Differential algebraic observer-based trajectory tracking for parallel robots via linear matrix inequalities

References

• Abdellatif, H., & Heimann, B. (2009). Advanced model-based control of a 6-DOF hexapod robot: A case study. IEEE/ASME Transactions On Mechatronics, 15(2), 269–279. https://doi.org/https://doi.org/10.1109/TMECH.2009.2024682
   Web of Science ®Google Scholar
• Allouche, B., Dequidt, A., Vermeiren, L., & Dambrine, M. (2017). Modeling and PDC fuzzy control of planar parallel robot: A differential–algebraic equations approach. International Journal of Advanced Robotic Systems, 14(1), 1–13. https://doi.org/https://doi.org/10.1177/1729881416687112
   Web of Science ®Google Scholar
• Alvarez, J., Arceo, J. C., Armenta, C., Lauber, J., & Bernal, M. (2019). An extension of computed-torque control for parallel robots in Ankle reeducation. IFAC-PapersOnLine, 52(11), 1–6. https://doi.org/https://doi.org/10.1016/j.ifacol.2019.09.109
   Google Scholar
• Arceo, J. C., Alvarez, J., Armenta, C., Lauber, J., Cremoux, S., Simoneau-Buessinger, E., & Bernal, M. (2021). Novel solutions on model-based and model-free robotic-assisted ankle rehabilitation. Archives of Control Sciences, 31(1), 5–27. https://doi.org/https://doi.org/10.24425/acs.2021.136878
   Web of Science ®Google Scholar
• Arceo, J. C., Sánchez, M., Estrada-Manzo, V., & Bernal, M. (2018). Convex stability analysis of nonlinear singular systems via linear matrix inequalities. IEEE Transactions on Automatic Control, 64(4), 1740–1745. https://doi.org/https://doi.org/10.1109/TAC.9
   Web of Science ®Google Scholar
• Åström, K., & Wittenmark, B. (2013). Computer-controlled systems: Theory and design. Courier Corporation.
   Google Scholar
• Azar, A. T., Zhu, Q., Khamis, A., & Zhao, D. (2017). Control design approaches for parallel robot manipulators: A review. International Journal of Modelling, Identification and Control, 28(3), 199–211. https://doi.org/https://doi.org/10.1504/IJMIC.2017.086563
   Web of Science ®Google Scholar
• Begovich, O., Sanchez, E. N., & Maldonado, M. (2002). Takagi-Sugeno fuzzy scheme for real-time trajectory tracking of an underactuated robot. IEEE Transactions on Control Systems Technology, 10(1), 14–20. https://doi.org/https://doi.org/10.1109/87.974334
   Web of Science ®Google Scholar
• Bergerman, M. (1996). Dynamics and control of underactuated manipulators.
   Google Scholar
• Boyd, S., Ghaoui, L. E., Feron, E., & Belakrishnan, V. (1994). Linear matrix inequalities in system and control theory (Vol. 15). SIAM: Studies In Applied Mathematics.
   Google Scholar
• Brown, P. N., Hindmarsh, A. C., & Petzold, L. R. (1998). Consistent initial condition calculation for differential-algebraic systems. SIAM Journal on Scientific Computing, 19(5), 1495–1512. https://doi.org/https://doi.org/10.1137/S1064827595289996
   Web of Science ®Google Scholar
• Chang, Y. C., & Chen, B. S. (2000). Robust tracking designs for both holonomic and nonholonomic constrained mechanical systems: Adaptive fuzzy approach. IEEE Transactions on Fuzzy Systems, 8(1), 46–66. https://doi.org/https://doi.org/10.1109/91.824768
   Web of Science ®Google Scholar
• Cheng, H., Yiu, Y. K., & Li, Z. (2003). Dynamics and control of redundantly actuated parallel manipulators. IEEE/ASME Transactions on Mechatronics, 8(4), 483–491. https://doi.org/https://doi.org/10.1109/TMECH.2003.820006
   Web of Science ®Google Scholar
• Codourey, A. (1998). Dynamic modeling of parallel robots for computed-torque control implementation. The International Journal of Robotics Research, 17(12), 1325–1336. https://doi.org/https://doi.org/10.1177/027836499801701205
   Web of Science ®Google Scholar
• Craig, J. J. (2005). Introduction to robotics: mechanics and control, 3/e. Pearson Education International.
   Google Scholar
• De Luca, A., Panzieri, S., & Ulivi, G. (1998). Stable inversion control for flexible link manipulators. In Proceedings. 1998 IEEE International Conference on Robotics and Automation (cat. no. 98ch36146) (Vol. 1, pp. 799–805). IEEE.
   Google Scholar
• Díaz, J. A., & Bernal, M. (2019). A novel LMI computed-torque technique for stabilization of underactuated systems. In Congreso Nacional de Control Automatico (pp. 797–802). IFAC, Asociación de México de Control Automático (AMCA).
   Google Scholar
• Díaz, J. A., Ibarra, J., & Bernal, M. (2020). Improving robustness of computed-torque schemes via lmi-based nonlinear feedback. In 2020 17th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE) (pp. 1–6). IEEE.
   Google Scholar
• Duan, G. R. (2010). Analysis and design of descriptor linear systems (Vol. 23). Springer Science & Business Media.
   Google Scholar
• Gahinet, P., Nemirovski, A., Laub, A. J., & Chilali, M. (1995). LMI control toolbox. Math Works.
   Google Scholar
• Han, S., Wang, H., Tian, Y., & Christov, N. (2020). Time-delay estimation based computed torque control with robust adaptive RBF neural network compensator for a rehabilitation exoskeleton. ISA Transactions, 97, 171–181. https://doi.org/https://doi.org/10.1016/j.isatra.2019.07.030
   PubMed Web of Science ®Google Scholar
• Isidori, A. (1995). Nonlinear control systems (3rd ed.). Springer.
   Google Scholar
• Jiang, B., Karimi, H. R., Yang, S., Gao, C., & Kao, Y. (2020). Observer-based adaptive sliding mode control for nonlinear stochastic Markov jump systems via T–S fuzzy modeling: Applications to robot arm model. IEEE Transactions on Industrial Electronics, 68(1), 466–477. https://doi.org/https://doi.org/10.1109/TIE.41
   Web of Science ®Google Scholar
• Khalil, H. (2014). Nonlinear control. Prentice Hall.
   Google Scholar
• Le, T. D., Kang, H. J., & Suh, Y. S. (2013). Chattering-free neuro-sliding mode control of 2-DOF planar parallel manipulators. International Journal of Advanced Robotic Systems, 10(1), 22. https://doi.org/https://doi.org/10.5772/55102
   Web of Science ®Google Scholar
• Lewis, F., Dawson, D., & Abdallah, C. (2003). Robot manipulator control: Theory and practice. CRC Press.
   Google Scholar
• Lewis, F., & Kamen, E. (1994). Applied optimal control and estimation. IEEE Transactions on Automatic Control, 39(8), 1773–1773.
   Web of Science ®Google Scholar
• Litim, M., Allouche, B., Omari, A., Dequidt, A., & Vermeiren, L. (2014). Sliding mode control of biglide planar parallel manipulator. In 2014 11th International Conference on Informatics in Control, Automation and Robotics (ICINCO) (Vol. 2, pp. 303–310). IEEE.
   Google Scholar
• Litim, M., Omari, A., & Larbi, M. E. A. (2015). Control of 2dof planar parallel manipulator using backstepping approach. CEAI], 17(2), 90–98.
   Google Scholar
• Londhe, P., Singh, Y., Santhakumar, M., Patre, B. M., & Waghmare, L. (2016). Robust nonlinear PID-like fuzzy logic control of a planar parallel (2PRP-PPR) manipulator. ISA Transactions, 63, 218–232. https://doi.org/https://doi.org/10.1016/j.isatra.2016.02.016
   PubMed Web of Science ®Google Scholar
• Merlet, J. P. (2006). Parallel robots (Vol. 128). Springer Science & Business Media.
   Google Scholar
• Nedialkov, N. S., Pryce, J. D., & Tan, G. (2013). DAESA–a matlab tool for structural analysis of differential-algebraic equations: Software. ACM Transactions on Mathematical Software, 41(2), 1–14. https://doi.org/https://doi.org/10.1145/2689664
   Web of Science ®Google Scholar
• Oliveira, M., & Skelton, R. (2001). Stability tests for constrained linear systems. In Perspectives in robust control (Vol. 268, pp. 241–257). Springer-Verlag.
   Google Scholar
• Omran, A., & Elshabasy, M. (2010). A note on the inverse dynamic control of parallel manipulators. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 224(1), 25–32. https://doi.org/https://doi.org/10.1243/09544062JMES1684
   Web of Science ®Google Scholar
• Pantelides, C. C. (1988). The consistent initialization of differential-algebraic systems. SIAM Journal on Scientific and Statistical Computing, 9(2), 213–231. https://doi.org/https://doi.org/10.1137/0909014
   Web of Science ®Google Scholar
• Piltan, F., Yarmahmoudi, M. H., Shamsodini, M., Mazlomian, E., & Hosainpour, A. (2012). PUMA-560 robot manipulator position computed torque control methods using Matlab/Simulink and their integration into graduate nonlinear control and Matlab courses. International Journal of Robotics and Automation, 3(3), 167–191.
   Google Scholar
• Quintana, D., Estrada-Manzo, V., & Bernal, M. (2021). An exact handling of the gradient for overcoming persistent problems in nonlinear observer design via convex optimization techniques. Fuzzy Sets and Systems, 416, 125–140. https://doi.org/https://doi.org/10.1016/j.fss.2020.04.012
   Web of Science ®Google Scholar
• Rabier, P. J., & Rheinboldt, W. C. (2002). Theoretical and numerical analysis of differential-algebraic equations. Handbook of Numerical Analysis, 8, 183–540. https://doi.org/https://doi.org/10.1016/S1570-8659(02)08004-3
   Google Scholar
• Santos, L., & Cortesão, R. (2018). Computed-torque control for robotic-assisted tele-echography based on perceived stiffness estimation. IEEE Transactions on Automation Science and Engineering, 15(3), 1337–1354. https://doi.org/https://doi.org/10.1109/TASE.2018.2790900
   Web of Science ®Google Scholar
• Servín, J., Álvarez, J., & Bernal, M. (2020). Trajectory tracking of parallel robots: A relaxed differential-algebraic-equation approach. In 2020 17th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE) (pp. 1–6). IEEE.
   Google Scholar
• Shang, W., & Cong, S. (2009). Nonlinear computed torque control for a high-speed planar parallel manipulator. Mechatronics, 19(6), 987–992. https://doi.org/https://doi.org/10.1016/j.mechatronics.2009.04.002
   Web of Science ®Google Scholar
• Shin, K., & McKay, N. (1985). Minimum-time control of robotic manipulators with geometric path constraints. IEEE Transactions on Automatic Control, 30(6), 531–541. https://doi.org/https://doi.org/10.1109/TAC.1985.1104009
   Web of Science ®Google Scholar
• Su, Y., Sun, D., & Zheng, C. (2004). Nonlinear trajectory tracking control of a closed-chain manipulator. In Fifth World Congress on Intelligent Control and Automation (IEEE Cat. no. 04ex788) (Vol. 6, pp. 5012–5016). IEEE.
   Google Scholar
• Tanaka, K., & Wang, H. (2001). Fuzzy control systems design and analysis: A linear matrix inequality approach. John Wiley & Sons.
   Google Scholar
• Taniguchi, T., Tanaka, K., & Wang, H. (2001). Model construction, rule reduction and robust compensation for generalized form of Takagi-Sugeno fuzzy systems. IEEE Transactions on Fuzzy Systems, 9(2), 525–537. https://doi.org/https://doi.org/10.1109/91.940966
   Web of Science ®Google Scholar
• Tsai, L. W. (1999). Robot analysis: The mechanics of serial and parallel manipulators. John Wiley & Sons.
   Google Scholar
• Udawatta, L., Watanabe, K., Izumi, K., & Kiguchi, K. (2002). Obstacle avoidance of three-dof underactuated manipulator by using switching computed torque method. Transactions on Control, Automation and Systems Engineering, 4(4), 347–355. https://doi.org/https://doi.org/10.1109/TFUZZ.2002.1006443
   Web of Science ®Google Scholar
• Udawatta, L., Watanabe, K., Izumi, K., & Kiguchi, K. (2003). Control of underactuated robot manipulators using switching computed torque method: GA based approach. Soft Computing, 8(1), 51–60. https://doi.org/https://doi.org/10.1007/s00500-002-0257-8
   Web of Science ®Google Scholar
• Vermeiren, L., Dequidt, A., Afroun, M., & Guerra, T. M. (2012). Motion control of planar parallel robot using the fuzzy descriptor system approach. ISA Transactions, 51(5), 596–608. https://doi.org/https://doi.org/10.1016/j.isatra.2012.04.001
   PubMed Web of Science ®Google Scholar
• Vinogradov, O. (2000). Fundamentals of kinematics and dynamics of machines and mechanisms. CRC press.
   Google Scholar
• Yang, T., Sun, N., & Fang, Y. (2021). Adaptive fuzzy control for a class of MIMO underactuated systems with plant uncertainties and actuator deadzones: Design and experiments. IEEE Transactions on Cybernetics. https://doi.org/https://doi.org/10.1109/TCYB.2021.3050475
   Web of Science ®Google Scholar
• Yao, S., Li, H., Zeng, L., & Zhang, X. (2018). Vision-based adaptive control of a 3-RRR parallel positioning system. Science China Technological Sciences, 61(8), 1253–1264. https://doi.org/https://doi.org/10.1007/s11431-017-9181-9
   Web of Science ®Google Scholar
• Zhao, D., Li, S., & Gao, F. (2008). Fully adaptive feedforward feedback synchronized tracking control for Stewart Platform systems. International Journal of Control, Automation, and Systems, 6(5), 689–701.
   Web of Science ®Google Scholar