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1

Robust Trajectory Tracking Control of Space Manipulators in Extended Task Space

Banaszkiewicz Marek, Węgrzyn Marek, Basmadji Fatina L., Galicki Mirosław

Pomiary Automatyka Robotyka

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2022

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R. 26, nr 4

27--35

EN

This study provides a new class of controllers for freeflying space manipulators subject to unknown undesirable disturbing forces exerted on the end-effector. Based on suitably defined taskspace non-singular terminal sliding manifold and the Lyapunov stability theory, we derive a class of estimated extended transposed Jacobian controllers which seem to be effective in counteracting the unstructured disturbing forces. The numerical computations which are carried out for a space manipulator consisting of a spacecraft propelled by eight thrusters and holonomic manipulator of three revolute kinematic pairs, illustrate the performance of the proposed controller.

PL

W pracy zaproponowano nową klasę sterowników dla manipulatorów kosmicznych przy uwzględnieniu nieznanych, niepożądanych sił zakłócających wywieranych na koniec efektora. W oparciu o odpowiednio zdefiniowane nieosobliwą, końcową rozmaitość ślizgową i teorię stabilności Lapunowa wyprowadzono klasę rozszerzonych estymowanych transponowanych sterowników Jakobianowych, ktore wydają się być efektywne w przeciwdziałaniu nieustrukturyzowanych sił zakłócających. Podejście zilustrowano również obliczeniami numerycznymi dla manipulatora kosmicznego składającego się z bazy napędzanej przez osiem pędników typu cold-gas i manipulatora holonomicznego o trzech parach kinematycznych obrotowych.

2

Robust H∞ fuzzy approach design via Takagi‐Sugeno descriptor model. application for 2‐DOF serial manipulator tracking control

Thi Van Anh Nguyen, Pham Duc Binh, Nguyen Danh Huy, Nguyen Tung Lam

Journal of Automation Mobile Robotics and Intelligent Systems

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2022

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Vol. 16, No. 3

22--29

EN

This paper focuses on trajectory tracking control for ro‐ bot manipulators. While much research has been done on this issue, many other aspects of this field have not been fully addressed. Here, we present a new solution using feedforward controller to eliminate parametric uncer‐ tainties and unknown disturbances. The Takagi‐Sugeno fuzzy descriptor system (TSFDS) is chosen to describe the dynamic characteristics of the robot. The combination of this fuzzy system and the robust H∞ performance makes the system almost isolated from external factors. The li‐ near matrix inequalities based on the theory of Lyapunov stability is considered for control design. The proposed method has proven its effectiveness through simulation results.

3

Firefly algorithm optimization of manipulator robotic control based on fast terminal sliding mode

Mallem Ali, Douak Fouzi, Benaziza Walid, Bounouara Asma

Journal of Automation Mobile Robotics and Intelligent Systems

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2022

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Vol. 16, No. 4

44--52

EN

In this paper a new algorithm of optimization in the field of manipulator robotic control is presented. The proposed control approach is based on fast terminal sliding mode control (FTSMC), in order to guarantee the convergence of the position articulations errors to zero in finite time without chattering phenomena, and the Firefly algorithm in order to generate the optimal parameters that ensure minimum reaching time and mean square error and achieve better performances. This ensures the asymptotic stability of the system using a Lyapunov candidate in the presence of disturbances. The simulations are applied on a two-link robotic manipulator with different tracking references by using Matlab/ Simulink. Results show the efficiency and confirm the robustness of the proposed control strategy.

4

Lyapunov stability based sliding mode observer for sensorless control of permanent magnet synchronous motor

Navaneethan Soundirarajan, Kanthalakshmi Srinivasan, Aandrew Baggio S.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2022

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Vol. 70, nr 2

art. no. e140353

EN

In recent years there has been an increasing demand for electric vehicles due to their attractive features including low pollution and increase in efficiency. Electric vehicles use electric motors as primary motion elements and permanent magnet machines found a proven record of use in electric vehicles. Permanent magnet synchronous motor (PMSM) as electric propulsion in electric vehicles supersedes the performance compared to other motor types. However, in order to eliminate the cumbersome mechanical sensors used for feedback, sensorless control of motors has been proposed. This paper proposes the design of sliding mode observer (SMO) based on Lyapunov stability for sensorless control of PMSM. The designed observer is modeled with a simulated PMSM model to evaluate the tracking efficiency of the observer. Further, the SMO is coded using MATLAB/Xilinx block models to investigate the performance at real-time.

5

Trajectory tracking control of a mobile manipulator with an external force compensation

Galicki Mirosław

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2021

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Vol. 69, nr 5

art. no. e137943

EN

This paper considers the problem of the accurate task space finite-time control susceptible to both undesirable disturbance forces exerted on the end-effector and unknown friction forces coming from joints directly driven by the actuators as well as unstructured forces resulting from the kinematic singularities appearing on the mechanism trajectory. We obtain a class of estimated extended transposed Jacobian controllers which seem to successfully counteract the external disturbance forces on the basis of a suitably defined task-space non-singular terminal sliding manifold (TSM) and the Lyapunov stability theory. Moreover, in order to overcome (or to minimise) the undesirable chattering effects, the proposed robust control law involves the second-order sliding technique. The numerical simulations (closely related to an experiment) ran for a mobile manipulator consisting of a non-holononic platform of (2;0) type and a holonomic manipulator of two revolute kinematic pairs show the performance of the proposed controllers and make a comparison with other well-known control schemes.

6

Global stability of backsteping control with robust nonlinear observer of induction motor in (α,β) frame

Chenafa Amine, Chenafa Mohammed, Mansouri Abdellah, Chaker Abdelkader

Przegląd Elektrotechniczny

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2019

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R. 95, nr 1

191--196

EN

This paper deals with the design of an advanced control law by backstepping with an observer for a special class of nonlinear systems. We design an observer with a single adjustment gain as a function of speed. Our contribution is developed by demonstrating a nonlinear control law by backstepping using the global Lyapunov stability of the controller, the nonlinear observer and the induction motor. We study the behavior of the torque tracking and the rotor flux of the induction motor in the natural frame(α,β). The control algorithm obtained is studied through simulations and applied in many configurations (flux and speed and torque disturbances), and is shown to be very efficient.

PL

Niniejszy artykuł dotyczy projektowania zaawansowanego prawa kontroli poprzez odtwarzanie z obserwatorem specjalnej klasy systemów nieliniowych. Projektujemy obserwatora z jednym wzmocnieniem regulacji w funkcji prędkości. Nasz układ jest rozwijany przez demonstrowanie nieliniowego prawa kontrolnego poprzez odtwarzanie za pomocą globalnej stabilności Lapunowa kontrolera, nieliniowego obserwatora i silnika indukcyjnego. Badamy zachowanie śledzenia momentu i strumienia wirnika silnika indukcyjnego w naturalnej ramie (α, β). Uzyskany algorytm sterowania jest badany za pomocą symulacji i stosowany w wielu konfiguracjach (strumień i zakłócenia prędkości i momentu obrotowego) i jest bardzo wydajny.

7

PD terminal sliding mode control using fuzzy genetic algorithm for mobile robot in presence of disturbances

Benaziza W., Slimane N., Mallem A.

Journal of Automation Mobile Robotics and Intelligent Systems

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2018

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Vol. 12, No. 2

52--60

EN

This paper presents a new approach in the field of trajectory tracking for nonholonomic mobile robot in presence of disturbances. The proposed control design is constructed by a kinematic controller, based on PD sliding surface using fuzzy sliding mode for the angular and linear velocities disturbances, in order to tend asymptotically the robot posture error to zero. Thereafter a dynamic controller is presented using as a sliding surface design, a fast terminal function (FTF) whose parameters are generated by a genetic algorithm in order to converge the velocity errors to zero in finite time and guarantee the asymptotic stability of the system using a Lyapunov candidate. The elaborated simulation works in the case of different trajectories confirm the robustness of the proposed approach.

8

Fuzzy-Lyapunov based controller for a quadrocopter

Kusznir T., Smoczek J.

Journal of KONES

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2017

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Vol. 24, No. 4

125--132

EN

Quadrocopters are nonlinear and inherently unstable systems. To be able to account for the nonlinearities during more aggressive manoeuvres nonlinear control methods need to be utilized to obtain the desired position while at the same time guaranteeing stability. In the article, the quadrocopter dynamics is modelled using the Newton-Euler method. The propeller aerodynamics is modelled using a combination of momentum theory and blade element theory. There are two different control objectives; the 1st objective requires the quadrocopter to reach a desired attitude set point using, while the 2nd objective requires the quadrocopter to track an attitude trajectory. In both cases, Lyapunov stability criterion, in conjunction with LaSalle’s invariance principle, is used to guarantee the system becomes asymptotically stable. In the case of reaching the desired attitude set point, a direct Lyapunov control method is implemented with the control constants determined empirically. For the trajectory tracking, limited knowledge is assumed on the system dynamics and the Mamdani fuzzy controller is used with a rule base that satisfy the Lyapunov stability criterion. The fuzzy membership functions developed empirically and a centre of gravity defuzzification method is used. All simulations are done in MATLAB/Simulink. The results of the numerical simulation are presented in the article.

9

Kinematically optimal robust control of redundant manipulators

Galicki M.

International Journal of Applied Mechanics and Engineering

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2017

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Vol. 22, no. 4

839--865

EN

This work deals with the problem of the robust optimal task space trajectory tracking subject to finite-time convergence. Kinematic and dynamic equations of a redundant manipulator are assumed to be uncertain. Moreover, globally unbounded disturbances are allowed to act on the manipulator when tracking the trajectory by the endeffector. Furthermore, the movement is to be accomplished in such a way as to minimize both the manipulator torques and their oscillations thus eliminating the potential robot vibrations. Based on suitably defined task space non-singular terminal sliding vector variable and the Lyapunov stability theory, we derive a class of chattering-free robust kinematically optimal controllers, based on the estimation of transpose Jacobian, which seem to be effective in counteracting both uncertain kinematics and dynamics, unbounded disturbances and (possible) kinematic and/or algorithmic singularities met on the robot trajectory. The numerical simulations carried out for a redundant manipulator of a SCARA type consisting of the three revolute kinematic pairs and operating in a two-dimensional task space, illustrate performance of the proposed controllers as well as comparisons with other well known control schemes.

10

Stabilization of a certain class of fuzzy control systems with uncertainties

Taieb N. H., Hammami M. A., Delmotte F.

Archives of Control Sciences

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2017

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Vol. 27, no. 3

453--481

EN

In this paper, we investigate the global uniform practical exponential stability for a class of uncertain Takagi-Sugeno fuzzy systems. The uncertainties are supposed uniformly to be bounded by some known integrable functions to obtain an exponential convergence toward a neighborhood of the origin. Therefore, we use common quadratic Lyapunov function (CQLF) and parallel distributed compensation (PDC) controller techniques to show the global uniform practical exponential stability of the closed-loop system. Numeric simulations are given to validate the proposed approach.

11

Robust task space trajectory tracking control of robotic manipulators

Galicki M.

International Journal of Applied Mechanics and Engineering

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2016

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Vol. 21, no. 3

547--568

EN

This work deals with the problem of the accurate task space trajectory tracking subject to finite-time convergence. Kinematic and dynamic equations of a redundant manipulator are assumed to be uncertain. Moreover, globally unbounded disturbances are allowed to act on the manipulator when tracking the trajectory by the end-effector. Furthermore, the movement is to be accomplished in such a way as to reduce both the manipulator torques and their oscillations thus eliminating the potential robot vibrations. Based on suitably defined task space non-singular terminal sliding vector variable and the Lyapunov stability theory, we propose a class of chattering-free robust controllers, based on the estimation of transpose Jacobian, which seem to be effective in counteracting both uncertain kinematics and dynamics, unbounded disturbances and (possible) kinematic and/or algorithmic singularities met on the robot trajectory. The numerical simulations carried out for a redundant manipulator of a SCARA type consisting of the three revolute kinematic pairs and operating in a two-dimensional task space, illustrate performance of the proposed controllers as well as comparisons with other well known control schemes.

12

Controlling continuous bioreactor via nonlinear feedback: modelling and simulations approach

Aguilar-López R., Neria-González I.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2016

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Vol. 64, nr 1

235--241

EN

The aim of this work is to present a class of nonlinear controller with an exponential-type feedback in order to regulate the sulfate mass concentration via the input flow in a continuous stirred tank bioreactor of an anaerobic sulfate-reducing process. The corresponding kinetic terms in the bioreactor’s modeling are modeled by unstructured modeling approach, which was experimentally corroborated. A sketch of proof of the closed-loop stability of the considered system is done under the framework of Lyapunov theory. Numerical experiments are conducted to show the performance of the proposed methodology in comparison with a well-tuned sigmoid controller.

13

Adaptive control of the Scorbot-ER 4PC manipulator

Gierlak P.

Zeszyty Naukowe Politechniki Rzeszowskiej. Mechanika

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2014

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z. 86 [290], nr 4

501--516

EN

The problem of the manipulator tracking control is not trivial because the manipulator is a nonlinear object, whose parameters may be unknown and variable. The control law should enable the manipulator to behave correctly even when operational conditions are changeable. The adaptive control system meets this requirement. In this paper, both kinematic and dynamic equations of motion for the Scorbot-ER 4pc are presented. The adaptive control algorithm was derived for this manipulator. The presented control and adaptive laws guarantee practical Lyapunov stability. The results of verification of theoretical investigations are presented. Experiments were carried out on a work station which consists of the Scorbot-ER 4pc robotic manipulator, a computer with Matlab and dSPACE ControlDesk software and a DS1006 digital signal processing board. In the experiments, the specified point of the manipulator has moved on a desired circular path and the gripper of the manipulator was loaded in variable ways. The operation of adaptive control system was compared with the computed moment method. From the result of the comparison we can see that, in practice, the adaptive control gives better results.

PL

Sterowanie ruchem nadążnym manipulatora nie jest prostym zagadnieniem, ponieważ manipulator jest nieliniowym obiektem, którego parametry mogą być nieznane i zmienne. Prawo sterowania powinno uwzględniać te aspekty i umożliwiać manipulatorowi poprawne działanie nawet wtedy, gdy warunki jego pracy są zmienne. Wymaganie to jest spełnione przy zastosowaniu adaptacyjnych układów sterowania. W artykule przedstawiono równania kinematyki i dynamiczne równania ruchu manipulatora Scorbot-ER 4pc. Zaprezentowane prawa sterownia i adaptacji gwarantują praktyczną stabilność w sensie Lapunowa. W pracy zamieszczono rezultaty weryfikacji prezentowanych rozwiązań teoretycznych. Eksperymenty przeprowadzono na stanowisku, które składa się z robota manipulacyjnego Scorbot-ER 4pc, komputera PC z oprogramowaniem Matlab i dSPACE ControlDesk oraz karty kontrolno-pomiarowej DS1006. Podczas eksperymentów wybrany punkt manipulatora poruszał się pożądanym torze kołowym, a chwytak manipulatora był obciążany zmiennym ładunkiem. Działanie adaptacyjnego układu sterowania porównano z działaniem układu z zaimplementowaną metodą wyliczanego momentu. Z porównania jakości sterowania wynika, że w praktyce lepsze wyniki zapewnia stosowanie sterowania adaptacyjnego.

14

Neural Network Identifier of a Four-wheeled Mobile Robot Subject to Wheel Slip

Hendzel Z, Trojnacki M.

Journal of Automation Mobile Robotics and Intelligent Systems

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2014

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Vol. 8, No. 4

24--30

EN

The paper presents a sequential neural network (NN) identification scheme for the four-wheeled mobile robot subject to wheel slip. The sequential identification scheme, different from conventional methods of optimization of a cost function, attempts to ensure stability of the overall system while the neural network learns the nonlinearities of the mobile robot. An on-line weight learning algorithm is developed to adjust the weights so that the identified model can adapt to variations of the characteristics and operating points in the four-wheeled mobile robot. The proposed identification system that can guarantee stability is derived from the Lyapunov stability theory. Computer simulations have been conducted to illustrate the performance of the proposed solution by a series of experiments on the emulator of the wheeled mobile robot.

15

An analytical method for well-formed workflow/Petri net verification of classical soundness

Clempner J.

International Journal of Applied Mathematics and Computer Science

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2014

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Vol. 24, no. 4

931--939

EN

In this paper we consider workflow nets as dynamical systems governed by ordinary difference equations described by a particular class of Petri nets. Workflow nets are a formal model of business processes. Well-formed business processes correspond to sound workflow nets. Even if it seems necessary to require the soundness of workflow nets, there exist business processes with conditional behavior that will not necessarily satisfy the soundness property. In this sense, we propose an analytical method for showing that a workflow net satisfies the classical soundness property using a Petri net. To present our statement, we use Lyapunov stability theory to tackle the classical soundness verification problem for a class of dynamical systems described by Petri nets. This class of Petri nets allows a dynamical model representation that can be expressed in terms of difference equations. As a result, by applying Lyapunov theory, the classical soundness property for workflow nets is solved proving that the Petri net representation is stable. We show that a finite and non-blocking workflow net satisfies the sound property if and only if its corresponding PN is stable, i.e., given the incidence matrix A of the corresponding PN, there exists a Φ strictly positive m vector such that AΦ ≤ 0. The key contribution of the paper is the analytical method itself that satisfies part of the definition of the classical soundness requirements. The method is designed for practical applications, guarantees that anomalies can be detected without domain knowledge, and can be easily implemented into existing commercial systems that do not support the verification of workflows. The validity of the proposed method is successfully demonstrated by application examples.

16

Lyapunov Stability Analysis of DC-DC Power Electronic Converters: A Brief Overview

Grzesik B., Siewniak P.

Przegląd Elektrotechniczny

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2012

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R. 88, nr 9a

162-166

EN

The brief overview of problems on Lyapunov stability analysis of DC-DC power electronic converters (PECs) is presented in this article. Problems of the PECs global and local stability analysis based on both continuous-time and discrete-time PECs models are discussed here. Special attention is addressed to the PECs stability analysis using direct Lyapunov method.

PL

W artykule przedstawiono zwięzły przegląd tematyki analizy stabilności Lapunowa przekształtników energoelektronicznych DC-DC. Omówiono tutaj problematykę analizy stabilności globalnej i lokalnej PECs na podstawie modeli PECs czasu ciągłego i czasu dyskretnego. Szczególną uwagę zwrócono na analizę stabilności PECs za pomocą bezpośredniej metody Lapunowa.

17

Dimension Reduction and Domains of Attraction of Nonlinear Dynamical Systems

Hochlenert D.

Machine Dynamics Research

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2011

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Vol. 35, No. 4

32-48

EN

The appropriate modeling of technical systems usually results in dynamical systems having many or even an infinite number of degrees of freedom. Moreover, nonlinearities play an important role in many applications, so that the arising systems of nonlinear differential equations are difficult to analyze. However, it is well known that the asymptotic behavior of some high dimensional systems can be described by corresponding systems of much smaller dimension. The present paper deals with the dimension reduction of nonlinear systems close to a bifurcation point. Using the ideas of normal form theory, the asymptotic dynamics of the system is extracted by a nonlinear coordinate transformation. The solutions of the reducedordsr system are analyzed analytically with respect to their stability and their domains of attraction. Furthermore, the inverse of the near-identity transformations is used to construct adapted Lyapunov functions for the original system to estimate the attractors of the solutions as well. The procedure is applied to the Duffing equation and the equations of motion of a railway wheelset and compared with numerical solutions.

18

On stability of equilibrium in linear thermoviscoelasticity

Ciobanu G. Gr.

Archives of Mechanics

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2006

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Vol. 58, nr 1

3-16

EN

We present some results concerning the uniform Lyapunov stability of the generalized solution of an equilibrium problem for thermoviscoelastic materials [9]. These results are similar to those obtained in [4-7]. The results in [4] were subsequently developed for exterior domains in [8].

19

Stability of a class of adaptive nonlinear systems

Dzieliński A.

International Journal of Applied Mathematics and Computer Science

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2005

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Vol. 15, no 4

455-462

EN

This paper presents a research effort focused on the problem of robust stability of the closed-loop adaptive system. It is aimed at providing a general framework for the investigation of continuous-time, state-space systems required to track a (stable) reference model. This is motivated by the model reference adaptive control (MRAC) scheme, traditionally considered in such a setting. The application of differential inequlities results to the analysis of the Lyapunov stability for a class of nonlinear systems is investigated and it is shown how the problem of model following control may be tackled using this methodology.

20

Path tracking by the end-effector of a redundant manipulator

Galicki M.

Archives of Control Sciences

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2001

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Vol. 11, no. 3/4

245-261

EN

This study deals with the problem of tracking a prescribed geometric path by the end-effector of a kinematically redundant manipulator at the control-loop level. During the robot motion, the control constraints resulting from the physical abilities of robot actuators are taken into account. The Lyapunov stability theory is used to derive the control scheme. The numerical simulation results carried out for a planar manipulator whose end-effector tracks a segment line in a two-dimensional work space, illustrate the trajectory performance of the proposed control scheme.