Robust task-space control of robot manipulators using Legendre polynomials for uncertainty estimation

Khorashadizadeh, Saeed; Fateh, Mohammad Mehdi

doi:10.1007/s11071-014-1730-5

Cited by 47 publications

(40 citation statements)

References 21 publications

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“…The case study is a SCARA manipulator actuated by permanent magnet DC motors. 28 Simulation 1 deals with the estimation effects of Fourier series. In the simulations, the arm which consists of the first three joints is used to perform the proposed taskspace control law and the fourth joint is locked.…”

Section: Simulation Resultsmentioning

confidence: 99%

Uncertainty estimation in robust tracking control of robot manipulators using the Fourier series expansion

Khorashadizadeh

Fateh

2015

Robotica

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SUMMARYThis paper presents a novel control algorithm for electrically driven robot manipulators. The proposed control law is simple and model-free based on the voltage control strategy with the decentralized structure and only joint position feedback. It works for both repetitive and non-repetitive tasks. Recently, some control approaches based on the uncertainty estimation using the Fourier series have been presented. However, the proper value for the fundamental period duration has been left as an open problem. This paper addresses this issue and intuitively shows that in order to perform repetitive tasks; the least common multiple (LCM) of fundamental period durations of the desired trajectories of the joints is a proper value for the fundamental period duration of the Fourier series expansion. Selecting the LCM results in the least tracking error. Moreover, the truncation error is compensated by the proposed control law to make the tracking error as small as possible. Adaptation laws for determining the Fourier series coefficients are derived according to the stability analysis. The case study is an SCARA robot manipulator driven by permanent magnet DC motors. Simulation results and comparisons with a voltage-based controller using adaptive neuro-fuzzy systems show the effectiveness of the proposed control approach in tracking various periodic trajectories. Moreover, the experimental results on a real SCARA robot manipulator verify the successful practical implementation of the proposed controller.

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Section: Simulation Resultsmentioning

confidence: 99%

Uncertainty estimation in robust tracking control of robot manipulators using the Fourier series expansion

Khorashadizadeh

Fateh

2015

Robotica

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“…Suppose that V is the space of all real-valued continuous-time functions. According to the [17,20,24], a nonlinear function h(x), which defined on the interval [x 1 x 2 ] in V, can be represented as the function approximation of Equation (6a).…”

Section: Legendre Polynomial Function Approximationmentioning

confidence: 99%

“…In [13], a feedforward neural network is employed to learn the parametric uncertainties, existing in the dynamical model of the robot manipulator, and the influence of weight and bias weight of the two-layer neural network are considered, but this increases the difficulty of designing the weight adjustment law, and an excellent neural network has relatively more control parameters, and selection of initial values of neural network parameters will increase the difficulty of the controller design and the complexity of the stability analysis, and also the adaptive adjustment of control parameters will increase the load on the hardware system. In [14], a novel robust decentralized control of electrically driven robot manipulators by adaptive fuzzy estimation and compensation of uncertainty, and in the fuzzy controllers, it uses expert's knowledge, the trial and error method, or an optimization algorithm such as particle swarm optimization (PSO) to design the fuzzy rules, and the design process may be more complicated and not online.Recently, some researchers have proposed the regressor-free control of manipulators based on function approximation technique (FAT) [17][18][19][20], in which the uncertainty factors have been estimated or approximated using the Taylor function expansion [18], Fourier series [19], or Legendre polynomial [17,20]. Compared with the neural network and fuzzy control, its control strategy is simpler, and the influence of the initial value selection on the controller is reduced since the tuning parameters are less.…”

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confidence: 99%

“…Recently, some researchers have proposed the regressor-free control of manipulators based on function approximation technique (FAT) [17][18][19][20], in which the uncertainty factors have been estimated or approximated using the Taylor function expansion [18], Fourier series [19], or Legendre polynomial [17,20]. Compared with the neural network and fuzzy control, its control strategy is simpler, and the influence of the initial value selection on the controller is reduced since the tuning parameters are less.…”

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Adaptive Sliding Mode PID Control for Underwater Manipulator Based on Legendre Polynomial Function Approximation and Its Experimental Evaluation

et al. 2020

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The joint control problem of the underwater manipulator is addressed in this paper, under the influence of uncertainty factors such as model uncertainty, external disturbance, and manipulator joint lag. In general, for the uncertainty factors, it is usually approximated online, but it is difficult to select a reasonable value for the approximation error boundary, too conservative estimated values would cause chattering problem easily. And the influence of joint lag on the manipulator control should be considered in actual work. Unlike most previous control method, in this paper, the function approximation technique (FAT), which uses the Legendre polynomial, is adopted to approximate the uncertainty factors online. Then, based on the proportion integral differential (PID) sliding manifold with the integral and differential of tracking error, a sliding model PID controller is designed to speed up the response and reduce the effects of joint lag. For the error boundary, the adaptive law is proposed, and it will reduce chattering of the control quantity under the steady state of the system. It was proved that the joint error of the control system is uniformly asymptotic convergence through the stability analysis. Finally, the effectiveness of the proposed approach is demonstrated with pool comparison experiments of the underwater manipulator installed in the autonomous underwater vehicles (AUVs).Appl. Sci. 2020, 10, 1728 2 of 15 developed and equipped on multipurpose intervention-AUV [4]. An underwater electric manipulator (MARIS 7080, 7 DOF manipulator) was equipped on semi-autonomous underwater vehicle for the intervention mission (SAUVIM) [5].In UVMS, the underwater manipulator is a key component, and its joint control accuracy directly determines the operating accuracy of the UVMS. At present, underwater manipulators are mostly control objects with joint redundancy, and the accuracy mainly depends on the control performance of joints [6]. However, due to the nonlinear, time-variation of dynamic properties and other factors (i.e., external disturbances such as ocean current disturbance) [7,8], the system dynamic model has uncertainties, which will affect the joint control of the manipulator based on the dynamic model. Besides, for most hydraulic manipulators, the joint control performance is also affected by joint lag [6,9,10], which means that the joint lag will affect the control accuracy of manipulator joint. In conclusion, under the influence of the above factors, it has great research significance and practical value to develop the joint control technology of underwater manipulators for improving the accuracy and efficiency of underwater operation.Currently, many methods have achieved high control accuracy, which uses the online approximation to deal with the uncertainty factors, and determine the controller and adaptive law of parameter through stability analysis [11,12]. Among them, in view of the nonlinear and uncertain identification ability [11][12][13][14][15][16], neural network and fuzzy control has b...

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“…In other words, they are model-free control approaches. Sometimes, obtaining a nominal model is a challenging task [9][10][11]. In these cases, intelligent controllers are proposed that highlights the necessity of studying these controllers.…”

Section: Introductionmentioning

confidence: 99%

Voltage tracking control of DC-DC boost converter using brain emotional learning

Khorashadizadeh

Mahdian²

2016

2016 4th International Conference on Control, Instrumentation, and Automation (ICCIA)

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This paper presents an intelligent controller for voltage tracking control of DC-DC boost converters. The control law is a brain emotional learning based intelligent controller (BELBIC). It uses the inductor current error and the output voltage error to calculate the desired duty cycle. The controller design is free from the mathematical model of the system. In fact, all of the system dynamics and parameters are considered as uncertainty. In comparison with other intelligent controllers such as fuzzy systems and neural networks, BELBIC controllers are simpler, since they have fewer parameters. As a result, the tuning procedure of BELBIC controllers is simpler. Simulation results show the satisfactory performance of this controller in rejecting the external disturbances caused by the sudden changes in the load resistance and the input voltage.

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Robust task-space control of robot manipulators using Legendre polynomials for uncertainty estimation

Cited by 47 publications

References 21 publications

Uncertainty estimation in robust tracking control of robot manipulators using the Fourier series expansion

Uncertainty estimation in robust tracking control of robot manipulators using the Fourier series expansion

Adaptive Sliding Mode PID Control for Underwater Manipulator Based on Legendre Polynomial Function Approximation and Its Experimental Evaluation

Voltage tracking control of DC-DC boost converter using brain emotional learning

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