Search results for: Robot kinematics

Authors: Seongcheol Kwon, Jeongmin Kim, Kwang Ryel Ryu

Abstract:

We assume an IoT-based smart-home environment where the on-off status of each of the electrical appliances including the room lights can be recognized in a real time by monitoring and analyzing the smart meter data. At any moment in such an environment, we can recognize what the household or the user is doing by referring to the status data of the appliances. In this paper, we focus on a smart-home service that is to activate a robot vacuum cleaner at right time by recognizing the user situation, which requires a situation-aware model that can distinguish the situations that allow vacuum cleaning (Yes) from those that do not (No). We learn as our candidate models a few classifiers such as naïve Bayes, decision tree, and logistic regression that can map the appliance-status data into Yes and No situations. Our training and test data are obtained from simulations of user behaviors, in which a sequence of user situations such as cooking, eating, dish washing, and so on is generated with the status of the relevant appliances changed in accordance with the situation changes. During the simulation, both the situation transition and the resulting appliance status are determined stochastically. To compare the performances of the aforementioned classifiers we obtain their learning curves for different types of users through simulations. The result of our empirical study reveals that naïve Bayes achieves a slightly better classification accuracy than the other compared classifiers.

Keywords: Situation-awareness, Smart home, IoT, Machine learning, Classifier.

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Authors: Brahmi Brahim, Mohammad Habibur Rahman, Maarouf Saad, Cristóbal Ochoa Luna

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A repetitive training movement is an efficient method to improve the ability and movement performance of stroke survivors and help them to recover their lost motor function and acquire new skills. The ETS-MARSE is seven degrees of freedom (DOF) exoskeleton robot developed to be worn on the lateral side of the right upper-extremity to assist and rehabilitate the patients with upper-extremity dysfunction resulting from stroke. Practically, rehabilitation activities are repetitive tasks, which make the assistive/robotic systems to suffer from repetitive/periodic uncertainties and external perturbations induced by the high-order dynamic model (seven DOF) and interaction with human muscle which impact on the tracking performance and even on the stability of the exoskeleton. To ensure the robustness and the stability of the robot, a new nonlinear backstepping control was implemented with designed tests performed by healthy subjects. In order to limit and to reject the periodic/repetitive disturbances, an iterative estimator was integrated into the control of the system. The estimator does not need the precise dynamic model of the exoskeleton. Experimental results confirm the robustness and accuracy of the controller performance to deal with the external perturbation, and the effectiveness of the iterative estimator to reject the repetitive/periodic disturbances.

Keywords: Backstepping control, iterative control, rehabilitation, ETS-MARSE.

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

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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: Wai Phyo Aung

Abstract:

Wheeled Mobile Robots (WMRs) are built with their Wheels- drive machine, Motors. Depend on their desire design of WMR, Technicians made used of DC Motors for motion control. In this paper, the author would like to analyze how to choose DC motor to be balance with their applications of especially for WMR. Specification of DC Motor that can be used with desire WMR is to be determined by using MATLAB Simulink model. Therefore, this paper is mainly focus on software application of MATLAB and Control Technology. As the driving system of DC motor, a Peripheral Interface Controller (PIC) based control system is designed including the assembly software technology and H-bridge control circuit. This Driving system is used to drive two DC gear motors which are used to control the motion of WMR. In this analyzing process, the author mainly focus the drive system on driving two DC gear motors that will control with Differential Drive technique to the Wheeled Mobile Robot . For the design analysis of Motor Driving System, PIC16F84A is used and five inputs of sensors detected data are tested with five ON/OFF switches. The outputs of PIC are the commands to drive two DC gear motors, inputs of Hbridge circuit .In this paper, Control techniques of PIC microcontroller and H-bridge circuit, Mechanism assignments of WMR are combined and analyzed by mainly focusing with the “Modeling and Simulink of DC Motor using MATLAB".

Keywords: Control System Design, DC Motors, DifferentialDrive, H-bridge control circuit, MATLAB Simulink model, Peripheral Interface Controller (PIC), Wheeled Mobile Robots.

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Authors: Marc Diesse, Hochschule Heilbronn

Abstract:

We address the question of identifying the configuration space singularities of linkages, i.e., points where the configuration space is not locally a submanifold of Euclidean space. Because the configuration space cannot be smoothly parameterized at such points, these singularity types have a significantly negative impact on the kinematics of the linkage. It is known that Jacobian methods do not provide sufficient conditions for the existence of CS-singularities. Herein, we present several additional algebraic criteria that provide the sufficient conditions. Further, we use those criteria to analyze certain classes of planar linkages. These examples will also show how the presented criteria can be checked using algorithmic methods.

Keywords: Linkages, configuration space singularities, real algebraic geometry, analytic geometry, computer algebra.

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Authors: Panagiotis Kyratsis, Konstantinos Kakoulis

Abstract:

Nowadays, the rapid development of CAD systems’ programming environments results in the creation of multiple downstream applications, which are developed and becoming increasingly available. CAD based manufacturing simulations is gradually following the same trend. Drilling is the most popular holemaking process used in a variety of industries. A specially built piece of software that deals with the drilling kinematics is presented. The cutting forces are calculated based on the tool geometry, the cutting conditions and the tool/work-piece materials. The results are verified by experimental work. Finally, the response surface methodology (RSM) is applied and mathematical models of the total thrust force and the thrust force developed because of the main cutting edges are proposed.

Keywords: Application programming interface, CAD, drilling, response surface methodology, RSM.

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Authors: Hamidreza Hoshyarmanesh, Hosein Madieh, Sanju Lama, Yaser Maddahi, Garnette R. Sutherland, Kourosh Zareinia

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This paper illustrates the concept of an algorithm to register specified markers on the neuroArm surgical manipulators, an image-guided MR-compatible tele-operated robot for microsurgery and stereotaxy. Two range-finding algorithms, namely time-of-flight and phase-shift, are evaluated for registration and supervisory control. The time-of-flight approach is implemented in a semi-field experiment to determine the precise position of a tiny retro-reflective moving object. The moving object simulates a surgical tool tip. The tool is a target that would be connected to the neuroArm end-effector during surgery inside the magnet bore of the MR imaging system. In order to apply flight approach, a 905-nm pulsed laser diode and an avalanche photodiode are utilized as the transmitter and receiver, respectively. For the experiment, a high frequency time to digital converter was designed using a field-programmable gate arrays. In the phase-shift approach, a continuous green laser beam with a wavelength of 530 nm was used as the transmitter. Results showed that a positioning error of 0.1 mm occurred when the scanner-target point distance was set in the range of 2.5 to 3 meters. The effectiveness of this non-contact approach exhibited that the method could be employed as an alternative for conventional mechanical registration arm. Furthermore, the approach is not limited by physical contact and extension of joint angles.

Keywords: 3D laser scanner, intraoperative MR imaging, neuroArm, real time registration, robot-assisted surgery, supervisory control.

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Authors: A. Arockia Selvakumar, R. Sivaramakrishnan, Srinivasa Karthik.T.V, Valluri Siva Ramakrishna, B.Vinodh.

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Industrial robots play a vital role in automation however only little effort are taken for the application of robots in machining work such as Grinding, Cutting, Milling, Drilling, Polishing etc. Robot parallel manipulators have high stiffness, rigidity and accuracy, which cannot be provided by conventional serial robot manipulators. The aim of this paper is to perform the modeling and the workspace analysis of a 3 DOF Parallel Manipulator (3 DOF PM). The 3 DOF PM was modeled and simulated using 'ADAMS'. The concept involved is based on the transformation of motion from a screw joint to a spherical joint through a connecting link. This paper work has been planned to model the Parallel Manipulator (PM) using screw joints for very accurate positioning. A workspace analysis has been done for the determination of work volume of the 3 DOF PM. The position of the spherical joints connected to the moving platform and the circumferential points of the moving platform were considered for finding the workspace. After the simulation, the position of the joints of the moving platform was noted with respect to simulation time and these points were given as input to the 'MATLAB' for getting the work envelope. Then 'AUTOCAD' is used for determining the work volume. The obtained values were compared with analytical approach by using Pappus-Guldinus Theorem. The analysis had been dealt by considering the parameters, link length and radius of the moving platform. From the results it is found that the radius of moving platform is directly proportional to the work volume for a constant link length and the link length is also directly proportional to the work volume, at a constant radius of the moving platform.

Keywords: Three Degrees of freedom Parallel Manipulator (3DOF PM), ADAMS, Work volume, MATLAB, AUTOCAD, Pappus- Guldinus Theorem.

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Authors: L. Parisi

Abstract:

Kinematic data wisely correlate vector quantities in space to scalar parameters in time to assess the degree of symmetry between the intact limb and the amputated limb with respect to a normal model derived from the gait of control group participants. Furthermore, these particular data allow a doctor to preliminarily evaluate the usefulness of a certain rehabilitation therapy. Kinetic curves allow the analysis of ground reaction forces (GRFs) to assess the appropriateness of human motion. Electromyography (EMG) allows the analysis of the fundamental lower limb force contributions to quantify the level of gait asymmetry. However, the use of this technological tool is expensive and requires patient’s hospitalization. This research work suggests overcoming the above limitations by applying artificial neural networks.

Keywords: Kinetics, kinematics, cyclograms, neural networks.

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Authors: Javier Romera, Alberto Justo, Ignacio Fidalgo, Javier Araluce, Joshué Pérez

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Nowadays, individuals with mobility needs face a significant challenge when docking vehicles. In many cases, after parking, they encounter insufficient space to exit, leading to two undesired outcomes: either avoiding parking in that spot or settling for improperly placed vehicles. To address this issue, this paper presents a parking control system employing gestural teleoperation. The system comprises three main phases: capturing body markers, interpreting gestures, and transmitting orders to the vehicle. The initial phase is centered around the MediaPipe framework, a versatile tool optimized for real-time gesture recognition. MediaPipe excels at detecting and tracing body markers, with a special emphasis on hand gestures. Hands detection is done by generating 21 reference points for each hand. Subsequently, after data capture, the project employs the MultiPerceptron Layer (MPL) for in-depth gesture classification. This tandem of MediaPipe’s extraction prowess and MPL’s analytical capability ensures that human gestures are translated into actionable commands with high precision. Furthermore, the system has been trained and validated within a built-in dataset. To prove the domain adaptation, a framework based on the Robot Operating System 2 (ROS2), as a communication backbone, alongside CARLA Simulator, is used. Following successful simulations, the system is transitioned to a real-world platform, marking a significant milestone in the project. This real-vehicle implementation verifies the practicality and efficiency of the system beyond theoretical constructs.

Keywords: Gesture detection, MediaPipe, MultiLayer Perceptron Layer, Robot Operating System.

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Authors: T. C. Manjunath, C. Ardil

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This paper presents an efficient method of obtaining a straight-line motion in the tool configuration space using an articulated robot between two specified points. The simulation results & the implementation results show the effectiveness of the method.

Keywords: Bounded deviation algorithm, Straight line motion, Tool configuration space, Joint space, TCV.

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Authors: Xie Kefeng, Zhang He

Abstract:

For the stability and control demand of offshore small floating platform, a 2-HUS/U parallel mechanism was presented as offshore platform. Inverse kinematics was obtained by institutional constraint equation, and the dynamic model of offshore 2-HUS/U parallel platform was derived based on rigid body’s Lagrangian method. The equivalent moment of inertia, damping and driving force/torque variation of offshore 2-HUS/U parallel platform were analyzed. A numerical example shows that, for parallel platform of given motion, system’s equivalent inertia changes 1.25 times maximally. During the movement of platform, they change dramatically with the system configuration and have coupling characteristics. The maximum equivalent drive torque is 800 N. At the same time, the curve of platform’s driving force/torque is smooth and has good sine features. The control system needs to be adjusted according to kinetic equation during stability and control and it provides a basis for the optimization of control system.

Keywords: 2-HUS/U platform, Dynamics, Lagrange, Parallel platform.

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Authors: S. C. Kattimani

Abstract:

This article deals with the analysis of active constrained layer damping (ACLD) of smart multiferroic or magneto-electro-elastic doubly curved shells. The kinematics of deformations of the multiferroic doubly curved shell is described by a layer-wise shear deformation theory. A three-dimensional finite element model of multiferroic shells has been developed taking into account the electro-elastic and magneto-elastic couplings. A simple velocity feedback control law is employed to incorporate the active damping. Influence of layer stacking sequence and boundary conditions on the response of the multiferroic doubly curved shell has been studied. In addition, for the different orientation of the fibers of the constraining layer, the performance of the ACLD treatment has been studied.

Keywords: Active constrained layer damping, doubly curved shells, magneto-electro-elastic, multiferroic composite, smart structures.

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Authors: Waleed Maqableh, Ahmad Al-Hamad, Manjit Sidhu

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Augmented reality (AR) technology has the capability to provide many benefits in the field of education as a modern technology which aided learning and improved the learning experience. This paper evaluates AR based application with multiple markers interaction technique (touch-to-print) which is designed for analyzing the kinematics of 4BL mechanism in mechanical engineering. The application is termed as AR-4BL-MAST and it allows the users to touch the symbols on a paper in natural way of interaction. The evaluation of this application was performed with mechanical engineering students and human–computer interaction (HCI) experts to test its effectiveness as a tangible user interface application where the statistical results show its ability as an interaction technique, and it gives the users more freedom in interaction with the virtual mechanical objects.

Keywords: Augmented reality, engineering, four-bar linkage, Multimedia, user interface, visualization.

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Authors: Byung Ki Kim, Ho Min Jung, Jae-Bong Yoo, Wan Yeon Lee, Chan Young Park, Young Woong Ko

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In this paper, we present a novel approach to location system under indoor environment. The key idea of our work is accurate distance estimation with cricket-based location system using A* algorithm. We also use magnetic sensor for detecting obstacles in indoor environment. Finally, we suggest how this system can be used in various applications such as asset tracking and monitoring.

Keywords: Cricket, Indoor Location Tracking, Mobile Robot, Localization.

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Authors: Li Jie, Zhang Wei

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In this paper, the problem of posture stabilization for a kinematic model of differential drive robots is studied. A more complex model of the kinematics of differential drive robots is used for the design of stabilizing control. This model is formulated in terms of the physical parameters of the system such as the radius of the wheels, and velocity of the wheels are the control inputs of it. In this paper, the framework of Lyapunov-based control design has been used to solve posture stabilization problem for the comprehensive model of differential drive robots. The results of the simulations show that the devised controller successfully solves the posture regulation problem. Finally, robustness and performance of the controller have been studied under system parameter uncertainty.

Keywords: Differential drive robots, nonlinear control, Lyapunov-based control design, posture regulation.

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Authors: Hirohide Ushida

Abstract:

This paper discusses an artificial mind model and its applications. The mind model is based on some theories which assert that emotion is an important function in human decision making. An artificial mind model with emotion is built, and the model is applied to action selection of autonomous agents. In three examples, the agents interact with humans and their environments. The examples show the proposed model effectively work in both virtual agents and real robots.

Keywords: Artificial mind, emotion, interactive agent, pet robot

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Authors: P. Zamov, H. Spangenberg

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Presents a concept for a multidisciplinary process supporting effective task transitions between different technical domains during the architectural design stage. A system configuration challenge is the multifunctional driven increased solution space. As a consequence, more iteration is needed to find a global optimum, i.e. a compromise between involved disciplines without negative impact on development time. Since state of the art standards like ISO 15288 and VDI 2206 do not provide a detailed methodology on multidisciplinary design process, higher uncertainties regarding final specifications arise. This leads to the need of more detailed and standardized concepts or processes which could mitigate risks. The performed work is based on analysis of multidisciplinary interaction, of modeling and simulation techniques. To demonstrate and prove the applicability of the presented concept, it is applied to the design of aircraft high lift systems, in the context of the engineering disciplines kinematics, actuation, monitoring, installation and structure design.

Keywords: Systems engineering, multidisciplinary, architectural design, high lift system.

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Authors: Chung-Chun Hsiao, Yu-Kai, Ting, Kai-Yuan Liu, Pang-Wei Yen, Jia-Ying Tu

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In this paper, a new design of spherical robotic system based on the concepts of gimbal structure and gyro dynamics is presented. Robots equipped with multiple wheels and complex steering mechanics may increase the weight and degrade the energy transmission efficiency. In addition, the wheeled and legged robots are relatively vulnerable to lateral impact and lack of lateral mobility. Therefore, the proposed robotic design uses a spherical shell as the main body for ground locomotion, instead of using wheel devices. Three spherical shells are structured in a similar way to a gimbal device and rotate like a gyro system. The design and mechanism of the proposed robotic system is introduced. In addition, preliminary results of the dynamic model based on the principles of planar rigid body kinematics and Lagrangian equation are included. Simulation results and rig construction are presented to verify the concepts.

Keywords: Gyro, gimbal, Lagrange equation, spherical robots.

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Authors: S. F. Wong, S. S. Dol

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Automotive designers have been trying to use dimples to reduce drag in vehicles. In this work, a car model has been applied with dimple surface with a parameter called dimple ratio DR, the ratio between the depths of the half dimple over the print diameter of the dimple, has been introduced and numerically simulated via k-ε turbulence model to study the aerodynamics performance with the increasing depth of the dimples The Ahmed body car model with 25 degree slant angle is simulated with the DR of 0.05, 0.2, 0.3 0.4 and 0.5 at Reynolds number of 176387 based on the frontal area of the car model. The geometry of dimple changes the kinematics and dynamics of flow. Complex interaction between the turbulent fluctuating flow and the mean flow escalates the turbulence quantities. The maximum level of turbulent kinetic energy occurs at DR = 0.4. It can be concluded that the dimples have generated extra turbulence energy at the surface and as a result, the application of dimples manages to reduce the drag coefficient of the car model compared to the model with smooth surface.

Keywords: Aerodynamics, Boundary Layer, Dimple, Drag, Kinetic Energy, Turbulence.

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Authors: Pavel Dostrašil, Petr Jirásko

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The paper deals with the kinematics and automated calculation of intermittent mechanisms with radial cams. Currently, electronic cams are increasingly applied in the drives of working link mechanisms. Despite a huge advantage of electronic cams in their reprogrammability or instantaneous change of displacement diagrams, conventional cam mechanisms have an irreplaceable role in production and handling machines. With high frequency of working cycle periods, the dynamic load of the proper servomotor rotor increases and efficiency of electronic cams strongly decreases. Though conventional intermittent mechanisms with radial cams are representatives of fixed automation, they have distinct advantages in their high speed (high dynamics), positional accuracy and relatively easy manufacture. We try to remove the disadvantage of firm displacement diagram by reducing costs for simple design and automated calculation that leads reliably to high-quality and inexpensive manufacture.

Keywords: Cam mechanism, displacement diagram, intermittentmechanism, radial parallel cam

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Authors: A. Emre Ozturk, Ergun Ercelebi

Abstract:

Autonomous robotic systems need an equipment like a human eye for their movement. In this study a 3D laser scanner has been designed and implemented for those autonomous robotic systems. In general 3D laser scanners are using 2 dimension laser range finders that are moving on one-axis (1D) to generate the model. In this study, the model has been obtained by a one-dimensional laser range finder that is moving in two –axis (2D) and because of this the laser scanner has been produced cheaper.

Keywords: 3D Laser Scanner, embedded systems.

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Authors: Sanda Win, Tin Shein, Khin Maung Latt

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This document describes an electronic speed control designed to drive two DC motors from a 6 V battery pack to be controlled by a commercial universal infrared remote control hand set. Conceived for a tank-like vehicle, one motor drives the left side wheels or tracks and the other motor drives the right side. As it is shown here, there is a left-right steering input and a forward– backward throttles input, like would be used on a model car. It is designed using a microcontroller PIC16F873A.

Keywords: Assembly Language, Direction Control, SpeedControl, PIC 16F 873A

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Authors: J. Bouchard, B. Prosperi, G. Bavre, M. Daudé, E. Jeandupeux

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Young patients suffering from Cerebral Palsy are facing difficult choices concerning heavy surgeries. Diagnosis settled by surgeons can be complex and on the other hand decision for patient about getting or not such a surgery involves important reflection effort. Proposed software combining prediction for surgeries and post surgery kinematic values, and from 3D model representing the patient is an innovative tool helpful for both patients and medicine professionals. Beginning with analysis and classification of kinematics values from Data Base extracted from gait analysis in 3 separated clusters, it is possible to determine close similarity between patients. Prediction surgery best adapted to improve a patient gait is then determined by operating a suitable preconditioned neural network. Finally, patient 3D modeling based on kinematic values analysis, is animated thanks to post surgery kinematic vectors characterizing the closest patient selected from patients clustering.

Keywords: Cerebral Palsy, Clustering, Crouch Gait, 3-D Modeling.

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Authors: A. Denker, U. Akıncıoğlu

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In this paper a neural adaptive control method has been developed and applied to robot control. Simulation results are presented to verify the effectiveness of the controller. These results show that the performance by using this controller is better than those which just use either direct inverse control or predictive control. In addition, they show that the resulting is a useful method which combines the advantages of both direct inverse control and predictive control.

Keywords: Neural networks, robotics, direct inverse control, predictive control.

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Authors: Miloš Šeda, Tomáš Březina

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In this paper, we focus on the use of knowledge bases in two different application areas – control of systems with unknown or strongly nonlinear models (i.e. hardly controllable by the classical methods), and robot motion planning in eight directions. The first one deals with fuzzy logic and the paper presents approaches for setting and aggregating the rules of a knowledge base. Te second one is concentrated on a case-based reasoning strategy for finding the path in a planar scene with obstacles.

Keywords: fuzzy controller, fuzzification, rule base, inference, defuzzification, genetic algorithm, neural network, case-based reasoning

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Authors: Peter Kostal, Karol Velisek

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Flexible manufacturing system is a system that is able to respond to changed conditions. In general, this flexibility is divided into two key categories and several subcategories. The first category is the so called machine flexibility which enables to make various products by the given machinery. The second category is routing flexibility enabling to execute the same operation by various machines. Flexible manufacturing systems usually consist of three main parts: CNC machine tools, transport system and control system. A higher level of flexible manufacturing systems is represented by the so called intelligent manufacturing systems.

Keywords: drawing-free manufacturing, flexible manufacturing system, industrial robot, material flow.

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Authors: Mario Gianni, Manuel A. Ruiz Garcia, Fiora Pirri

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In this work, we present a Bayesian non-parametric approach to model the motion control of ATVs. The motion control model is based on a Dirichlet Process-Gaussian Process (DP-GP) mixture model. The DP-GP mixture model provides a flexible representation of patterns of control manoeuvres along trajectories of different lengths and discretizations. The model also estimates the number of patterns, sufficient for modeling the dynamics of the ATV.

Keywords: Dirichlet processes, Gaussian processes, robot control learning, tracked vehicles.

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Authors: Eileen Chih-Ying Yang, Liang-Han Wu, Chieh-Min Chang

Abstract:

The design of an active leg orthosis for tumble protection is proposed in this paper. The orthosis would be applied to assist elders or invalids in rebalancing while they fall unexpectedly. We observe the regain balance motion of healthy and youthful people, and find the difference to elders or invalids. First, the physical model of leg would be established, and we consider the leg motions are achieve through four joints (phalanx stem, ankle, knee, and hip joint) and five links (phalanges, talus, tibia, femur, and hip bone). To formulate the dynamic equations, the coordinates which can clearly describe the position in 3D space are first defined accordance with the human movement of leg, and the kinematics and dynamics of the leg movement can be formulated based on the robotics. For the purpose, assisting elders and invalids in avoiding tumble, the posture variation of unbalance and regaining balance motion are recorded by the motion-capture image system, and the trajectory is taken as the desire one. Then we calculate the force and moment of each joint based on the leg motion model through programming MATLAB code. The results would be primary information of the active leg orthosis design for tumble protection.

Keywords: Active leg orthosis, Tumble protection

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Authors: Gabriela R. Fernandes, Renato F. Denadai, Guido J. Denipotti

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In this work, are discussed two formulations of the boundary element method - BEM to perform linear bending analysis of plates reinforced by beams. Both formulations are based on the Kirchhoff's hypothesis and they are obtained from the reciprocity theorem applied to zoned plates, where each sub-region defines a beam or a slab. In the first model the problem values are defined along the interfaces and the external boundary. Then, in order to reduce the number of degrees of freedom kinematics hypothesis are assumed along the beam cross section, leading to a second formulation where the collocation points are defined along the beam skeleton, instead of being placed on interfaces. On these formulations no approximation of the generalized forces along the interface is required. Moreover, compatibility and equilibrium conditions along the interface are automatically imposed by the integral equation. Thus, these formulations require less approximation and the total number of the degree s of freedom is reduced. In the numerical examples are discussed the differences between these two BEM formulations, comparing as well the results to a well-known finite element code.

Keywords: Boundary elements, Building floor structures, Platebending.

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