Robust adaptive control of robot manipulators using Bernstein polynomials as universal approximator

Abstract

This article presents a robust adaptive controller for electrically driven robots using Bernstein polynomials as universal approximator. The lumped uncertainties including unmodeled dynamics, external disturbances, and nonimplemented control signals (they assumed as a function of time, instead a function of several variables) are represented with this powerful mathematical tool. The polynomial coefficients are then tuned based on the adaptation law obtained in the stability analysis. A comprehensive approach is adopted to include the saturated and unsaturated areas and also the transition between these areas in the stability analysis. As a result, the stability and the performance of the proposed controller have been improved considerably in dealing with actuator saturation. Also, in comparison with a recent paper based on uncertainty estimation using Taylor series, the proposed controller is less computational due to reducing the size of the matrix of convergence rate. A performance evaluation has been carried out to verify satisfactory performance of transient response of the controller.Simulation results on a Puma560 manipulator actuated by geared permanent magnet dc motors have been presented to guarantee its satisfactory performance. K E Y W O R D Sactuator saturation, adaptive uncertainty estimation, Bernstein polynomials, electrically driven robots, stability analysis 1 Int J Robust Nonlinear Control. 2020;30:2719-2735.wileyonlinelibrary.com/journal/rnc

Polynomial-Based Robust Adaptive Impedance Control of Electrically Driven Robots

“…Notice that the set of functions 1, t, t 2 , ...t N 1 form a basis for function for this vector space. Now, substituting (24) and ( 25) into (23), we obtain the output-tracking loop dynamics aṡ…”

“…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.…”

Trajectory-Tracking Control for Manipulators Based on Fuzzy Equivalence and a Terminal Sliding Mode

“…Manipulators are mostly used for heavy-load operations, such as palletizing, handling, and so on, in which small chattering and high torque control ability are required, while the trajectory tracking precision and robustness requirements are insignificant [3]. At this present, some control methods have been used in trajectory tracking for manipulators, mainly including sliding mode control [4] and [5], neural network control [6] to [8], the PID control [9] to [11] and robust control [12] and [13]. In order to reduce the chattering of manipulators under heavy-load operations, a the FETSM control method for manipulators was proposed in this article.…”

Szász–Mirakyan‐based adaptive controller design for chaotic synchronization

“…To solve the aforementioned problems, some robust and adaptive approaches based on uncertainty estimation have been proposed. Function approximation methods like Bernstein polynomials, 21 Fourier series expansion, 22‐25 and differential equations 26,27 are being used in robust adaptive control of a significant number of nonlinear systems. From the classical real analysis' point of view, the Stone–Weierstrass theorem can be applied to guarantee that these architectures contain the universal approximation property.…”