A Review on Fractional-Order Modelling and Control of Robotic Manipulators

Abstract

Robot manipulators are widely used in many fields and play a vital role in the assembly, maintenance, and servicing of future complex in-orbit infrastructures. They are also helpful in areas where it is undesirable for humans to go, for instance, during undersea exploration, in radioactive surroundings, and other hazardous places. Robotic manipulators are highly coupled and non-linear multivariable mechanical systems designed to perform one of these specific tasks. Further, the time-varying constraints and uncertainties of robotic manipulators will adversely affect the characteristics and response of these systems. Therefore, these systems require effective modelling and robust controllers to handle such complexities, which is challenging for control engineers. To solve this problem, many researchers have used the fractional-order concept in the modelling and control of robotic manipulators; yet it remains a challenge. This review paper presents comprehensive and significant research on state-of-the-art fractional-order modelling and control strategies for robotic manipulators. It also aims to provide a control engineering community for better understanding and up-to-date knowledge of fractional-order modelling, control trends, and future directions. The main table summarises around 95 works closely related to the mentioned issue. Key areas focused on include modelling, fractional-order modelling type, model order, fractional-order control, controller parameters, comparison controllers, tuning techniques, objective function, fractional-order definitions and approximation techniques, simulation tools and validation type. Trends for existing research have been broadly studied and depicted graphically. Further, future perspective and research gaps have also been discussed comprehensively.

Optimal Fractional-Order Controller for the Voltage Stability of a DC Microgrid Feeding an Electric Vehicle Charging Station

“…Scholars have proposed various definitions in order to make the concept of fractional order (FO) more accessible, as it can be challenging to comprehend its physical implications. One such definition, known as the Riemann-Liouville (R-L) approach, offers a method to calculate the function's order derivative, aiding our understanding of the underlying principles of FO [23]:…”

Improved Performance of the PMSM Sensorless Control System Based on DTC Strategy and SMC Using Fractional Order and Fractal Dimension Calculus

“…A special type of controller can be obtained by using fractional elements. Thus, a number of advanced integer-order controllers can be described by fractional means, with the following control system performance improvements [15][16][17][18][19][20].…”

A Novel Numerical Scheme for Fractional Bernoulli Equations and the Rössler Model: A Comparative Analysis using Atangana-Baleanu Caputo Fractional Derivative

“…The methods outlined in the literature have demonstrated broad applicability across diverse domains, showcasing their effectiveness in advancing technologies, these methodologies have found resonance in robotics [9], differential equations [39], image processing [21], control systems [35], solving partial differential equations [25,31] and various other interdisciplinary arenas. They have facilitated significant strides in Controlling robotic manipulators with fractional-order modeling [9], offering innovative schemes in order to solve fractional differential equations and chaotic systems [39]. Moreover, these techniques have contributed to the development of cutting-edge edge-detection methodologies using fractional derivatives with with kernels that are both nonlocal and nonsingular [21].…”