Search results for: Robotic manipulators

Authors: T. C. Kuo, Y. J. Huang, B. W. Hong

Abstract:

This paper proposes an adaptive sliding mode controller which combines adaptive control and sliding mode control to control a nonlinear robotic manipulator with uncertain parameters. We use an adaptive algorithm based on the concept of sliding mode control to alleviate the chattering phenomenon of control input. Adaptive laws are developed to obtain the gain of switching input and the boundary layer parameters. The stability and convergence of the robotic manipulator control system are guaranteed by applying the Lyapunov theorem. Simulation results demonstrate that the chattering of control input can be alleviated effectively. The proposed controller scheme can assure robustness against a large class of uncertainties and achieve good trajectory tracking performance.

Keywords: Robotic manipulators, sliding mode control, adaptive law, Lyapunov theorem, robustness.

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Authors: A. Pashkevich, A. Klimchik, D. Chablat

Abstract:

The paper focuses on the enhanced stiffness modeling of robotic manipulators by taking into account influence of the external force/torque acting upon the end point. It implements the virtual joint technique that describes the compliance of manipulator elements by a set of localized six-dimensional springs separated by rigid links and perfect joints. In contrast to the conventional formulation, which is valid for the unloaded mode and small displacements, the proposed approach implicitly assumes that the loading leads to the non-negligible changes of the manipulator posture and corresponding amendment of the Jacobian. The developed numerical technique allows computing the static equilibrium and relevant force/torque reaction of the manipulator for any given displacement of the end-effector. This enables designer detecting essentially nonlinear effects in elastic behavior of manipulator, similar to the buckling of beam elements. It is also proposed the linearization procedure that is based on the inversion of the dedicated matrix composed of the stiffness parameters of the virtual springs and the Jacobians/Hessians of the active and passive joints. The developed technique is illustrated by an application example that deals with the stiffness analysis of a parallel manipulator of the Orthoglide family

Keywords: Robotic manipulators, Stiffness model, Loaded mode, Nonlinear effects, Buckling, Orthoglide manipulator

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Authors: V. K. Banga

Abstract:

Robots are now playing a very promising role in industries. Robots are commonly used in applications in repeated operations or where operation by human is either risky or not feasible. In most of the industrial applications, robotic arm manipulators are widely used. Robotic arm manipulator with two link or three link structures is commonly used due to their low degrees-of-freedom (DOF) movement. As the DOF of robotic arm increased, complexity increases. Instrumentation involved with robotics plays very important role in order to interact with outer environment. In this work, optimal control for movement of various DOFs of robotic arm using various soft computing techniques has been presented. We have discussed about different robotic structures having various DOF robotics arm movement. Further stress is on kinematics of the arm structures i.e. forward kinematics and inverse kinematics. Trajectory planning of robotic arms using soft computing techniques is demonstrating the flexibility of this technique. The performance is optimized for all possible input values and results in optimized movement as resultant output. In conclusion, soft computing has been playing very important role for achieving optimized movement of robotic arm. It also requires very limited knowledge of the system to implement soft computing techniques.

Keywords: Artificial intelligence, kinematics, robotic arm, neural networks, fuzzy logic.

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Authors: D. Maneetham, L. Sivhour

Abstract:

Robotic arm manipulators are widely used to accomplish many kinds of tasks. SCORBOT-ER 4u is a 5-degree of freedom (DOF) vertical articulated educational robotic arm, and all joints are revolute. It is specifically designed to perform pick and place task with its gripper. The pick and place task consists of consideration of the end effector coordinate of the robotic arm and the desired position coordinate in its workspace. This paper describes about forward kinematics modeling and analysis of the robotic end effector motion through joint space. The kinematics problems are defined by the transformation from the Cartesian space to the joint space. Denavit-Hartenberg (D-H) model is used in order to model the robotic links and joints with 4x4 homogeneous matrix. The forward kinematics model is also developed and simulated in MATLAB. The mathematical model is validated by using robotic toolbox in MATLAB. By using this method, it may be applicable to get the end effector coordinate of this robotic arm and other similar types to this arm. The software development of SCORBOT-ER 4u is also described here. PC-and EtherCAT based control technology from BECKHOFF is used to control the arm to express the pick and place task.

Keywords: Forward kinematics, D-H model, robotic toolbox, PC-and EtherCAT based control.

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Authors: Dimitrie Marinceu

Abstract:

The newest Canadian Used Fuel Container (UFC)- (called also “Mark II”) modifies the design approach for its Assembly Robotic Cell (ARC) in the Canadian Used (Nuclear) Fuel Packing Plant (UFPP). Some of the robotic design solutions are presented in this paper. The design indicates that robots and manipulators are expected to be used in the Canadian UFPP. As normally, the UFPP design will incorporate redundancy of all equipment to allow expedient recovery from any postulated upset conditions. Overall, this paper suggests that robot usage will have a significant positive impact on nuclear safety, quality, productivity, and reliability.

Keywords: Used fuel packing plant, robotic assembly cell, used fuel container, deep geological repository.

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Authors: T. C. Kuo

Abstract:

In this paper, a novel adaptive fuzzy sliding mode control method is proposed for the robust tracking control of robotic manipulators. The proposed controller possesses the advantages of adaptive control, fuzzy control, and sliding mode control. First, system stability and robustness are guaranteed based on the sliding mode control. Further, fuzzy rules are developed incorporating with adaptation law to alleviate the input chattering effectively. Stability of the control system is proven by using the Lyapunov method. An application to a three-degree-of-freedom robotic manipulator is carried out. Accurate trajectory tracking as well as robustness is achieved. Input chattering is greatly eliminated.

Keywords: Fuzzy control, sliding mode control, roboticmanipulator, adaptive control.

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Authors: Ibrahim F. Jasim, Najah F. Jasim

Abstract:

The problem of controlling a two link robotic manipulator, consisting of a rotating and a prismatic links, is addressed. The actuations of both links are assumed to have unknown dead zone nonlinearities and friction torques modeled by LuGre friction model. Because of the existence of the unknown dead zone and friction torque at the actuations, unknown parameters and unmeasured states would appear to be part of the overall system dynamics that need for estimation. Unmeasured states observer, unknown parameters estimators, and robust adaptive control laws have been derived such that closed loop global stability is achieved. Simulation results have been performed to show the efficacy of the suggested approach.

Keywords: Adaptive Robust Control, Dead Zone, Friction Torques, Robotic Manipulators.

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Authors: Hassan M. Alkomy, Hesham A. Elkaranshawy, Ahmed S. Ashour, Khaled T. Mohamed

Abstract:

For a rigid body sliding on a rough surface, a range of uncertainty or non-uniqueness of solution could be found, which is termed: Painlevé paradox. Painlevé paradox is the reason of a wide range of bouncing motion, observed during sliding of robotic manipulators on rough surfaces. In this research work, the existence of the paradox zone during the sliding motion of a two-link (P-R) robotic manipulator with a unilateral constraint is investigated. Parametric study is performed to investigate the effect of friction, link-length ratio, total height and link-mass ratio on the paradox zone.

Keywords: Dynamical system, friction, multibody system, Painlevé paradox, robotic systems, sliding robots, unilateral constraint.

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Authors: Shonal Singh, Bibhya Sharma, Jito Vanualailai, Avinesh Prasad

Abstract:

This paper considers the autonomous navigation problem of multiple n-link nonholonomic mobile manipulators within an obstacle-ridden environment. We present a set of nonlinear acceleration controllers, derived from the Lyapunov-based control scheme, which generates collision-free trajectories of the mobile manipulators from initial configurations to final configurations in a constrained environment cluttered with stationary solid objects of different shapes and sizes. We demonstrate the efficiency of the control scheme and the resulting acceleration controllers of the mobile manipulators with results through computer simulations of an interesting scenario.

Keywords: Artificial potential fields, kinodynamic constraints, Lyapunov-based control scheme, Lyapunov stability, minimum distance technique, nonholonomic manipulator.

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Authors: H. Sadjadian , H.D. Taghirad Member, A. Fatehi

Abstract:

In this paper, different approaches to solve the forward kinematics of a three DOF actuator redundant hydraulic parallel manipulator are presented. On the contrary to series manipulators, the forward kinematic map of parallel manipulators involves highly coupled nonlinear equations, which are almost impossible to solve analytically. The proposed methods are using neural networks identification with different structures to solve the problem. The accuracy of the results of each method is analyzed in detail and the advantages and the disadvantages of them in computing the forward kinematic map of the given mechanism is discussed in detail. It is concluded that ANFIS presents the best performance compared to MLP, RBF and PNN networks in this particular application.

Keywords: Forward Kinematics, Neural Networks, Numerical Solution, Parallel Manipulators.

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Authors: Hasanifard Goran, Habib Nejad Korayem Moharam, Nikoobin Amin

Abstract:

A new robust nonlinear control scheme of a manipulator is proposed in this paper which is robust against modeling errors and unknown disturbances. It is based on the principle of variable structure control, with sliding mode control (SMC) method. The variable structure control method is a robust method that appears to be well suited for robotic manipulators because it requers only bounds on the robotic arm parameters. But there is no single systematic procedure that is guaranteed to produce a suitable control law. Also, to reduce chattring of the control signal, we replaced the sgn function in the control law by a continuous approximation such as tangant function. We can compute the maximum load with regard to applied torque into joints. The effectivness of the proposed approach has been evaluated analitically demonstrated through computer simulations for the cases of variable load and robot arm parameters.

Keywords: Variable structure control, robust control, switching surface, robot manipulator.

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Authors: M. S. Sreejith, Steffy Joy, Abhishesh Pal, Beom-Sahng Ryuh, V. R. Sanal Kumar

Abstract:

In this paper, an attempt has been made for the design of a robotic library using an intelligent system. The robot works on the ARM microprocessor, motor driver circuit with 5 degrees of freedom with Wi-Fi and GPS based communication protocol. The authenticity of the library books is controlled by RFID. The proposed robotic library system is facilitated with embedded system and ARM. In this library issuance system, the previous potential readers’ authentic review reports have been taken into consideration for recommending suitable books to the deserving new users and the issuance of books or periodicals is based on the users’ decision. We have conjectured that the Wi-Fi based robotic library management system would allow fast transaction of books issuance and it also produces quality readers.

Keywords: GPS based based robotic library, library management system, robotic library, Wi-Fi library.

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Authors: S. Parasuraman

Abstract:

In this work, a new approach is proposed to control the manipulators for Humanoid robot. The kinematics of the manipulators in terms of joint positions, velocity, acceleration and torque of each joint is computed using the Denavit Hardenberg (D-H) notations. These variables are used to design the manipulator control system, which has been proposed in this work. In view of supporting the development of a controller, a simulation of the manipulator is designed for Humanoid robot. This simulation is developed through the use of the Virtual Reality Toolbox and Simulink in Matlab. The Virtual Reality Toolbox in Matlab provides the interfacing and controls to an environment which is developed based on the Virtual Reality Modeling Language (VRML). Chains of bones were used to represent the robot.

Keywords: Mobile robot, Robot Kinematics, Robot Navigation, MATLAB.

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Authors: Haijie Li, Xuping Zhang

Abstract:

This paper presents a computationally efficient method for the modeling of robot manipulators with flexible links and joints. This approach combines the Discrete Time Transfer Matrix Method with the Finite Segment Method, in which the flexible links are discretized by a number of rigid segments connected by torsion springs; and the flexibility of joints are modeled by torsion springs. The proposed method avoids the global dynamics and has the advantage of modeling non-uniform manipulators. Experiments and simulations of a single-link flexible manipulator are conducted for verifying the proposed methodologies. The simulations of a three-link robot arm with links and joints flexibility are also performed.

Keywords: Flexible manipulator, transfer matrix method, linearization, finite segment method.

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Authors: Jiewei Li, Hongyan Cui, Chunqi Chang, Yong Hu

Abstract:

It was expected to benefit patient with hemiparesis after stroke by extensive arm rehabilitation, to partially regain forearm and hand function. This paper propose a robotic rehabilitation arm in assisting the hemiparetic patient to learn new ways of using and moving their weak arms. In this study, the robotic arm was driven by a somatosensory stimulated brain computer interface (BCI), which is a new modality BCI. The use of somatosensory stimulation is not only an input for BCI, but also a electrical stimulation for treatment of hemiparesis to strengthen the arm and improve its range of motion. A trial of this robotic rehabilitation arm was performed in a stroke patient with pure motor hemiparesis. The initial trial showed a promising result from the patient with great motivation and function improvement. It suggests that robotic rehabilitation arm driven by somatosensory BCI can enhance the rehabilitation performance and progress for hemiparetic patients after stroke.

Keywords: Robotic rehabilitation arm, brain computer interface (BCI), hemiparesis, stroke, somatosensory stimulation.

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Authors: A. Pajaziti, H. Cana

Abstract:

In this paper, the structural genetic algorithm is used to optimize the neural network to control the joint movements of robotic arm. The robotic arm has also been modeled in 3D and simulated in real-time in MATLAB. It is found that Neural Networks provide a simple and effective way to control the robot tasks. Computer simulation examples are given to illustrate the significance of this method. By combining Genetic Algorithm optimization method and Neural Networks for the given robotic arm with 5 D.O.F. the obtained the results shown that the base joint movements overshooting time without controller was about 0.5 seconds, while with Neural Network controller (optimized with Genetic Algorithm) was about 0.2 seconds, and the population size of 150 gave best results.

Keywords: Robotic Arm, Neural Network, Genetic Algorithm, Optimization.

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Authors: Chun-Ta Chen, Te-Tan Liao, Hoang-Vuong Pham

Abstract:

In this paper motion analysis on a winding stair-climbing is investigated using our proposed rotational arm type of robotic wheelchair. For now, the robotic wheelchair is operated in an open mode to climb winding stairs by a dynamic turning, therefore, the dynamics model is required to ensure a passenger-s safety. Equations of motion based on the skid-steering analysis are developed for the trajectory planning and motion analysis on climbing winding stairs. Since the robotic wheelchair must climb a winding staircase stably, the winding trajectory becomes a constraint equation to be followed, and the Baumgarte-s method is used to solve for the constrained dynamics equations. Experimental results validate the behavior of the prototype as it climbs a winding stair.

Keywords: Climb, robotic wheelchair, skid-steering, windingstair .

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Authors: Martin Leroux, Sylvain Brisebois

Abstract:

Eating a meal is among the Activities of Daily Living, but it takes a lot of time and effort for people with physical or functional limitations. Dedicated technologies are cumbersome and not portable, while general-purpose assistive robots such as wheelchair-based manipulators are too hard to control for elaborate continuous motion like eating. Eating with such devices has not previously been automated, since there existed no description of a feeding motion for uncontrolled environments. In this paper, we introduce a feeding mode for assistive manipulators, including a mathematical description of trajectories for motions that are difficult to perform manually such as gathering and scooping food at a defined/desired pace. We implement these trajectories in a sequence of movements for a semi-automated feeding mode which can be controlled with a very simple 3-button interface, allowing the user to have control over the feeding pace. Finally, we demonstrate the feeding mode with a JACO robotic arm and compare the eating speed, measured in bites per minute of three eating methods: a healthy person eating unaided, a person with upper limb limitations or disability using JACO with manual control, and a person with limitations using JACO with the feeding mode. We found that the feeding mode allows eating about 5 bites per minute, which should be sufficient to eat a meal under 30min.

Keywords: Assistive robotics, Automated feeding, Elderly care, Trajectory design, Human-Robot Interaction.

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Authors: V. K. Banga, Jasjit Kaur, R. Kumar, Y. Singh

Abstract:

In this research paper we have presented control architecture for robotic arm movement and trajectory planning using Fuzzy Logic (FL) and Genetic Algorithms (GAs). This architecture is used to compensate the uncertainties like; movement, friction and settling time in robotic arm movement. The genetic algorithms and fuzzy logic is used to meet the objective of optimal control movement of robotic arm. This proposed technique represents a general model for redundant structures and may extend to other structures. Results show optimal angular movement of joints as result of evolutionary process. This technique has edge over the other techniques as minimum mathematics complexity used.

Keywords: Kinematics, Genetic algorithms (GAs), Fuzzy logic(FL), Optimal control.

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Authors: Tao Yin, Zeqiang Zhang, Wei Liang, Yanqing Zeng, Yu Zhang

Abstract:

To accelerate the remanufacturing process of electronic waste products, this study designs a partial disassembly line with the multi-robotic station to effectively dispose of excessive wastes. The multi-robotic partial disassembly line is a technical upgrade to the existing manual disassembly line. Balancing optimization can make the disassembly line smoother and more efficient. For partial disassembly line balancing with the multi-robotic station (PDLBMRS), a mixed-integer programming model (MIPM) considering the robotic efficiency differences is established to minimize cycle time, energy consumption and hazard index and to calculate their optimal global values. Besides, an enhanced NSGA-II algorithm (HNSGA-II) is proposed to optimize PDLBMRS efficiently. Finally, MIPM and HNSGA-II are applied to an actual mixed disassembly case of two types of computers, the comparison of the results solved by GUROBI and HNSGA-II verifies the correctness of the model and excellent performance of the algorithm, and the obtained Pareto solution set provides multiple options for decision-makers.

Keywords: Waste disposal, disassembly line balancing, multi-robot station, robotic efficiency difference, HNSGA-II.

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Authors: Amer S. Al-Yahmadi, T.C. Hsia

Abstract:

This paper seeks to develop simple yet practical and efficient control scheme that enables cooperating arms to handle a flexible beam. Specifically the problem studied herein is that of two arms rigidly grasping a flexible beam and such capable of generating forces/moments in such away as to move a flexible beam along a predefined trajectory. The paper develops a sliding mode control law that provides robustness against model imperfection and uncertainty. It also provides an implicit stability proof. Simulation results for two three joint arms moving a flexible beam, are presented to validate the theoretical results.

Keywords: Sliding mode control, cooperative manipulators.

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Authors: Ghasem Abbasnejad, Soheil Zarkandi, Misagh Imani

Abstract:

In this article the homotopy continuation method (HCM) to solve the forward kinematic problem of the 3-PRS parallel manipulator is used. Since there are many difficulties in solving the system of nonlinear equations in kinematics of manipulators, the numerical solutions like Newton-Raphson are inevitably used. When dealing with any numerical solution, there are two troublesome problems. One is that good initial guesses are not easy to detect and another is related to whether the used method will converge to useful solutions. Results of this paper reveal that the homotopy continuation method can alleviate the drawbacks of traditional numerical techniques.

Keywords: Forward kinematics, Homotopy continuationmethod, Parallel manipulators, Rotation matrix

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Authors: Jolly Shah, S.S.Rattan, B.C.Nakra

Abstract:

Automatic control of the robotic manipulator involves study of kinematics and dynamics as a major issue. This paper involves the forward and inverse kinematics of 2-DOF robotic manipulator with revolute joints. In this study the Denavit- Hartenberg (D-H) model is used to model robot links and joints. Also forward and inverse kinematics solution has been achieved using Artificial Neural Networks for 2-DOF robotic manipulator. It shows that by using artificial neural network the solution we get is faster, acceptable and has zero error.

Keywords: Artificial Neural Network, Forward Kinematics, Inverse Kinematics, Robotic Manipulator

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Authors: Namal A. Senanayake, Khoo B. How, Quah W. Wai

Abstract:

In this project, a tele-operated anthropomorphic robotic arm and hand is designed and built as a versatile robotic arm system. The robot has the ability to manipulate objects such as pick and place operations. It is also able to function by itself, in standalone mode. Firstly, the robotic arm is built in order to interface with a personal computer via a serial servo controller circuit board. The circuit board enables user to completely control the robotic arm and moreover, enables feedbacks from user. The control circuit board uses a powerful integrated microcontroller, a PIC (Programmable Interface Controller). The PIC is firstly programmed using BASIC (Beginner-s All-purpose Symbolic Instruction Code) and it is used as the 'brain' of the robot. In addition a user friendly Graphical User Interface (GUI) is developed as the serial servo interface software using Microsoft-s Visual Basic 6. The second part of the project is to use speech recognition control on the robotic arm. A speech recognition circuit board is constructed with onboard components such as PIC and other integrated circuits. It replaces the computers- Graphical User Interface. The robotic arm is able to receive instructions as spoken commands through a microphone and perform operations with respect to the commands such as picking and placing operations.

Keywords: Tele-operated Anthropomorphic Robotic Arm and Hand, Robot Motion System, Serial Servo Controller, Speech Recognition Controller.

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Authors: Jimmy W. Soto Martell, Giuseppina Gini

Abstract:

In this paper we intend to ascertain the state of the art on multifingered end-effectors, also known as robotic hands or dexterous robot hands, and propose an experimental setup for an innovative task based design approach, involving cutting edge technologies in motion capture. After an initial description of the capabilities and complexity of a human hand when grasping objects, in order to point out the importance of replicating it, we analyze the mechanical and kinematical structure of some important works carried out all around the world in the last three decades and also review the actuators and sensing technologies used. Finally we describe a new design philosophy proposing an experimental setup for the first stage using recent developments in human body motion capture systems that might lead to lighter and always more dexterous robotic hands.

Keywords: Dexterous manipulation, grasp, multifingered endeffector, robotic hand.

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Authors: Maria P. Tzamtzi, Fotis N. Koumboulis

Abstract:

We propose a control design scheme that aims to prevent undesirable liquid outpouring and suppress sloshing during the forward and backward tilting phases of the pouring process, for the case of liquid containers carried by manipulators. The proposed scheme combines a partial inverse dynamics controller with a PID controller, tuned with the use of a “metaheuristic" search algorithm. The “metaheuristic" search algorithm tunes the PID controller based on simulation results of the plant-s linearization around the operating point corresponding to the critical tilting angle, where outpouring initiates. Liquid motion is modeled using the well-known pendulumtype model. However, the proposed controller does not require measurements of the liquid-s motion within the tank.

Keywords: Robotic systems, Controller design, Sloshingsuppression, Metaheuristic optimization.

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Authors: Rafael Jorge Menezes Santos, Ginalber Luiz de Oliveira Serra, Carlos César Teixeira Ferreira

Abstract:

This paper proposes a methodology for analysis of the dynamic behavior of a robotic manipulator in continuous time. Initially this system (nonlinear system) will be decomposed into linear submodels and analyzed in the context of the Linear and Parameter Varying (LPV) Systems. The obtained linear submodels, which represent the local dynamic behavior of the robotic manipulator in some operating points were grouped in a Takagi-Sugeno fuzzy structure. The obtained fuzzy model was analyzed and validated through analog simulation, as universal approximator of the robotic manipulator.

Keywords: modeling of nonlinear dynamic systems, Takagi- Sugeno fuzzy model, Linear and Parameter Varying (LPV) System.

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Authors: Ahmet Denker, Tuğrul Adıgüzel

Abstract:

In this paper, a solution is presented for a robotic manipulation problem in industrial settings. The problem is sensing objects on a conveyor belt, identifying the target, planning and tracking an interception trajectory between end effector and the target. Such a problem could be formulated as combining object recognition, tracking and interception. For this purpose, we integrated a vision system to the manipulation system and employed tracking algorithms. The control approach is implemented on a real industrial manipulation setting, which consists of a conveyor belt, objects moving on it, a robotic manipulator, and a visual sensor above the conveyor. The trjectory for robotic interception at a rendezvous point on the conveyor belt is analytically calculated. Test results show that tracking the raget along this trajectory results in interception and grabbing of the target object.

Keywords: robotics, robot vision, rendezvous planning, self organizingmaps.

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Authors: Ahmed Amin Mousa, Tamer M. Ismail, M. Abd El Salam

Abstract:

This work presents a robot called Conceptual Robotic Cube, CR-Cube. The robot can be used as an educational tool for children from the age of three. It has a cube shape attached with a camera colours sensor. In addition, it contains four wheels to move smoothly. The researchers prepared a questionnaire to measure the efficiency of the robot. The design and the questionnaire was presented to 11 experts who agreed that the robot is appropriate for learning numbering and colours for preschool children.

Keywords: CR-Cube, robotic cube, conceptual robot, conceptual cube, colour concept, early childhood education.

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Authors: J. G. Batista, L. J. de Bessa Neto, M. A. F. B. Lima, J. R. Leite, J. I. de Andrade Nunes

Abstract:

The robot manipulator is an equipment that stands out for two reasons: Firstly because of its characteristics of movement and reprogramming, resembling the arm; secondly, by adding several areas of knowledge of science and engineering. The present work shows the development of the prototype of a robotic manipulator driven by a Programmable Logic Controller (PLC), having two degrees of freedom, which allows the movement and displacement of mechanical parts, tools, and objects in general of small size, through an electronic system. The aim is to study direct and inverse kinematics of the robotic manipulator to describe the translation and rotation between two adjacent links of the robot through the Denavit-Hartenberg parameters. Currently, due to the many resources that microcomputer systems offer us, robotics is going through a period of continuous growth that will allow, in a short time, the development of intelligent robots with the capacity to perform operations that require flexibility, speed and precision.

Keywords: Direct and inverse kinematics, Denavit-Hartenberg, microcontrollers, robotic manipulator.

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