Abstract
Remote control has been the most promising yet challenging problem in robotic manipulation. In this paper, the stabilization control problem of a quadruped robot’s manipulator is described as Euler–Bernoulli beam model. Considering time-delay characteristic of remote-control input or networked motion control input, the target system is presented as delay-wave equations. By formulating the equation into beam-transport cascade system without delay, predictor feedback is estimated. Then, the stabilization controller, which achieve the exponential stability, is proposed based on the derived predictor feedback. Both the stability and well-posedeness are proofed through mathematical analysis. Finally, the simulations are conducted and discussed. Results show the efficiency stability of proposed method.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availability
Not applicable.
References
Abdallah, C.,. Dorato, P, Benites-Read, J., Byrne, R. Delayed Positive Feedback Can Stabilize Oscillatory Systems, in: 1993 Am. Control Conf., IEEE (1993): pp. 3106–3107. https://doi.org/10.23919/ACC.1993.4793475.
Aida-zade, K.R., Hashimov, V.A.: Feedback control of the plate heating process with optimization of the locations of sources and control. Autom. Remote Control. 81, 670–685 (2020). https://doi.org/10.1134/S0005117920040098
Auriol, J., Aarsnes, U.J.F., Di Meglio, F., Shor, R.: Robust Control Design of Underactuated 2 × 2 PDE-ODE-PDE Systems. IEEE Control Syst. Lett. 5, 469–474 (2021). https://doi.org/10.1109/LCSYS.2020.3003514
Chu, Y., Liu, F., Qin, L., Pan, Q.: Remote manipulation of a microdroplet in water by near-infrared laser. ACS Appl. Mater. Interfaces. 8, 1273–1279 (2016). https://doi.org/10.1021/acsami.5b09952
Chentouf, B., Han, Z.-J.: On the stabilization of an overhead crane system with dynamic and delayed boundary conditions. IEEE Trans. Automat. Contr. 65, 4273–4280 (2020). https://doi.org/10.1109/TAC.2019.2953782
Chiba, K., Komatsu, T., Kato, H., Nakakita, K.: Remote and feedback control of the flap angle in a wind tunnel test model by optical measurement. Aerospace 7, 1–11 (2020). https://doi.org/10.3390/aerospace7020011
Chen, Z., Huang, F., Chen, W., Zhang, J., Sun, W., Chen, J., Gu, J., Zhu, S.: RBFNN-based adaptive sliding mode control design for delayed nonlinear multilateral telerobotic system with cooperative manipulation. IEEE Trans. Ind. Informatics. 16, 1236–1247 (2020). https://doi.org/10.1109/TII.2019.2927806
Chen, Z., Wang, S., Wang, J., Xu, K., Lei, T., Zhang, H., Wang, X., Liu, D., Si, J.: Control strategy of stable walking for a hexapod wheel-legged robot. ISA Trans. 108, 367–380 (2021). https://doi.org/10.1016/j.isatra.2020.08.033
Correa, M., Cárdenas, D., Carvajal, D., Ruiz-del-Solar, J.: Haptic teleoperation of impact hammers in underground mining. Appl. Sci. 12, 1428 (2022). https://doi.org/10.3390/app12031428
Datko, R.: Not all feedback stabilized hyperbolic systems are robust with respect to small time delays in their feedbacks. SIAM J. Control Optim. 26, 697–713 (1988). https://doi.org/10.1137/0326040
Das, B., Dobie, G. Delay compensated state estimation for Telepresence robot navigation, Rob. Auton. Syst. \textbf{146} 103890 (2021). https://doi.org/10.1016/j.robot.2021.103890.
Dobson, J.: Remote control of cellular behaviour with magnetic nanoparticles. Nat. Nanotechnol. 3, 139–143 (2008). https://doi.org/10.1038/nnano.2008.39
El Rassi, I., El Rassi, J.-M.: A review of haptic feedback in tele-operated robotic surgery. J. Med. Eng. Technol. 44, 247–254 (2020). https://doi.org/10.1080/03091902.2020.1772391
Ferrell, W.R., Sheridan, T.B.: Supervisory control of remote manipulation. IEEE Spectr. 4, 81–88 (1967). https://doi.org/10.1109/MSPEC.1967.5217126
Krstic, M. On compensating long actuator delays in nonlinear control, in: 2008 Am. Control Conf., IEEE, 2008: pp. 2921–2926. https://doi.org/10.1109/ACC.2008.4586939
Krstic, M., Smyshlyaev, A.: Backstepping boundary control for first-order hyperbolic PDEs and application to systems with actuator and sensor delays. Syst. Control Lett. 57, 750–758 (2008). https://doi.org/10.1016/j.sysconle.2008.02.005
Krstic, M. Control of an unstable reaction-diffusion PDE with long input delay, in: Proc. 48h IEEE Conf. Decis. Control Held Jointly with 2009 28th Chinese Control Conf., IEEE,pp. 4452–4457 (2009). https://doi.org/10.1109/CDC.2009.5400098.
Keqin Gu, S.-I. Niculescu, Additional dynamics in transformed time-delay systems, IEEE Trans. Automat. Contr. 45 (2000) 572–575. https://doi.org/10.1109/9.847747.
Kutia, J.R., Stol, K.A., Xu, W.: Aerial manipulator interactions with trees for canopy sampling. IEEE/ASME Trans. Mechatronics. 23, 1740–1749 (2018). https://doi.org/10.1109/TMECH.2018.2837005
Lee, T., Dianat, S.: Stability of time-delay systems. IEEE Trans. Automat. Contr. 26, 951–953 (1981). https://doi.org/10.1109/TAC.1981.1102755
Li, M., Li, S., Ahn, C. K.. Xiang, Z. Adaptive fuzzy event-triggered command-filtered control for nonlinear time-delay systems, IEEE Trans. Fuzzy Syst. 1–1 (2021a). https://doi.org/10.1109/TFUZZ.2021.3052095.
Li, Z., Yue, D., Ma, Y., Zhao, J. Neural-Networks-Based Prescribed Tracking for Nonaffine Switched Nonlinear Time-Delay Systems, IEEE Trans. Cybern. 1–12 (2021b) https://doi.org/10.1109/TCYB.2020.3042232.
Marescaux, J., Leroy, J., Gagner, M., Rubino, F., Mutter, D., Vix, M., Butner, S.E., Smith, M.K.: Transatlantic robot-assisted telesurgery. Nature 413, 379–380 (2001). https://doi.org/10.1038/35096636
Mason, M.T.: Toward Robotic Manipulation. Annu. Rev. Control. Robot. Auton. Syst. 1, 1–28 (2018). https://doi.org/10.1146/annurev-control-060117-104848
Mondie, S., Michiels, W.: Finite spectrum assignment of unstable time-delay systems with a safe implementation. IEEE Trans. Automat. Contr. 48, 2207–2212 (2003). https://doi.org/10.1109/TAC.2003.820147
Nguyen, D.D., Van Chu, D., Van Sy, L.: Dynamic analysis and simulation of the hydraulic control system on the remote-controlled explosive ordnance disposal machine. Int. J. Manuf. Mater. Mech. Eng. 11, 37–54 (2021). https://doi.org/10.4018/IJMMME.2021070103
Schmaus, P., Leidner, D., Kruger, T., Schiele, A., Pleintinger, B., Bayer, R., Lii, N.Y.: Preliminary insights from the METERON SUPVIS justin space-robotics experiment. IEEE Robot. Autom. Lett. 3, 3836–3843 (2018). https://doi.org/10.1109/LRA.2018.2856906
Shang, Y.F., Xu, G.Q.: Stabilization of an Euler-Bernoulli beam with input delay in the boundary control. Syst. Control Lett. 61, 1069–1078 (2012). https://doi.org/10.1016/j.sysconle.2012.07.012
Suh, H., Bien, Z.: Use of time-delay actions in the controller design. IEEE Trans. Automat. Contr. 25, 600–603 (1980). https://doi.org/10.1109/TAC.1980.1102347
Taguchi, E., Ishibashi, Y., Tateiwa, Y., Miyoshi, T., Huang, P. Comparison of Stabilization Control in Cooperation between Remote Robot Systems with Force Feedback, Int. J. Mech. Eng. Robot. Res. \textbf{9}, 87–92 (2020). https://doi.org/10.18178/ijmerr.9.1.87-92.
Wang, Y.L., Han, Q.L.: Network-based modelling and dynamic output feedback control for unmanned marine vehicles in network environments. Automatica 91, 43–53 (2018). https://doi.org/10.1016/j.automatica.2018.01.026
Wang, L., Liu, Y., Gu, K., Wu, T. A radial basis function artificial neural network (RBF ANN) based method for uncertain distributed force reconstruction considering signal noises and material dispersion, Comput. Methods Appl. Mech. Eng. \textbf{364}, 112954 (2020a) https://doi.org/10.1016/j.cma.2020.112954.
Wang, T., Li, Y., Zhang, J., Zhang, Y. A novel bilateral impedance controls for underwater tele-operation systems, Appl. Soft Comput. \textbf{91},106194 (2020b) https://doi.org/10.1016/j.asoc.2020.106194.
Xie, Z., Berseth, G., Clary, P., Hurst, J., van de Panne, M. Feedback Control For Cassie With Deep Reinforcement Learning, in: 2018 IEEE/RSJ Int. Conf. Intell. Robot. Syst., IEEE,pp. 1241–1246 (2018) https://doi.org/10.1109/IROS.2018.8593722
Xu, G.Q., Yung, S.P., Li, L.K.: Stabilization of wave systems with input delay in the boundary control. ESAIM Control. Optim. Calc. Var. 12, 770–785 (2006). https://doi.org/10.1051/cocv:2006021
Yang, C., Xie, Y., Liu, S., Sun, D. Force modeling, identification, and feedback control of robot-assisted needle insertion: a survey of the literature, Sensors (Switzerland). 18 (2018) https://doi.org/10.3390/s18020561.
Zhou, J., Mei, Z.. Miao, J., Mao, J., Wang, L., Wu, D., Sun, D., Zhao, Y. A remote-controlled robotic system with safety protection strategy based on force-sensing and bending feedback for transcatheter arterial chemoembolization, Micromachines. 11 (2020). https://doi.org/10.3390/MI11090805.
Zhang, X., Kim, D., Bang, J., Lee, J.: Time delay compensation of a robotic arm based on multiple sensors for indirect teaching. Int. J. Precis. Eng. Manuf. 22, 1841–1851 (2021). https://doi.org/10.1007/s12541-021-00542-w
Zhou, W., Wang, Y., Liang, Y.: Sliding mode control for networked control systems: a brief survey. ISA Trans. (2021). https://doi.org/10.1016/j.isatra.2020.12.049
Acknowledgements
This work is supported by the National Natural Science Foundation of China (No. 52004034) and Science and Technology Re-search Program of Chongqing Municipal Education Commission (No. KJQN202101413).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
All authors declare no conflicts of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Zhang, L., Zheng, X., Wang, C. et al. Remote closed-loop stabilization of robotic Euler–Bernoulli manipulator through predictor feedback. Int J Intell Robot Appl 7, 631–640 (2023). https://doi.org/10.1007/s41315-023-00287-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s41315-023-00287-x