A critical review of modelling methods for flexible and rigid link manipulators

Abstract

Mathematical modelling plays an important role for robotic manipulators in order to design their particular controllers. Also, it is hard challenge to obtain an accurate mathematical model or obtain a suitable modelling method in such vast field. Thus, this critical review is advantageous and indispensable for researchers who are interested in the area to gain fruitful knowledge on the mathematical modelling methods. This paper is classified based on the type of robotic manipulators such as flexible link manipulators (FLMs), rigid link manipulators (RLMs) and hybrid manipulators which involves rigid links and flexible links. The used modelling methods for FLMs are the assumed mode method, the finite element method, and the lumped parameter method as approximation techniques which are well explained and reviewed. The Lagrangian method has inclusive explanation and review which is widely participated for obtaining the dynamic equations of FLMs, and it is appropriate and commonly employed for modelling RLMs. The Newtonian method, the forward kinematic, and the inverse kinematic are also well discussed and reviewed which are suitable and commonly employed for modelling RLMs. The critical discussion of 170 articles reported in this paper guides researchers to select the suitable method for modelling. This paper reviews the published articles in the period of 2010-2020 except for few older articles for the need of providing essential theoretical knowledge. The advantages and disadvantages of each method are well summarized at the end of the paper. The intelligent identification methods are briefly discussed due to the lack of publications especially on the period of 2010-2020.

Nonlinear Tracking Control Algorithm for Dynamical Output Systems Manipulated by the Hardly Constrained Oscillatory Actuator

“…In many mechanical engineering applications in the feld of robotics, haptics, industrial machining, instrumentation, and the optical industry, vibration-sensitive equipment might be mounted on one or more fexible co-operative arms carried by the moving support [1][2][3][4][5]. Generally, ignoring mechanical phenomena, such as deformation and vibration, causes poor performance or even the controller instability, when using fexible components in mechanical systems such as robotic arms [6][7][8]. In order to control the vibrations of fexible systems, from the point of view of installation (mounting) techniques of sensors and actuators, the command control input can be applied into the system as a distributed input or as a concentrated (point) input.…”

“…On the other hand, in the approach of the concentrated command control input, sensors and actuators are usually installed at a limited number of points within the boundaries of the fexible system, and it is possible that stabilization and tracking control can be performed successfully by controlling the boundaries. Among the most important methods of mathematical modeling and control of fexible systems, modal methods, the method of assume modes, the linear or nonlinear fnite elements method, the method of lines, and variable separation methods, can be mentioned [7,8]. Another technique of mechanical systems' control with fexible arms is the boundary control method, in which the dynamic equations of the system that are in the form of PDE are used directly by methods such as functional analysis, operators' techniques, and the semigroup theory, and the diferential geometry calculus is included in the design of the control system [9,10].…”

Feedback control of actuation‐constrained moving structure carrying Timoshenko beam

“…In the second method, each PDE of the system is converted to a system of ODEs. In fact, the second method is a finite‐dimensional approximation of the real infinite‐dimensional system 16 . It can be performed using the methods of reduced order modeling (ROM) such as AMM, FEM and so forth.…”

Vibration control of a translational coupled double flexible beam system using sliding mode neural network fuzzy control

“…Lou et al (2020) presented a general electricity-structure-fluid coupled model of a cantilever with partially distributed actuators by using the AMM. For a given flexible manipulator system, it is a difficult problem to select the appropriate modal eigen function (Lee and Alandoli, 2020). Therefore, the AMM is recommended for manipulators with uniform cross-sectional geometry and single-link flexible manipulators.…”