Affiliation:
Chair of Automatic Control Engineering, Department of Electrical and Computer Engineering, Technical University of Munich, Theresienstr. 90, 80333, Munich, Germany E-mail: marion.leibold@tum.de TUM Institute of Advanced Study, Technical University of Munich, Lichtenbergstrasse 2a, 85748 Garching, Germany E-mail: mb@tum.de
*
*Corresponding author. E-mail: rameez.hayat@tum.de
Rights & Permissions [Opens in a new window]

Summary

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

This paper addresses three control implementation issues for trajectory tracking of robotic manipulators: unmodeled dynamics, unknown input saturation and peaking effects during the transient phase. A model-free first-order robust-adaptive control method is used to deal with the unmodeled dynamics. Robust optimality and stability of the controller are proved using the 𝓗∞ technique and the game-algebraic Riccati equation. An intuitive approach is devised to incorporate the unknown input saturation by modifying the speed of the desired trajectory. The trajectory scaling is performed by using only the state errors. Furthermore, two different techniques are utilized to suppress peaking during the transient response of the trajectory tracking. The first method adds an extra term in the input while the second method uses variable gain to improve the transient response. A systematic procedure for finding the controller parameters is formulated using features, such as rise time and settling time. A three-degree-of-freedom robot manipulator is used for the validation of the proposed controller in simulations and experiments.

Keywords

𝓗∞ optimal controlInput-to-state stabilityAdaptive controlOrbital stabilityComputed torqueEuler–Lagrange

Information

Type
Articles
Information
Robotica , Volume 38 , Issue 1 , January 2020 , pp. 171 - 184
Copyright
© Cambridge University Press 2019 

References

Pchelkin, S. S., Shiriaev, A. S., Robertsson, A., Freidovich, L. B., Kolyubin, S. A., Paramonov, L. V. and Gusev, S. V., “On orbital stabilization for industrial manipulators: Case study in evaluating performances of modified PD+ and inverse dynamics controllers,” IEEE Trans. Control Syst. Technol. 25(1), 101–117 (2017).10.1109/TCST.2016.2554520CrossRefGoogle Scholar
Feng, Y., Yu, X. and Man, Z., “Non-singular terminal sliding mode control of rigid manipulators,” Automatica 38(12), 2159–2167 (2002).10.1016/S0005-1098(02)00147-4CrossRefGoogle Scholar
Hayat, R. and Buss, M.,“Model identification for robot manipulators using regressor-free adaptive control,” UKACC 11th International Conference on Control (UKACC) (2016) pp. 1–7.Google Scholar
Hayat, R., Leibold, M. and Buss, M., “Robust-adaptive controller design for robot manipulators using the 𝓗∞ approach,” IEEE Access 6, 51626–51639 (2018).10.1109/ACCESS.2018.2870292CrossRefGoogle Scholar
Park, J. and Chung, W. K.,“Analytic nonlinear 𝓗∞ inverse-optimal control for Euler–Lagrange system,” IEEE Trans. Robot. Automat. 16(6), 847–854 (2000).10.1109/70.897796CrossRefGoogle Scholar
Choi, Y., Chung, W. K. and Suh, I. H., “Performance and 𝓗∞ optimality of PID trajectory tracking controller for Lagrangian systems,” IEEE Trans. Robot. Automat. 17(6), 857–869 (2001).10.1109/70.976011CrossRefGoogle Scholar
Kim, M. J., Choi, Y. and Chung, W. K., “Bringing nonlinear 𝓗∞ optimality to robot controllers,” IEEE Trans. Robot. 31(3), 682–698 (2015).10.1109/TRO.2015.2419871CrossRefGoogle Scholar
Slotine, J. J. and Li, W., “On the adaptive control of robot manipulators,” Int. J. Robot. Res. 6(3), 49–59 (1987).10.1177/027836498700600303CrossRefGoogle Scholar
Kai, C. Y. and Huang, A. C., “A regressor-free adaptive controller for robot manipulators without Slotine and Li’s modification,” Robotica 31(7), 1051–1058 (2013).10.1017/S0263574713000301CrossRefGoogle Scholar
Huang, A. C., Wu, S. C. and Ting, W. F., “A FAT-based adaptive controller for robot manipulators without regressor matrix: theory and experiments,” Robotica 24(2), 205–210 (2006).10.1017/S0263574705002031CrossRefGoogle Scholar
Shiriaev, A. S., Freidovich, L. B. and Gusev, S. V., “Transverse linearization for mechanical systems with several passive degrees of freedom with applications to orbital stabilization,” American Control Conference(2009) pp. 3039–3044.Google Scholar
Verscheure, D., Demeulenaere, B., Swevers, J., De Schutter, J. and Diehl, M., “Time-optimal path tracking for robots: A convex optimization approach,” IEEE Trans. Automat. Control. 54(10), 2318–2327 (2009).10.1109/TAC.2009.2028959CrossRefGoogle Scholar
Bobrow, J. E., Dubowsky, S. and Gibson, J. S., “Time-optimal control of robotic manipulators along specified paths,” Int. J. Robot. Res. 4(3), 3–17 (1985).10.1177/027836498500400301CrossRefGoogle Scholar
Khalil, Hassan K., “Nonlinear Systems,” (Prentice-Hall, NJ, 1996).Google Scholar
Craig, J. J., “Introduction to Robotics: Mechanics and Control,” (Pearson Prentice Hall, Upper Saddle River, NJ, 2005).Google Scholar
Lewis, F. L., Vrabie, D. and Syrmos, V. L., “Optimal control,” vol. 3 (Wiley, Hoboken, NJ, 2012).10.1002/9781118122631CrossRefGoogle Scholar
Sontag, E. D. and Wang, Y., “On characterizations of the input-to-state stability property,” Syst. Control Lett. 24(5), 351–359 (1995).10.1016/0167-6911(94)00050-6CrossRefGoogle Scholar
Sontag, E. D., “Input to state stability: Basic concepts and results,” In: Nonlinear and Optimal Control Theory (2008) pp. 163–220.10.1007/978-3-540-77653-6_3CrossRefGoogle Scholar
Kim, C. and Lee, K., “Robust control of robot manipulators using dynamic compensators under parametric uncertainty,” Int. J. Innov. Comput. Inf. Control 7(7), 4129–4137 (2011).Google Scholar
Shiriaev, A. S., Freidovich, L. B. and Manchester, I. R., “Can we make a robot ballerina perform a pirouette? Orbital stabilization of periodic motions of underactuated mechanical systems,” Ann. Rev. Control 32(2), 200–211 (2008).10.1016/j.arcontrol.2008.07.001CrossRefGoogle Scholar
Cloutier, J. R., D’souza, C. N. and Mracek, C. P., “Nonlinear Regulation and Nonlinear H Control via the State-Dependent Riccati Equation Technique: Part 1, Theory,” Proceedings of the First International Conference on Nonlinear Problems in Aviation and Aerospace (1996) pp. 117–130.Google Scholar
Xu, X., Zhu, J. J. and Zhang, P., “The optimal solution of a non-convex state-dependent LQR problem and its applications,” PloS One 9(4), e94925 (2014).10.1371/journal.pone.0094925CrossRefGoogle ScholarPubMed
Modares, H. A., Lewis, F. L. and Sistani, M.-B. N., “Online solution of nonquadratic two-player zero-sum games arising in the H control of constrained input systems,” Int. J. Adapt. Control Signal Process. 28(3–5), 232–254 (2014).10.1002/acs.2348CrossRefGoogle Scholar
Na, J., Herrmann, G. and Zhang, K., “Improving transient performance of adaptive control via a modified reference model and novel adaptation,” Int. J. Robust Nonlin. Control 27(8), 1351–1372 (2017).10.1002/rnc.3636CrossRefGoogle Scholar
Basar, T. and Olsder, G. J., “Dynamic noncooperative game theory,” SIAM 23 (1999).Google Scholar
Mahyuddin, M. N., Khan, S. G. and Herrmann, G., “A novel robust adaptive control algorithm with finite-time online parameter estimation of a humanoid robot arm,” Robot. Auton. Syst. 62(3), 294–305 (2014).10.1016/j.robot.2013.09.013CrossRefGoogle Scholar
Ahanda, J. J.-B.M., Mbede, J. B., Melingui, A. and Essimbi, B., “Robust adaptive control for robot manipulators: Support vector regression-based command filtered adaptive backstepping approach,” Robotica. 1–19 (2017).Google Scholar
Chen, B. S., Lee, T. S. and Feng, J. H., “A nonlinear 𝓗∞ control design in robotic systems under parameter perturbation and external disturbance,” Int. J. Control 59(2), 439–461 (1994).10.1080/00207179408923085CrossRefGoogle Scholar
Ogata, K., Modern Control Engineering, 5th edition (Prentice Hall, Upper Saddle River, NJ, 2009).Google Scholar
Zhang, D. and Wei, B., “Design, analysis and modelling of a hybrid controller for serial robotic manipulators,” Robotica 35(9), 1888–1905 (2017).10.1017/S0263574716000564CrossRefGoogle Scholar
Arteaga-Pérez, M. A. and Gutiérrez-Giles, A., “On the GPI approach with unknown inertia matrix in robot manipulators,” Int. J. Control 87(4), 844–860 (2014).10.1080/00207179.2013.861080CrossRefGoogle Scholar
Han, J., “From PID to active disturbance rejection control,” IEEE Trans. Ind. Electron. 56(3), 900–906 (2009).10.1109/TIE.2008.2011621CrossRefGoogle Scholar
Cimen, T., “State-Dependent Riccati Equation (SDRE) control: A survey,” IFAC Proceedings Volumes: Elsevier 41(2), 3761–3775 (2008).10.3182/20080706-5-KR-1001.00635CrossRefGoogle Scholar