Abstract:SummaryThis paper presents a robust tracking controller for electrically driven robots, without the need for velocity measurements of joint variables. Many observers require the system dynamics or nominal models, while a model-free observer is presented in this paper. The novelty of this paper is presenting a new observer–controller structure based on function approximation techniques and Stone–Weierstrass theorem using differential equations. In fact, it is assumed that the lumped uncertainty can be modeled b… Show more
This article addresses the problem of pose and force control in a cooperative system comprised of multiple n-degree-of-freedom (n-DOF) electrically driven robotic arms that move a payload. The proposed controller should be capable of maintaining the position and orientation of the payload in the desired path. In addition, the force exerted by robot end effectors on the object must remain limited. The system has unmodeled dynamics, and measuring the robot joint velocities is impossible. Therefore, a FAT-based observer–controller is designed to estimate the uncertainty and velocities based on universal approximation property of Fourier series expansion. The stability of the system is confirmed based on Lyapunov’s stability theorem. Finally, the proposed adaptive controller–observer is applied on two 3-DOF cooperative robotic arms carrying a payload, and the results are precisely analyzed. The results of the proposed approach are also compared with two state-of-art powerful approximation method.
This article addresses the problem of pose and force control in a cooperative system comprised of multiple n-degree-of-freedom (n-DOF) electrically driven robotic arms that move a payload. The proposed controller should be capable of maintaining the position and orientation of the payload in the desired path. In addition, the force exerted by robot end effectors on the object must remain limited. The system has unmodeled dynamics, and measuring the robot joint velocities is impossible. Therefore, a FAT-based observer–controller is designed to estimate the uncertainty and velocities based on universal approximation property of Fourier series expansion. The stability of the system is confirmed based on Lyapunov’s stability theorem. Finally, the proposed adaptive controller–observer is applied on two 3-DOF cooperative robotic arms carrying a payload, and the results are precisely analyzed. The results of the proposed approach are also compared with two state-of-art powerful approximation method.
“…In this regard, the function approximation technique (FAT) is one of the practical approaches. FAT-based observers are mainly developed based upon Fourier series expansion [22][23][24], differential equations [25,26], and Baskakov operator [27]. In this article, an adaptive FAT-based controller-observer structure will be introduced for robotic manipulators.…”
This article introduces a robust adaptive controller–observer structure for robotic manipulators such that the need for joints speed measurement is removed. Besides, it is presumed that the system model has uncertainties and is subject to disturbances, and the proposed method must eliminate the impact of these factors on the system response. According to this, for the first time in the robotics field, a model-free scheme is developed based on the Bernstein–Stancu polynomial. The universal approximation property of the Bernstein–Stancu polynomial enables it to accurately estimate the lumped uncertainty, including unmodeled dynamics and disturbances. Moreover, to increase the efficiency of the controller–observer structure, adaptive rules have been proposed to update polynomial coefficients. The boundedness of all system errors is proven using the Lyapunov theorem. Finally, the proposed robust Adaptive controller–observer is applied on a planer robot, and the results are precisely analyzed. The results of the proposed approach are also compared with two state-of-art powerful approximation methods.
“…To solve the aforementioned problems, some robust and adaptive approaches based on uncertainty estimation have been proposed. As pointed out in the paper, 10 function approximation methods such as neuro-fuzzy systems, [11][12][13] Szasz-Mirakyan Operator, 14 differential equations, 15,16 Fourier series expansion and Bernstein polynomials [17][18][19][20][21][22][23][24][25] have been utilized in robust adaptive control of many nonlinear systems. The Stone-Weierstrass theorem, from the classical real analysis' point of view, can be used to guarantee that these mathematical tools possess the universal approximation property.…”
SUMMARY
This paper presents a robust adaptive impedance controller for electrically driven robots using polynomials of degree N as a universal approximator. According to the universal approximation theorem, polynomials of degree N can approximate uncertainties including un-modeled dynamics and external disturbances. This fact is completely discussed and proved in this paper. The polynomial coefficients are estimated based on the adaptive law calculated in the stability analysis. A performance evaluation has been carried out to verify satisfactory performance of the controller. Simulation results on a two degree of freedom manipulator have been presented to guarantee its successful implementation.
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