Search results for: Robot kinematics

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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Authors: C. Schneider, M. M. Seizmeir, T. Suchanek, M. Hutter-Mironovová, M. Bdiwi, M. Putz

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In this paper, a suitable measurement setup is presented to conduct force and pressure measurements for transient contact cases at the example of lathe machine tending. Empirical measurements were executed on a selected collaborative robot’s behavior regarding allowable operating speeds under consideration of sensor- and workpiece-specific factors. Comparisons between the theoretic calculations proposed in ISO/TS 15066 and the practical measurement results reveal a basis for future research. With the created database, preliminary risk assessment and economic assessment procedures of collaborative machine tending cells can be facilitated.

Keywords: biomechanical thresholds, collaborative robots, force and pressure measurements, machine tending, transient contact

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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: Jie Cai, David C. Levy

Abstract:

Electronic nose (array of chemical sensors) are widely used in food industry and pollution control. Also it could be used to locate or detect the direction of the source of emission odors. Usually this task is performed by electronic nose (ENose) cooperated with mobile vehicles, but when a source is instantaneous or surrounding is hard for vehicles to reach, problem occurs. Thus a method for stationary ENose to detect the direction of the source and locate the source will be required. A novel method which uses the ratio between the responses of different sensors as a discriminant to determine the direction of source in natural wind surroundings is presented in this paper. The result shows that the method is accurate and easily to be implemented. This method could be also used in movably, as an optimized algorithm for robot tracking source location.

Keywords: Electronic nose, Nature wind situation, Source direction detection.

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Authors: Tudor Deaconescu, Andrea Deaconescu

Abstract:

Deployment of pneumatic muscles in various industrial applications is still in its early days, considering the relative newness of these components. The field of robotics holds particular future potential for pneumatic muscles, especially in view of their specific behaviour known as compliance. The paper presents and discusses an innovative constructive solution for a gripper system mountable on an industrial robot, based on actuation by a linear pneumatic muscle and transmission of motion by gear and rack mechanism. The structural, operational and constructive models of the new gripper are presented, along with some of the experimental results obtained subsequently to the testing of a prototype. Further presented are two control variants of the gripper system, one by means of a 3/2-way fast-switching solenoid valve, the other by means of a proportional pressure regulator. Advantages and disadvantages are discussed for both variants.

Keywords: Gripper system, pneumatic muscle, structural modeling.

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Authors: A. Naga Rajesh, S. Chandralingam, T. Anjaneyulu, K. Satyanarayana

Abstract:

Assistive robotics are playing a vital role in advancing the quality of life for disable people. There exist wide range of systems that can control and guide autonomous mobile robots. The objective of the control system is to guide an autonomous mobile robot using the movement of eyes by means of EOG signal. The EOG signal is acquired using Ag/AgCl electrodes and this signal is processed by a microcontroller unit to calculate the eye gaze direction. Then according to the guidance control strategy, the control commands of the wheelchair are sent. The classification of different eye movements allows us to generate simple code for controlling the wheelchair. This work was aimed towards developing a usable and low-cost assistive robotic wheel chair system for disabled people. To live more independent life, the system can be used by the handicapped people especially those with only eye-motor coordination.

Keywords: Electrooculography, Microcontroller, Motors, Wheelchair.

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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: P. H. Le, J. Molina, S. Hirai

Abstract:

In this work, we propose the application of Japanese “Origami” art for a floating function of a small aerial vehicle such as a hexarotor. A preliminary experiment was conducted using Origami magic balls mounted under a hexarotor. This magic ball can expand and shrink using an air pump during free flying. Using this interesting and functional concept, it promises to reduce the resistance of wind as well as reduce the energy consumption when the Origami balls are deflated. This approach can be particularly useful in rescue emergency situations. Furthermore, there are many unexpected reasons that may cause the multi-rotor has to land on the surface of water due to problems with the communication between the aircraft and the ground station. In addition, a complementary experiment was designed to prove that the hexarotor can fly maintaining the stability and also, takes off and lands on the surface of water using air balloons.

Keywords: Helicopter, Japanese Origami ball, Floating, Aerial Robots, Rescue.

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Authors: Byung Hoon Seo, Hyun Gyu Kim, Tae Won Seo

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Stair climbing is one of critical issues for field robots to widen applicable areas. This paper presents optimal design on kinematic parameters of a new robotic platform for stair climbing. The robotic platform climbs various stairs by body flip locomotion with caterpillar type main platform. Kinematic parameters such as platform length, platform height, and caterpillar rotation speed are optimized to maximize stair climbing stability. Three types of stairs are used to simulate typical user conditions. The optimal design process is conducted based on Taguchi methodology, and resulting parameters with optimized objective function are presented. In near future, a prototype is assembled for real environment testing.

Keywords: Stair climbing robot, Optimal design, Taguchi methodology, Caterpillar, Kinematic parameters.

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

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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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Authors: Yuanqing Li, Changyi Lei, Zhaopeng Xue, Zhuo Zheng, Yanbo Long

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In agricultural production and breeding, implementing automatic picking robot in orchard farming to reduce human labour and error is challenging. The core function of it is automatic identification based on machine vision. This paper focuses on apple detection and counting in orchards and implements several deep learning methods. Extensive datasets are used and a semi-automatic annotation method is proposed. The proposed deep learning models are in state-of-the-art YOLO family. In view of the essence of the models with various backbones, a multi-dimensional comparison in details is made in terms of counting accuracy, mAP and model memory, laying the foundation for realising automatic precision agriculture.

Keywords: Agricultural object detection, Deep learning, machine vision, YOLO family.

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Authors: Avinesh Prasad, Bibhya Sharma, Jito Vanualailai

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In this paper, we propose a solution to the motion control problem of a 2-link revolute manipulator arm. We require the end-effector of the arm to move safely to its designated target in a priori known workspace cluttered with fixed circular obstacles of arbitrary position and sizes. Firstly a unique velocity algorithm is used to move the end-effector to its target. Secondly, for obstacle avoidance a turning angle is designed, which when incorporated into the control laws ensures that the entire robot arm avoids any number of fixed obstacles along its path enroute the target. The control laws proposed in this paper also ensure that the equilibrium point of the system is asymptotically stable. Computer simulations of the proposed technique are presented.

Keywords: 2-link revolute manipulator, motion control, obstacle avoidance, asymptotic stability.

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Authors: Amir Hossein Pakshir, A. Hossein Pour, N. Jahandar, Ali Paydar

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Roundabout work on the principle of circulation and entry flows, where the maximum entry flow rates depend largely on circulating flow bearing in mind that entry flows must give away to circulating flows. Where an existing roundabout has a road hump installed at the entry arm, it can be hypothesized that the kinematics of vehicles may prevent the entry arm from achieving optimum performance. Road humps are traffic calming devices placed across road width solely as speed reduction mechanism. They are the preferred traffic calming option in Malaysia and often used on single and dual carriageway local routes. The speed limit on local routes is 30mph (50 km/hr). Road humps in their various forms achieved the biggest mean speed reduction (based on a mean speed before traffic calming of 30mph) of up to 10mph or 16 km/hr according to the UK Department of Transport. The underlying aim of reduced speed should be to achieve a 'safe' distribution of speeds which reflects the function of the road and the impacts on the local community. Constraining safe distribution of speeds may lead to poor drivers timing and delayed reflex reaction that can probably cause accident. Previous studies on road hump impact have focused mainly on speed reduction, traffic volume, noise and vibrations, discomfort and delay from the use of road humps. The paper is aimed at optimal entry and circulating flow induced by road humps. Results show that roundabout entry and circulating flow perform better in circumstances where there is no road hump at entrance.

Keywords: Road hump, Roundabout, Speed Reduction

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Authors: Riku Hayashida, Tomoaki Hashimoto

Abstract:

This paper provides a robust stabilization method for rotational motion of underwater robots against parameter uncertainties. Underwater robots are expected to be used for various work assignments. The large variety of applications of underwater robots motivates researchers to develop control systems and technologies for underwater robots. Several control methods have been proposed so far for the stabilization of nominal system model of underwater robots with no parameter uncertainty. Parameter uncertainties are considered to be obstacles in implementation of the such nominal control methods for underwater robots. The objective of this study is to establish a robust stabilization method for rotational motion of underwater robots against parameter uncertainties. The effectiveness of the proposed method is verified by numerical simulations.

Keywords: Robust control, stabilization method, underwater robot, parameter uncertainty.

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Authors: Cheng-En Tsai, Chung-Chun Hsiao, Fu-Yuan Chang, Liang-Lun Lan, Jia-Ying Tu

Abstract:

New design of three dimensional (3D) flywheel system based on gimbal and gyro mechanics is proposed. The 3D flywheel device utilizes the rotational motion of three spherical shells and the conservation of angular momentum to achieve planar locomotion. Actuators mounted to the ring-shape frames are installed within the system to drive the spherical shells to rotate, for the purpose of steering and stabilization. Similar to the design of 2D flywheel system, it is expected that the spherical shells may function like a “flyball” to store and supply mechanical energy; additionally, in comparison with typical single-wheel and spherical robots, the 3D flywheel can be used for developing omnidirectional robotic systems with better mobility. The Lagrangian method is applied to derive the equation of motion of the 3D flywheel system, and simulation studies are presented to verify the proposed design.

Keywords: Gimbal, spherical robot, gyroscope, Lagrangian formulation, flyball.

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Authors: Cheng-En Tsai, Chung-Chun Hsiao, Fu-Yuan Chang, Liang-Lun Lan, Jia-Ying Tu

Abstract:

New design of three dimensional (3D) flywheel system based on gimbal and gyro mechanics is proposed. The 3D flywheel device utilizes the rotational motion of three spherical shells and the conservation of angular momentum to achieve planar locomotion. Actuators mounted to the ring-shape frames are installed within the system to drive the spherical shells to rotate, for the purpose of steering and stabilization. Similar to the design of 2D flywheel system, it is expected that the spherical shells may function like a “flyball” to store and supply mechanical energy; additionally, in comparison with typical single-wheel and spherical robots, the 3D flywheel can be used for developing omnidirectional robotic systems with better mobility. The Lagrangian method is applied to derive the equation of motion of the 3D flywheel system, and simulation studies are presented to verify the proposed design.

Keywords: Gimbal, spherical robot, gyroscope, Lagrangian formulation, flyball.

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Authors: Dušan Kravec, Ondrej Staš, Marián Tolnay, Michal Bachratý

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This article gives a short preview of the new software created especially for palletizing process in automated production systems. Each chapter of this article is about problem solving in development of modules in Java programming language. First part describes structure of the software, its modules and data flow between them. Second part describes all deployment methods, which are implemented in the software. Next chapter is about twodimensional editor created for manipulation with objects in each layer of the load and gives calculations for collision control. Module of virtual reality used for three-dimensional preview and creation of the load is described in the fifth chapter. The last part of this article describes communication and data flow between control system of the robot, vision system and software.

Keywords: Palletizing, deployment methods, palletizing software, virtual reality in palletizing.

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Authors: Ong Sing Goh, C. Ardil, Chun Che Fung, Kok Wai Wong, Arnold Depickere

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In this paper, we proposed a new framework to incorporate an intelligent agent software robot into a crisis communication portal (CCNet) in order to send alert news to subscribed users via email and other mobile services such as Short Message Service (SMS), Multimedia Messaging Service (MMS) and General Packet Radio Services (GPRS). The content on the mobile services can be delivered either through mobile phone or Personal Digital Assistance (PDA). This research has shown that with our proposed framework, the embodied conversation agents system can handle questions intelligently with our multilayer architecture. At the same time, the extended framework can take care of delivery content through a more humanoid interface on mobile devices.

Keywords: Crisis Communication Network (CCNet), EmbodiedConversational Agents (ECAs), Mobile Services, ArtificialIntelligence Neural-network Identity (AINI)

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Authors: Gulshan Taj M. N. A., Anupam Chakrabarti, Vipul Prakash

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In the present investigation, free vibration of functionally graded material (FGM) skew plates under thermal environment is studied. Kinematics equations are based on the Reddy’s higher order shear deformation theory and a nine noded isoparametric Lagrangian element is adopted to mesh the plate geometry. The issue of C₁ continuity requirement related to the assumed displacement field has been circumvented effectively to develop C₀ finite element formulation. Effective mechanical properties of the constituents of the plate are considered to be as position and temperature dependent and assumed to vary in the thickness direction according to a simple power law distribution. The displacement components of a rectangular plate are mapped into skew plate geometry by means of suitable transformation rule. One dimensional Fourier heat conduction equation is used to ascertain the temperature profile of the plate along thickness direction. Influence of different parameters such as volume fraction index, boundary condition, aspect ratio, thickness ratio and temperature field on frequency parameter of the FGM skew plate is demonstrated by performing various examples and the related findings are discussed briefly. New results are generated for vibration of the FGM skew plate under thermal environment, for the first time, which may be implemented in the future research involving similar kind of problems.

Keywords: Functionally graded material, finite element method, higher order shear deformation theory, skew plate, thermal vibration.

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Authors: Ružarovský, Roman, Danišová, Nina, Velíšek, Karol

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In this contribution is presented a complex design of individual objects identification in the workplace of intelligent assembly cell. Intelligent assembly cell is situated at Institute of Manufacturing Systems and Applied Mechanics and is used for pneumatic actuator assembly. Pneumatic actuator components are pneumatic roller, cover, piston and spring. Two identification objects alternatives for assembly are designed in the workplace of industrial robot. In the contribution is evaluated and selected suitable alternative for identification – 2D codes reader. The complex design of individual object identification is going out of intelligent manufacturing systems knowledge. Intelligent assembly and manufacturing systems as systems of new generation are gradually loaded in to the mechanical production, when they are removeing human operation out of production process and they also short production times.

Keywords: system, cell, intelligent, mechanics, device

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Authors: Xinde Li, Xinhan Huang, Min Wang

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In this paper, we propose the pre-processor based on the Evidence Supporting Measure of Similarity (ESMS) filter and also propose the unified fusion approach (UFA) based on the general fusion machine coupled with ESMS filter, which improve the correctness and precision of information fusion in any fields of application. Here we mainly apply the new approach to Simultaneous Localization And Mapping (SLAM) of Pioneer II mobile robots. A simulation experiment was performed, where an autonomous virtual mobile robot with sonar sensors evolves in a virtual world map with obstacles. By comparing the result of building map according to the general fusion machine (here DSmT-based fusing machine and PCR5-based conflict redistributor considereded) coupling with ESMS filter and without ESMS filter, it shows the benefit of the selection of the sources as a prerequisite for improvement of the information fusion, and also testifies the superiority of the UFA in dealing with SLAM.

Keywords: DSmT, ESMS filter, SLAM, UFA

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Authors: Junichiro Kawaguchi

Abstract:

Space debris problems have emerged and threatened the use of low earth orbit around the Earth owing to a large number of spacecrafts.. The robots should be sophisticated enough to access automatically the debris articulating the attitude and the translation motion with respect to the debris. This paper presents the idea of using the torpedo-like third unsophisticated and disposable body, in addition to the first body of the servicing robot and the second body of the target debris. The third body is launched from the first body from a distance further than the size of the second body. This paper presents the method and the system, so that the third body is launched from the first body. The third body carries both a net and an inflatable or extendible drag deceleration device and is built small and light. This method enables even micro to nano satellites to perform contactless and multiple debris removal even via a single flight.

Keywords: Ballute, Debris Removal, Echo satellite, Gossamer, Gun-Net, Inflatable Space Structure, Small Satellite, Un-cooperated Target.

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Authors: Ahmet Denker, Tuğrul Adıgüzel

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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: Mohammadhosein Hasanbeig, Lacra Pavel

Abstract:

In this paper, we study a distributed control algorithm for the problem of unknown area coverage by a network of robots. The coverage objective is to locate a set of targets in the area and to minimize the robots’ energy consumption. The robots have no prior knowledge about the location and also about the number of the targets in the area. One efficient approach that can be used to relax the robots’ lack of knowledge is to incorporate an auxiliary learning algorithm into the control scheme. A learning algorithm actually allows the robots to explore and study the unknown environment and to eventually overcome their lack of knowledge. The control algorithm itself is modeled based on game theory where the network of the robots use their collective information to play a non-cooperative potential game. The algorithm is tested via simulations to verify its performance and adaptability.

Keywords: Distributed control, game theory, multi-agent learning, reinforcement learning.

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Authors: Azadeh Rouhandeh, Chris Joslin, Zhen Qu, Yuu Ono

Abstract:

The centre of rotation of the hip joint is needed for an accurate simulation of the joint performance in many applications such as pre-operative planning simulation, human gait analysis, and hip joint disorders. In human movement analysis, the hip joint center can be estimated using a functional method based on the relative motion of the femur to pelvis measured using reflective markers attached to the skin surface. The principal source of errors in estimation of hip joint centre location using functional methods is soft tissue artefacts due to the relative motion between the markers and bone. One of the main objectives in human movement analysis is the assessment of soft tissue artefact as the accuracy of functional methods depends upon it. Various studies have described the movement of soft tissue artefact invasively, such as intra-cortical pins, external fixators, percutaneous skeletal trackers, and Roentgen photogrammetry. The goal of this study is to present a non-invasive method to assess the displacements of the markers relative to the underlying bone using optical motion capture data and tissue thickness from ultrasound measurements during flexion, extension, and abduction (all with knee extended) of the hip joint. Results show that the artefact skin marker displacements are non-linear and larger in areas closer to the hip joint. Also marker displacements are dependent on the movement type and relatively larger in abduction movement. The quantification of soft tissue artefacts can be used as a basis for a correction procedure for hip joint kinematics.

Keywords: Hip joint centre, motion capture, soft tissue artefact, ultrasound depth measurement.

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Authors: C.Kia, M.R.Arshad, A.H.Adom, P.A.Wilson

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This paper presents recent work on the improvement of the robotics vision based control strategy for underwater pipeline tracking system. The study focuses on developing image processing algorithms and a fuzzy inference system for the analysis of the terrain. The main goal is to implement the supervisory fuzzy learning control technique to reduce the errors on navigation decision due to the pipeline occlusion problem. The system developed is capable of interpreting underwater images containing occluded pipeline, seabed and other unwanted noise. The algorithm proposed in previous work does not explore the cooperation between fuzzy controllers, knowledge and learnt data to improve the outputs for underwater pipeline tracking. Computer simulations and prototype simulations demonstrate the effectiveness of this approach. The system accuracy level has also been discussed.

Keywords: Fuzzy logic, Underwater target tracking, Autonomous underwater vehicles, Artificial intelligence, Simulations, Robot navigation, Vision system.

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Authors: Namchul Do, Gyeongseok Chae

Abstract:

This paper proposes a framework for product development including hardware and software components. It provides separation of hardware dependent software, modifications of current product development process, and integration of software modules with existing product configuration models and assembly product structures. In order to decide the dependent software, the framework considers product configuration modules and engineering changes of associated software and hardware components. In order to support efficient integration of the two different hardware and software development, a modified product development process is proposed. The process integrates the dependent software development into product development through the interchanges of specific product information. By using existing product data models in Product Data Management (PDM), the framework represents software as modules for product configurations and software parts for product structure. The framework is applied to development of a robot system in order to show its effectiveness.

Keywords: HW and SW Development Integration, ProductDevelopment with Software.

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Authors: B. Tondu, N. Bardou

Abstract:

In its attempt to offer new ways into autonomy for a large population of disabled people, assistive technology has largely been inspired by robotics engineering. Recent human-like robots carry new hopes that it seems to us necessary to analyze by means of a specific theory of anthropomorphism. We propose to distinguish a functional anthropomorphism which is the one of actual wheelchairs from a structural anthropomorphism based on a mimicking of human physiological systems. If functional anthropomorphism offers the main advantage of eliminating the physiological systems interdependence issue, the highly link between the robot for disabled people and their human-built environment would lead to privilege in the future the anthropomorphic structural way. In this future framework, we highlight a general interdependence principle : any partial or local structural anthropomorphism generates new anthropomorphic needs due to the physiological systems interdependency, whose effects can be evaluated by means of specific anthropomorphic criterions derived from a set theory-based approach of physiological systems.

Keywords: Anthropomorphism, Human-like machines, Systemstheory, Disability.

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Authors: Elmi Abu Bakar, Tetsuo Miyake, Zhong Zhang, Takashi Imamura

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Knowing the geometrical object pose of products in manufacturing line before robot manipulation is required and less time consuming for overall shape measurement. In order to perform it, the information of shape representation and matching of objects is become required. Objects are compared with its descriptor that conceptually subtracted from each other to form scalar metric. When the metric value is smaller, the object is considered closed to each other. Rotating the object from static pose in some direction introduce the change of value in scalar metric value of boundary information after feature extraction of related object. In this paper, a proposal method for indexing technique for retrieval of 3D geometrical models based on similarity between boundaries shapes in order to measure 3D CAD object pose using object shape feature matching for Computer Aided Testing (CAT) system in production line is proposed. In experimental results shows the effectiveness of proposed method.

Keywords: CAD, rendering, feature extraction, feature classification.

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Authors: Tawiwat Veeraklaew, Nathasit Phathana-im, Songkit Heama

Abstract:

Both the minimum energy consumption and smoothness, which is quantified as a function of jerk, are generally needed in many dynamic systems such as the automobile and the pick-and-place robot manipulator that handles fragile equipments. Nevertheless, many researchers come up with either solely concerning on the minimum energy consumption or minimum jerk trajectory. This research paper proposes a simple yet very interesting relationship between the minimum direct and indirect jerks approaches in designing the time-dependent system yielding an alternative optimal solution. Extremal solutions for the cost functions of direct and indirect jerks are found using the dynamic optimization methods together with the numerical approximation. This is to allow us to simulate and compare visually and statistically the time history of control inputs employed by minimum direct and indirect jerk designs. By considering minimum indirect jerk problem, the numerical solution becomes much easier and yields to the similar results as minimum direct jerk problem.

Keywords: Optimization, Dynamic, Linear Systems, Jerks.

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