Robust adaptive controller–observer scheme for robot manipulators: a Bernstein–Stancu approach

• Published in: Robotica Vol. 40; no. 5; pp. 1309 - 1325
• Main Authors: Izadbakhsh, Alireza, Nikdel, Nazila
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 01.05.2022
• Subjects: Adaptive control; Approximation; Controllers; Design; Disturbances; Fuzzy logic; Manipulators; Mathematical functions; Methods; Neural networks; Polynomials; Robot arms; Robotics; Robots; Robust control; Systems stability; Uncertainty; Velocity; Bernstein–Stancu operator; function approximation techniques; adaptive control; controller–observer structure
• ISSN: 0263-5747; 1469-8668
• DOI: 10.1017/S0263574721001120

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.