“…The LPM also does not develop sufficiently accurate dynamic model especially for less number of lumped masses and need to increase the number of lumped masses to represent the system well which imposes the difficulty of the modelling process. Even the Lagrangian [120,122,123,127,144,146,147] RLM Lagrange's equation [148][149][150][151][152][153][154][155][156] Newtonian method [150,151,[157][158][159][160] Kinematic method [149,157,158,[161][162][163][164][165][166][167] method is easy and appropriate for obtaining the equations of motion of FLMs, it is essential to use an approximation method to express the deflection of FLMs. Modelling RLMs is much easier than modelling FLMs as RLMs do not have any deflection or error on the manipulator's tip caused by the flexibility of the links.…”
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.
“…The LPM also does not develop sufficiently accurate dynamic model especially for less number of lumped masses and need to increase the number of lumped masses to represent the system well which imposes the difficulty of the modelling process. Even the Lagrangian [120,122,123,127,144,146,147] RLM Lagrange's equation [148][149][150][151][152][153][154][155][156] Newtonian method [150,151,[157][158][159][160] Kinematic method [149,157,158,[161][162][163][164][165][166][167] method is easy and appropriate for obtaining the equations of motion of FLMs, it is essential to use an approximation method to express the deflection of FLMs. Modelling RLMs is much easier than modelling FLMs as RLMs do not have any deflection or error on the manipulator's tip caused by the flexibility of the links.…”
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.
This paper presents a hybrid adaptive approximation-based control (HAAC) strategy for a class of uncertain robotic joints' system. The proposed control structure consists of a robust sliding mode controller and an adaptive approximation-based controller. The robust sliding mode controller is designed by using the super-twisting algorithm, which is a particularly effective method to decrease the chattering caused by the traditional sliding mode control (SMC) and compensate the disturbances. Another improvement of the robust sliding mode controller is that the robust control parameters only subject to the upper bound of the derivative of the external disturbances, rather than choosing a relatively large value. Moreover, the designed adaptive approximation-based controller has the following two distinctive features: 1) the control parameters are designed to be adjusted in real time and 2) the prior knowledge of actual robotic model is not required to be known. These features contribute to compensating the uncertainties. The stability of the closed-loop system is proved by using the Lyapunov theory, and the simulation results demonstrate the effectiveness of the proposed control method. Finally, the proposed HAAC could apply in the experiments of industrial robotic joints' system. INDEX TERMS Hybrid adaptive control, robust sliding mode control, approximation-based control, robotic joints system.
“…Considering a robotic manipulator of n-joint, its dynamic performance can be described by a second order nonlinear differential equation [6]:…”
Section: Dynamic Modelmentioning
confidence: 99%
“…The simulation results prove that this algorithm realize the automatic tracking of modeling error and uncertain interference, and improve the stability of the system. In [6], it combines the PD control with the feed forward control and there is an experiment act on a 2-DOF humanoid manipulator. The simulation results prove that this method successfully reduces the average absolute error of the robotic manipulator.…”
Pages 77-81 77 www.ijntr.org Abstract-The conventional adaptive control algorithm has a very high real-time requirement for six degrees-of-freedom (DOF) series robotic manipulator system. When the unknown parameters of the robotic manipulator are mutated, it is difficult to ensure the stability of the robotic manipulator system. Aiming at this phenomenon, an optimal algorithm based on adaptive robust control is proposed. When the algorithm is applied to the robotic manipulator system, the actual trajectory at the end of the manipulator is as close as possible to the desired trajectory in the simulation. The algorithm is based on the conventional algorithm, the design of the sliding mode surface to reduce the system position error, adding robust control algorithm to compensate for the instability of the system. The simulation results show that the actual trajectory can quickly track the desired trajectory, and the position error approaches zero.Index Terms-six-DOF, adaptive control algorithm, robust control algorithm.
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