Tracking Control of Robots Revisited Based on Taylor Series and Asymptotic Expansion
محورهای موضوعی : Automation and robotics in manufacturing
1 - Department of Electrical Engineering, Garmsar Branch, Islamic Azad University, Garmsar, Iran
کلید واژه: Taylor series, Actuator Saturation, Adaptive Uncertainty Estimation, Stone-Weierstrass Theorem,
چکیده مقاله :
This paper points out some errors based on the one-dimensional Taylor series for a multi-dimensional function that is used for robots manufacturing. It is argued that the proof of theorem 1 is not mathematically true, and consequently, the obtained results cannot be correct. In addition to this, the stability analysis presented in the paper does not address the saturated area properly. Therein, stability is analyzed separately in saturated and unsaturated operation areas. However, the stability of the closed-loop system may not be guaranteed through these separate analyses, since transitions from saturation area to unsaturated area and vice versa are neglected. This work is an extension of the above paper, based on the revised Taylor series and considering actuator saturation limit in both controller design and stability analysis.
[1] Rigatos, G. Gerasimos, and Busawon, K. 2018. Robotic Manipulators and Vehicles: control, Estimation and Filtering. Studies in Systems, Decision and Control. Springer.
[2] Izadbakhsh, A. 2017. FAT-based robust adaptive control of electrically driven robots without velocity measurements. Nonlinear Dynamics. 89: 289-304.
[3] Khorashadizadeh, S., and Fateh, M. 2017. Uncertainty estimation in robust tracking control of robot manipulators using the Fourier series expansion. Robotica. 35(2): 310-336.
[4] Khorashadizadeh, S., and Majidi, M. 2017. Chaos synchronization using the Fourier series expansion with application to secure communications. AEU - International Journal of Electronics and Communications. 82: 37-44.
[5] Samadi Gharajeh, M. and Jond. H. B. 2020. Hybrid Global Positioning System-Adaptive Neuro-Fuzzy Inference System based autonomous mobile robot navigation. Robotics and Autonomous Systems. 134:103669.
[6] Shi, Q., Lam, H-K., Xuan, Ch, and Chen, M. 2020. Adaptive neuro-fuzzy PID controller based on twin delayed deep deterministic policy gradient algorithm. Neurocomputing. 402: 183-194.
[7] Hoseini, S. M. 2020. Optimal control of linear pantograph-type delay systems via composite Legendre method. Journal of the Franklin Institute. 357(9): 5402-5427.
[8] Khorashadizadeh, S., Majidi, M. 2018. Synchronization of two different chaotic systems using Legendre polynomials with applications in secure communications. Frontiers of Information Technology & Electronic Engineering. 19: 1180–1190.
[9] Chen, X. 2017. Galerkin approximation with Legendre polynomials for a continuous-time nonlinear optimal control problem. Frontiers of Information Technology & Electronic Engineering. 18: 1479–1487.
[10] Ahmadi, S. M. and Fateh, M. 2019. On the Taylor series asymptotic tracking control of robots. Robotica. 37(3):405 – 427.
[11] Royden, H. L. Real Analysis, 2nd. New York: Macmillan, 1968.
