Search results for: nonholonomic manipulator.
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 89

Search results for: nonholonomic manipulator.

89 Autonomous Control of a Mobile Manipulator

Authors: Shonal Singh, Bibhya Sharma, Jito Vanualailai

Abstract:

This paper considers the design of a motion planner that will simultaneously accomplish control and motion planning of a n-link nonholonomic mobile manipulator, wherein, a n-link holonomic manipulator is coupled with a nonholonomic mobile platform, within an obstacle-ridden environment. This planner, derived from the Lyapunov-based control scheme, generates collision-free trajectories from an initial configuration to a final configuration 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 manipulator with results through computer simulations of an interesting scenario.

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

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88 Autonomous Control of Multiple Mobile Manipulators

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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87 Manipulator Development for Telediagnostics

Authors: Adam Kurnicki, Bartłomiej Stanczyk, Bartosz Kania

Abstract:

This paper presents development of the light-weight manipulator with series elastic actuation for medical telediagnostics (USG examination). General structure of realized impedance control algorithm was shown. It was described how to perform force measurements based mainly on elasticity of manipulator links.

Keywords: Telediagnostics, elastic manipulator, impedance control, force measurement.

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86 Singularity Loci of Actuation Schemes for 3RRR Planar Parallel Manipulator

Authors: S. Ramana Babu, V. Ramachandra Raju, K. Ramji

Abstract:

This paper presents the effect of actuation schemes on the performance of parallel manipulators and also how the singularity loci have been changed in the reachable workspace of the manipulator with the choice of actuation scheme to drive the manipulator. The performance of the eight possible actuation schemes of 3RRR planar parallel manipulator is compared with each other. The optimal design problem is formulated to find the manipulator geometry that maximizes the singularity free conditioned workspace for all the eight actuation cases, the optimization problem is solved by using genetic algorithms.

Keywords: Actuation schemes, GCI, genetic algorithms.

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85 A 7DOF Manipulator Control in an Unknown Environment based on an Exact Algorithm

Authors: Pavel K. Lopatin, Artyom S. Yegorov

Abstract:

An exact algorithm for a n-link manipulator movement amidst arbitrary unknown static obstacles is presented. The algorithm guarantees the reaching of a target configuration of the manipulator in a finite number of steps. The algorithm is reduced to a finite number of calls of a subroutine for planning a trajectory in the presence of known forbidden states. The polynomial approximation algorithm which is used as the subroutine is presented. The results of the exact algorithm implementation for the control of a seven link (7 degrees of freedom, 7DOF) manipulator are given.

Keywords: Manipulator, trajectory planning, unknown obstacles

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84 Real-time Detection of Space Manipulator Self-collision

Authors: Zhang Xiaodong, Tang Zixin, Liu Xin

Abstract:

In order to avoid self-collision of space manipulators during operation process, a real-time detection method is proposed in this paper. The manipulator is fitted into a cylinder-enveloping surface, and then, a kind of detection algorithm of collision between cylinders is analyzed. The collision model of space manipulator self-links can be detected by using this algorithm in real-time detection during the operation process. To ensure security of the operation, a safety threshold is designed. The simulation and experiment results verify the effectiveness of the proposed algorithm for a 7-DOF space manipulator.

Keywords: Space manipulator, Collision detection, Self-collision, the real-time collision detection.

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83 Robust Control of a High-Speed Manipulator in State Space

Authors: M. M. Fateh, A. Izadbakhsh

Abstract:

A robust control approach is proposed for a high speed manipulator using a hybrid computed torque control approach in the state space. The high-speed manipulator is driven by permanent magnet dc motors to track a trajectory in the joint space in the presence of disturbances. Tracking problem is analyzed in the state space where the completed models are considered for actuators. The proposed control approach can guarantee the stability and a satisfactory tracking performance. A two-link elbow manipulator driven by electrical actuators is simulated and results are shown to satisfy conditions under technical specifications.

Keywords: Computed torque, manipulator, robust control, state space.

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82 Trajectory Tracking of a Redundant Hybrid Manipulator Using a Switching Control Method

Authors: Atilla Bayram

Abstract:

This paper presents the trajectory tracking control of a spatial redundant hybrid manipulator. This manipulator consists of two parallel manipulators which are a variable geometry truss (VGT) module. In fact, each VGT module with 3-degress of freedom (DOF) is a planar parallel manipulator and their operational planes of these VGT modules are arranged to be orthogonal to each other. Also, the manipulator contains a twist motion part attached to the top of the second VGT module to supply the missing orientation of the endeffector. These three modules constitute totally 7-DOF hybrid (parallel-parallel) redundant spatial manipulator. The forward kinematics equations of this manipulator are obtained, then, according to these equations, the inverse kinematics is solved based on an optimization with the joint limit avoidance. The dynamic equations are formed by using virtual work method. In order to test the performance of the redundant manipulator and the controllers presented, two different desired trajectories are followed by using the computed force control method and a switching control method. The switching control method is combined with the computed force control method and genetic algorithm. In the switching control method, the genetic algorithm is only used for fine tuning in the compensation of the trajectory tracking errors.

Keywords: Computed force control method, genetic algorithm, hybrid manipulator, inverse kinematics of redundant manipulators, variable geometry truss.

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81 Formation Control of Mobile Robots

Authors: Krishna S. Raghuwaiya, Shonal Singh, Jito Vanualailai

Abstract:

In this paper, we study the formation control problem for car-like mobile robots. A team of nonholonomic mobile robots navigate in a terrain with obstacles, while maintaining a desired formation, using a leader-following strategy. A set of artificial potential field functions is proposed using the direct Lyapunov method for the avoidance of obstacles and attraction to their designated targets. The effectiveness of the proposed control laws to verify the feasibility of the model is demonstrated through computer simulations

Keywords: Control, Formation, Lyapunov, Nonholonomic

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80 Lyapunov-Based Tracking Control for Nonholonomic Wheeled Mobile Robot

Authors: Raouf Fareh, Maarouf Saad, Sofiane Khadraoui, Tamer Rabie

Abstract:

This paper presents a tracking control strategy based on Lyapunov approach for nonholonomic wheeled mobile robot. This control strategy consists of two levels. First, a kinematic controller is developed to adjust the right and left wheel velocities. Using this velocity control law, the stability of the tracking error is guaranteed using Lyapunov approach. This kinematic controller cannot be generated directly by the motors. To overcome this problem, the second level of the controllers, dynamic control, is designed. This dynamic control law is developed based on Lyapunov theory in order to track the desired trajectories of the mobile robot. The stability of the tracking error is proved using Lupunov and Barbalat approaches. Simulation results on a nonholonomic wheeled mobile robot are given to demonstrate the feasibility and effectiveness of the presented approach.

Keywords: Mobile robot, trajectory tracking, Lyapunov, stability.

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79 Design and Analysis of a Novel 8-DOF Hybrid Manipulator

Authors: H. Mohammadipanah, H. Zohoor

Abstract:

This paper presents kinematic and dynamic analysis of a novel 8-DOF hybrid robot manipulator. The hybrid robot manipulator under consideration consists of a parallel robot which is followed by a serial mechanism. The parallel mechanism has three translational DOF, and the serial mechanism has five DOF so that the overall degree of freedom is eight. The introduced manipulator has a wide workspace and a high capability to reduce the actuating energy. The inverse and forward kinematic solutions are described in closed form. The theoretical results are verified by a numerical example. Inverse dynamic analysis of the robot is presented by utilizing the Iterative Newton-Euler and Lagrange dynamic formulation methods. Finally, for performing a multi-step arc welding process, results have indicated that the introduced manipulator is highly capable of reducing the actuating energy.

Keywords: hybrid robot, closed form, inverse dynamic, actuating energy, arc welding

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78 Sensor-Based Motion Planning for a Car-like Robot Based On Bug Family Algorithms

Authors: Dong-Hyung Kim, Ji Yeong Lee, Chang-Soo Han

Abstract:

This paper presents a sensor-based motion planning algorithm for 3-DOF car-like robots with a nonholonomic constraint. Similar to the classic Bug family algorithms, the proposed algorithm enables the car-like robot to navigate in a completely unknown environment using only the range sensor information. The car-like robot uses the local range sensor view to determine the local path so that it moves towards the goal. To guarantee that the robot can approach the goal, the two modes of motion are repeated, termed motion-to-goal and wall-following. The motion-to-goal behavior lets the robot directly move toward the goal, and the wall-following behavior makes the robot circumnavigate the obstacle boundary until it meets the leaving condition. For each behavior, the nonholonomic motion for the car-like robot is planned in terms of the instantaneous turning radius. The proposed algorithm is implemented to the real robot and the experimental results show the performance of proposed algorithm.

Keywords: Motion planning, car-like robot, bug algorithm, autonomous motion planning, nonholonomic constraint.

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77 Kinematic Analysis of 2-DOF Planer Robot Using Artificial Neural Network

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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76 Discrete Tracking Control of Nonholonomic Mobile Robots: Backstepping Design Approach

Authors: Alexander S. Andreev, Olga A. Peregudova

Abstract:

In this paper we propose a discrete tracking control of nonholonomic mobile robots with two degrees of freedom. The electromechanical model of a mobile robot moving on a horizontal surface without slipping, with two rear wheels controlled by two independent DC electric, and one front roal wheel is considered. We present backstepping design based on the Euler approximate discretetime model of a continuous-time plant. Theoretical considerations are verified by numerical simulation.

Keywords: Actuator Dynamics, Backstepping, Discrete-Time Controller, Lyapunov Function, Wheeled Mobile Robot.

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75 Optimization of Inverse Kinematics of a 3R Robotic Manipulator using Genetic Algorithms

Authors: J. Ramírez A., A. Rubiano F.

Abstract:

In this paper the direct kinematic model of a multiple applications three degrees of freedom industrial manipulator, was developed using the homogeneous transformation matrices and the Denavit - Hartenberg parameters, likewise the inverse kinematic model was developed using the same method, verifying that in the workload border the inverse kinematic presents considerable errors, therefore a genetic algorithm was implemented to optimize the model improving greatly the efficiency of the model.

Keywords: Direct Kinematic, Genetic Algorithm, InverseKinematic, Optimization, Robot Manipulator

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74 Trajectory Tracking of a 2-Link Mobile Manipulator Using Sliding Mode Control Method

Authors: Abolfazl Mohammadijoo

Abstract:

In this paper, we are investigating sliding mode control approach for trajectory tracking of a two-link-manipulator with wheeled mobile robot in its base. The main challenge of this work is dynamic interaction between mobile base and manipulator which makes trajectory tracking more difficult than n-link manipulators with fixed base. Another challenging part of this work is to avoid chattering phenomenon of sliding mode control that makes lots of damages for actuators in real industrial cases. The results show the effectiveness of sliding mode control approach for desired trajectory.

Keywords: Mobile manipulator, sliding mode control, dynamic interaction, mobile robotics.

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73 Artificial Neural Network with Steepest Descent Backpropagation Training Algorithm for Modeling Inverse Kinematics of Manipulator

Authors: Thiang, Handry Khoswanto, Rendy Pangaldus

Abstract:

Inverse kinematics analysis plays an important role in developing a robot manipulator. But it is not too easy to derive the inverse kinematic equation of a robot manipulator especially robot manipulator which has numerous degree of freedom. This paper describes an application of Artificial Neural Network for modeling the inverse kinematics equation of a robot manipulator. In this case, the robot has three degree of freedoms and the robot was implemented for drilling a printed circuit board. The artificial neural network architecture used for modeling is a multilayer perceptron networks with steepest descent backpropagation training algorithm. The designed artificial neural network has 2 inputs, 2 outputs and varies in number of hidden layer. Experiments were done in variation of number of hidden layer and learning rate. Experimental results show that the best architecture of artificial neural network used for modeling inverse kinematics of is multilayer perceptron with 1 hidden layer and 38 neurons per hidden layer. This network resulted a RMSE value of 0.01474.

Keywords: Artificial neural network, back propagation, inverse kinematics, manipulator, robot.

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72 Comparative Study of Some Adaptive Fuzzy Algorithms for Manipulator Control

Authors: Sudeept Mohan, Surekha Bhanot

Abstract:

The problem of manipulator control is a highly complex problem of controlling a system which is multi-input, multioutput, non-linear and time variant. In this paper some adaptive fuzzy, and a new hybrid fuzzy control algorithm have been comparatively evaluated through simulations, for manipulator control. The adaptive fuzzy controllers consist of self-organizing, self-tuning, and coarse/fine adaptive fuzzy schemes. These controllers are tested for different trajectories and for varying manipulator parameters through simulations. Various performance indices like the RMS error, steady state error and maximum error are used for comparison. It is observed that the self-organizing fuzzy controller gives the best performance. The proposed hybrid fuzzy plus integral error controller also performs remarkably well, given its simple structure.

Keywords: Hybrid fuzzy, Self-organizing, Self-tuning, Trajectory tracking.

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71 Design of a 4-DOF Robot Manipulator with Optimized Algorithm for Inverse Kinematics

Authors: S. Gómez, G. Sánchez, J. Zarama, M. Castañeda Ramos, J. Escoto Alcántar, J. Torres, A. Núñez, S. Santana, F. Nájera, J. A. Lopez

Abstract:

This paper shows in detail the mathematical model of direct and inverse kinematics for a robot manipulator (welding type) with four degrees of freedom. Using the D-H parameters, screw theory, numerical, geometric and interpolation methods, the theoretical and practical values of the position of robot were determined using an optimized algorithm for inverse kinematics obtaining the values of the particular joints in order to determine the virtual paths in a relatively short time.

Keywords: Kinematics, degree of freedom, optimization, robot manipulator.

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70 Nonlinear Effects in Stiffness Modeling of Robotic Manipulators

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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69 Flexible Arm Manipulator Control for Industrial Tasks

Authors: Mircea Ivanescu, Nirvana Popescu, Decebal Popescu, Dorin Popescu

Abstract:

This paper addresses the control problem of a class of hyper-redundant arms. In order to avoid discrepancy between the mathematical model and the actual dynamics, the dynamic model with uncertain parameters of this class of manipulators is inferred. A procedure to design a feedback controller which stabilizes the uncertain system has been proposed. A PD boundary control algorithm is used in order to control the desired position of the manipulator. This controller is easy to implement from the point of view of measuring techniques and actuation. Numerical simulations verify the effectiveness of the presented methods. In order to verify the suitability of the control algorithm, a platform with a 3D flexible manipulator has been employed for testing. Experimental tests on this platform illustrate the applications of the techniques developed in the paper.

Keywords: Distributed model, flexible manipulator, observer, robot control.

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68 Using the Polynomial Approximation Algorithm in the Algorithm 2 for Manipulator's Control in an Unknown Environment

Authors: Pavel K. Lopatin, Artyom S. Yegorov

Abstract:

The Algorithm 2 for a n-link manipulator movement amidst arbitrary unknown static obstacles for a case when a sensor system supplies information about local neighborhoods of different points in the configuration space is presented. The Algorithm 2 guarantees the reaching of a target position in a finite number of steps. The Algorithm 2 is reduced to a finite number of calls of a subroutine for planning a trajectory in the presence of known forbidden states. The polynomial approximation algorithm which is used as the subroutine is presented. The results of the Algorithm2 implementation are given.

Keywords: Manipulator, trajectory planning, unknown obstacles.

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67 Sliding Mode Control Based on Backstepping Approach for an UAV Type-Quadrotor

Authors: H. Bouadi, M. Bouchoucha, M. Tadjine

Abstract:

In this paper; we are interested principally in dynamic modelling of quadrotor while taking into account the high-order nonholonomic constraints in order to develop a new control scheme as well as the various physical phenomena, which can influence the dynamics of a flying structure. These permit us to introduce a new state-space representation. After, the use of Backstepping approach for the synthesis of tracking errors and Lyapunov functions, a sliding mode controller is developed in order to ensure Lyapunov stability, the handling of all system nonlinearities and desired tracking trajectories. Finally simulation results are also provided in order to illustrate the performances of the proposed controller.

Keywords: Dynamic modeling, nonholonomic constraints, Backstepping, sliding mode.

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66 Visual Inspection of Work Piece with a Complex Shape by Means of Robot Manipulator

Authors: A. Y. Bani Hashim, N. S. A. Ramdan

Abstract:

Inconsistency in manual inspection is real because humans get tired after some time. Recent trends show that automatic inspection is more appealing for mass production inspections. In such as a case, a robot manipulator seems the best candidate to run a dynamic visual inspection. The purpose of this work is to estimate the optimum workspace where a robot manipulator would perform a visual inspection process onto a work piece where a camera is attached to the end effector. The pseudo codes for the planned path are derived from the number of tool transit points, the delay time at the transit points, the process cycle time, and the configuration space that the distance between the tool and the work piece. It is observed that express start and swift end are acceptable in a robot program because applicable works usually in existence during these moments. However, during the mid-range cycle, there are always practical tasks programmed to be executed. For that reason, it is acceptable to program the robot such as that speedy alteration of actuator displacement is avoided. A dynamic visual inspection system using a robot manipulator seems practical for a work piece with a complex shape.

Keywords: Robot manipulator, Visual inspection, Work piece, Trajectory planning.

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65 Path Planning of a Robot Manipulator using Retrieval RRT Strategy

Authors: K. Oh, J. P. Hwang, E. Kim, H. Lee

Abstract:

This paper presents an algorithm which extends the rapidly-exploring random tree (RRT) framework to deal with change of the task environments. This algorithm called the Retrieval RRT Strategy (RRS) combines a support vector machine (SVM) and RRT and plans the robot motion in the presence of the change of the surrounding environment. This algorithm consists of two levels. At the first level, the SVM is built and selects a proper path from the bank of RRTs for a given environment. At the second level, a real path is planned by the RRT planners for the given environment. The suggested method is applied to the control of KUKA™,, a commercial 6 DOF robot manipulator, and its feasibility and efficiency are demonstrated via the cosimulatation of MatLab™, and RecurDyn™,.

Keywords: Path planning, RRT, 6 DOF manipulator, SVM.

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64 Technological Development and Implementation of a Robotic Arm Motioned by Programmable Logic Controller

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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63 Nonlinear Observer Design and Sliding Mode Control of Four Rotors Helicopter

Authors: H. Bouadi, M. Tadjine

Abstract:

In this paper; we are interested in dynamic modelling of quadrotor while taking into account the high-order nonholonomic constraints as well as the various physical phenomena, which can influence the dynamics of a flying structure. These permit us to introduce a new state-space representation and new control scheme. We present after the development and the synthesis of a stabilizing control laws design based on sliding mode in order to perform best tracking results. It ensures locally asymptotic stability and desired tracking trajectories. Nonlinear observer is then synthesized in order to estimate the unmeasured states and the effects of the external disturbances such as wind and noise. Finally simulation results are also provided in order to illustrate the performances of the proposed controllers.

Keywords: Dynamic modelling, nonholonomic constraints, sliding mode, nonlinear observer.

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62 Model Inversion of a Two Degrees of Freedom Linearized PUMA from Bicausal Bond Graphs

Authors: Gilberto Gonzalez-A, Ignacio Rodríguez- A., Dunia Nuñez-P

Abstract:

A bond graph model of a two degrees of freedom PUMA is described. System inversion gives the system input required to generate a given system output. In order to get the system inversion of the PUMA manipulator, a linearization of the nonlinear bond graph is obtained. Hence, the bicausality of the linearized bond graph of the PUMA manipulator is applied. Thus, the bicausal bond graph provides a systematic way of generating the equations of the system inversion. Simulation results to verify the calculated input for a given output are shown.

Keywords: Bond graph, system inversion, bicausality, PUMA manipulator

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61 Genetic Algorithm Based Optimal Control for a 6-DOF Non Redundant Stewart Manipulator

Authors: A. Omran, G. El-Bayiumi, M. Bayoumi, A. Kassem

Abstract:

Applicability of tuning the controller gains for Stewart manipulator using genetic algorithm as an efficient search technique is investigated. Kinematics and dynamics models were introduced in detail for simulation purpose. A PD task space control scheme was used. For demonstrating technique feasibility, a Stewart manipulator numerical-model was built. A genetic algorithm was then employed to search for optimal controller gains. The controller was tested onsite a generic circular mission. The simulation results show that the technique is highly convergent with superior performance operating for different payloads.

Keywords: Stewart kinematics, Stewart dynamics, task space control, genetic algorithm.

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60 Bio-mechanical Analysis of Human Joints and Extension of the Study to Robot

Authors: S. Parasuraman, Ler Shiaw Pei

Abstract:

In this paper, the bio-mechanical analysis of human joints is carried out and the study is extended to the robot manipulator. This study will first focus on the kinematics of human arm which include the movement of each joint in shoulder, wrist, elbow and finger complexes. Those analyses are then extended to the design of a human robot manipulator. A simulator is built for Direct Kinematics and Inverse Kinematics of human arm. In the simulation of Direct Kinematics, the human joint angles can be inserted, while the position and orientation of each finger tips (end-effector) are shown. Inverse Kinematics does the reverse of the Direct Kinematics. Based on previous materials obtained from kinematics analysis, the human manipulator joints can be designed to follow prescribed position trajectories.

Keywords: Kinematics, Human Joints, Robotics, Robot Dynamics, Manipulators.

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