Search results for: tracking systems

Authors: Javed Ahmed, M. N. Jafri, J. Ahmad, Muhammad I. Khan

Abstract:

Real-time object tracking is a problem which involves extraction of critical information from complex and uncertain imagedata. In this paper, we present a comprehensive methodology to design an artificial neural network (ANN) for a real-time object tracking application. The object, which is tracked for the purpose of demonstration, is a specific airplane. However, the proposed ANN can be trained to track any other object of interest. The ANN has been simulated and tested on the training and testing datasets, as well as on a real-time streaming video. The tracking error is analyzed with post-regression analysis tool, which finds the correlation among the calculated coordinates and the correct coordinates of the object in the image. The encouraging results from the computer simulation and analysis show that the proposed ANN architecture is a good candidate solution to a real-time object tracking problem.

Keywords: Image processing, machine vision, neural networks, real-time object tracking.

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Authors: Bang Young Kim, Sang Hoon Park, Chul Gyu Song

Abstract:

A conventional optical coherence tomography (OCT) system has limited imaging depth, which is 1-2 mm, and suffers unwanted noise such as speckle noise. The motorized-stage-based OCT system, using a common-path Fourier-domain optical coherence tomography (CP-FD-OCT) configuration, provides enhanced imaging depth and less noise so that we can overcome these limitations. Using this OCT systems, OCT images were obtained from an onion, and their subsurface structure was observed. As a result, the images obtained using the developed motorized-stage-based system showed enhanced imaging depth than the conventional system, since it is real-time accurate depth tracking. Consequently, the developed CP-FD-OCT systems and algorithms have good potential for the further development of endoscopic OCT for microsurgery.

Keywords: Common-path OCT, FD-OCT, OCT, Tracking algorithm.

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Authors: Muhammad Raza Ali, Tim Morris

Abstract:

Skin color is an important visual cue for computer vision systems involving human users. In this paper we combine skin color and optical flow for detection and tracking of skin regions. We apply these techniques to gesture recognition with encouraging results. We propose a novel skin similarity measure. For grouping detected skin regions we propose a novel skin region grouping mechanism. The proposed techniques work with any number of skin regions making them suitable for a multiuser scenario.

Keywords: Bayesian tracking, chromaticity space, optical flowgesture recognition

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Authors: J. Rizk, Y. Chaiko

Abstract:

This paper shows the potential system benefits of simple tracking solar system using a stepper motor and light sensor. This method is increasing power collection efficiency by developing a device that tracks the sun to keep the panel at a right angle to its rays. A solar tracking system is designed, implemented and experimentally tested. The design details and the experimental results are shown.

Keywords: Renewable Energy, Power Optimization.

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Authors: S. Ganesh, J. Janani, G. Besliya Angel

Abstract:

Photovoltaic (PV) energy is one of the most important renewable energy sources. Maximum Power Point Tracking (MPPT) techniques should be used in photovoltaic systems to maximize the PV panel output power by tracking continuously the maximum power point which depends on panel’s temperature and on irradiance conditions. Incremental conductance control method has been used as MPPT algorithm. The methodology is based on connecting a pulse width modulated dc/dc SEPIC converter, which is controlled by a microprocessor based unit. The SEPIC converter is one of the buck-boost converters which maintain the output voltage as constant irrespective of the solar isolation level. By adjusting the switching frequency of the converter the maximum power point has been achieved. The main difference between the method used in the proposed MPPT systems and other technique used in the past is that PV array output power is used to directly control the dc/dc converter thus reducing the complexity of the system. The resulting system has high efficiency, low cost and can be easily modified. The tracking capability has been verified experimentally with a 10 W solar panel under a controlled experimental setup. The SEPIC converter and their control strategies has been analyzed and simulated using Simulink/Matlab software.

Keywords: Maximum Power Point Tracking, Microprocessor, PV Module, SEPIC Converter.

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Authors: L. Yu, W. K. Li, S. K. Ong, A. Y. C. Nee

Abstract:

In this paper, a scalable augmented reality framework for handheld devices is presented. The presented framework is enabled by using a server-client data communication structure, in which the search for tracking targets among a database of images is performed on the server-side while pixel-wise 3D tracking is performed on the client-side, which, in this case, is a handheld mobile device. Image search on the server-side adopts a residual-enhanced image descriptors representation that gives the framework a scalability property. The tracking algorithm on the client-side is based on a gravity-aligned feature descriptor which takes the advantage of a sensor-equipped mobile device and an optimized intensity-based image alignment approach that ensures the accuracy of 3D tracking. Automatic content streaming is achieved by using a key-frame selection algorithm, client working phase monitoring and standardized rules for content communication between the server and client. The recognition accuracy test performed on a standard dataset shows that the method adopted in the presented framework outperforms the Bag-of-Words (BoW) method that has been used in some of the previous systems. Experimental test conducted on a set of video sequences indicated the real-time performance of the tracking system with a frame rate at 15-30 frames per second. The presented framework is exposed to be functional in practical situations with a demonstration application on a campus walk-around.

Keywords: Augmented reality framework, server-client model, vision-based tracking, image search.

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Authors: Boukerch Haroun, Luo Qing Sheng, Li Hua Shi, Boukraa Sebti

Abstract:

In this paper we present the design and the implementation of a target tracking system where the target is set to be a moving person in a video sequence. The system can be applied easily as a vision system for mobile robot. The system is composed of two major parts the first is the detection of the person in the video frame using the SVM learning machine based on the “HOG” descriptors. The second part is the tracking of a moving person it’s done by using a combination of the Kalman filter and a modified version of the Camshift tracking algorithm by adding the target motion feature to the color feature, the experimental results had shown that the new algorithm had overcame the traditional Camshift algorithm in robustness and in case of occlusion.

Keywords: Camshift Algorithm, Computer Vision, Kalman Filter, Object tracking.

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Authors: M. Ahmadnezhad, M. Soltanpour

Abstract:

Electrohydraulic servo system have been used in industry in a wide number of applications. Its dynamics are highly nonlinear and also have large extent of model uncertainties and external disturbances. In this paper, a robust back-stepping control (RBSC) scheme is proposed to overcome the problem of disturbances and system uncertainties effectively and to improve the tracking performance of EHS systems. In order to implement the proposed control scheme, the system uncertainties in EHS systems are considered as total leakage coefficient and effective oil volume. In addition, in order to obtain the virtual controls for stabilizing system, the update rule for the system uncertainty term is induced by the Lyapunov control function (LCF). To verify the performance and robustness of the proposed control system, computer simulation of the proposed control system using Matlab/Simulink Software is executed. From the computer simulation, it was found that the RBSC system produces the desired tracking performance and has robustness to the disturbances and system uncertainties of EHS systems.

Keywords: Electro hydraulic servo system, back-stepping control, robust back-stepping control, Lyapunov redesign

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Authors: M. Ahmadnezhad, M. Soltanpour

Abstract:

Electrohydraulic servo system have been used in industry in a wide number of applications. Its dynamics are highly nonlinear and also have large extent of model uncertainties and external disturbances. In this paper, a robust back-stepping control (RBSC) scheme is proposed to overcome the problem of disturbances and system uncertainties effectively and to improve the tracking performance of EHS systems. In order to implement the proposed control scheme, the system uncertainties in EHS systems are considered as total leakage coefficient and effective oil volume. In addition, in order to obtain the virtual controls for stabilizing system, the update rule for the system uncertainty term is induced by the Lyapunov control function (LCF). To verify the performance and robustness of the proposed control system, computer simulation of the proposed control system using Matlab/Simulink Software is executed. From the computer simulation, it was found that the RBSC system produces the desired tracking performance and has robustness to the disturbances and system uncertainties of EHS systems.

Keywords: Electro hydraulic servo system, back-stepping control, robust back-stepping control, Lyapunov redesign.

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Authors: Mohamed Azab

Abstract:

In this paper a new maximum power point tracking algorithm for photovoltaic arrays is proposed. The algorithm detects the maximum power point of the PV. The computed maximum power is used as a reference value (set point) of the control system. ON/OFF power controller with hysteresis band is used to control the operation of a Buck chopper such that the PV module always operates at its maximum power computed from the MPPT algorithm. The major difference between the proposed algorithm and other techniques is that the proposed algorithm is used to control directly the power drawn from the PV. The proposed MPPT has several advantages: simplicity, high convergence speed, and independent on PV array characteristics. The algorithm is tested under various operating conditions. The obtained results have proven that the MPP is tracked even under sudden change of irradiation level.

Keywords: Photovoltaic, maximum power point tracking, MPPT.

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Authors: Jungho Choi, Youngwan Cho

Abstract:

The paper proposes a way of parallel processing of SURF and Optical Flow for moving object recognition and tracking. The object recognition and tracking is one of the most important task in computer vision, however disadvantage are many operations cause processing speed slower so that it can-t do real-time object recognition and tracking. The proposed method uses a typical way of feature extraction SURF and moving object Optical Flow for reduce disadvantage and real-time moving object recognition and tracking, and parallel processing techniques for speed improvement. First analyse that an image from DB and acquired through the camera using SURF for compared to the same object recognition then set ROI (Region of Interest) for tracking movement of feature points using Optical Flow. Secondly, using Multi-Thread is for improved processing speed and recognition by parallel processing. Finally, performance is evaluated and verified efficiency of algorithm throughout the experiment.

Keywords: moving object recognition, moving object tracking, SURF, Optical Flow, Multi-Thread.

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Authors: Chen-Chien Hsu, Guo-Tang Dai

Abstract:

This paper presents a particle swarm optimization (PSO) based approach for multiple object tracking based on histogram matching. To start with, gray-level histograms are calculated to establish a feature model for each of the target object. The difference between the gray-level histogram corresponding to each particle in the search space and the target object is used as the fitness value. Multiple swarms are created depending on the number of the target objects under tracking. Because of the efficiency and simplicity of the PSO algorithm for global optimization, target objects can be tracked as iterations continue. Experimental results confirm that the proposed PSO algorithm can rapidly converge, allowing real-time tracking of each target object. When the objects being tracked move outside the tracking range, global search capability of the PSO resumes to re-trace the target objects.

Keywords: multiple object tracking, particle swarm optimization, gray-level histogram, image

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Authors: Thang V. Kieu, Long P. Nguyen

Abstract:

Kernelized Correlation Filter (KCF) based trackers have gained a lot of attention recently because of their accuracy and fast calculation speed. However, this algorithm is not robust in cases where the object is lost by a sudden change of direction, being obscured or going out of view. In order to improve KCF performance in long-term tracking, this paper proposes an anomaly detection method for target loss warning by analyzing the response map of each frame, and a classification algorithm for reliable target re-locating mechanism by using Random fern. Being tested with Visual Tracker Benchmark and Visual Object Tracking datasets, the experimental results indicated that the precision and success rate of the proposed algorithm were 2.92 and 2.61 times higher than that of the original KCF algorithm, respectively. Moreover, the proposed tracker handles occlusion better than many state-of-the-art long-term tracking methods while running at 60 frames per second.

Keywords: Correlation filter, long-term tracking, random fern, real-time tracking.

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Authors: Sanjoy Mukherjee

Abstract:

Discussions on concepts of Single Axis Tracker (SAT) are becoming more and more apt for developing countries like India not just as an advancement in racking technology but due to the utmost necessity of reaching at the lowest Levelized Cost of Energy (LCOE) targets. With this increasing competition and significant fall in feed-in tariffs of solar PV projects, developers are under constant pressure to secure investment for their projects and eventually earn profits from them. Moreover, being the second largest populated country, India suffers from scarcity of land because of higher average population density. So, to mitigate the risk of this dual edged sword with reducing trend of unit (kWh) cost at one side and utilization of land on the other, tracking evolved as the call of the hour. Therefore, the prime objectives of this paper are not only to showcase how STT proves to be an effective mechanism to get more gain in Global Incidence in collector plane (G_inc) with respect to traditional mounting systems but also to introduce Seasonally Tilted Tracker (STT) technology as a possible option for high latitude locations.

Keywords: Tracking system, grid-connected PV systems, cost reduction.

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Authors: Dangjun Zhao, Yongji Wang, Lei Liu

Abstract:

Based on general proportional integral (GPI) observers and sliding mode control technique, a robust control method is proposed for the master-slave synchronization of chaotic systems in the presence of parameter uncertainty and with partially measurable output signal. By using GPI observer, the master dynamics are reconstructed by the observations from a measurable output under the differential algebraic framework. Driven by the signals provided by GPI observer, a sliding mode control technique is used for the tracking control and synchronization of the master-slave dynamics. The convincing numerical results reveal the proposed method is effective, and successfully accommodate the system uncertainties, disturbances, and noisy corruptions.

Keywords: GPI observer, sliding mode control, master-slave synchronization, chaotic systems.

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Authors: Wookyong Kwon, Sangmoon Lee

Abstract:

In this paper, a sampled-data model predictive tracking control method is presented for mobile robots which is modeled as constrained continuous-time linear parameter varying (LPV) systems. The presented sampled-data predictive controller is designed by linear matrix inequality approach. Based on the input delay approach, a controller design condition is derived by constructing a new Lyapunov function. Finally, a numerical example is given to demonstrate the effectiveness of the presented method.

Keywords: Model predictive control, sampled-data control, linear parameter varying systems, LPV.

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Authors: Alireza Sadrmomtaz

Abstract:

Positron emission particle tracking (PEPT) is a technique in which a single radioactive tracer particle can be accurately tracked as it moves. A limitation of PET is that in order to reconstruct a tomographic image it is necessary to acquire a large volume of data (millions of events), so it is difficult to study rapidly changing systems. By considering this fact, PEPT is a very fast process compared with PET. In PEPT detecting both photons defines a line and the annihilation is assumed to have occurred somewhere along this line. The location of the tracer can be determined to within a few mm from coincident detection of a small number of pairs of back-to-back gamma rays and using triangulation. This can be achieved many times per second and the track of a moving particle can be reliably followed. This technique was invented at the University of Birmingham [1]. The attempt in PEPT is not to form an image of the tracer particle but simply to determine its location with time. If this tracer is followed for a long enough period within a closed, circulating system it explores all possible types of motion. The application of PEPT to industrial process systems carried out at the University of Birmingham is categorized in two subjects: the behaviour of granular materials and viscous fluids. Granular materials are processed in industry for example in the manufacture of pharmaceuticals, ceramics, food, polymers and PEPT has been used in a number of ways to study the behaviour of these systems [2]. PEPT allows the possibility of tracking a single particle within the bed [3]. Also PEPT has been used for studying systems such as: fluid flow, viscous fluids in mixers [4], using a neutrally-buoyant tracer particle [5].

Keywords: PET, BGO, Particle Tracking, ECAT 931, List mode, PEPT.

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Authors: Mahmood M. Al-Imam, M. Mustafa

Abstract:

In this paper, we present an experimental testing for a new algorithm that determines an optimal controller-s coefficients for output variance reduction related to Linear Time Invariant (LTI) Systems. The algorithm features simplicity in calculation, generalization to minimal and non-minimal phase systems, and could be configured to achieve reference tracking as well as variance reduction after compromising with the output variance. An experiment of DCmotor velocity control demonstrates the application of this new algorithm in designing the controller. The results show that the controller achieves minimum variance and reference tracking for a preset velocity reference relying on an identified model of the motor.

Keywords: Output variance, minimum variance, overparameterization, DC-Motor.

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Authors: Fernando Pérez, Humberto Sossa, Rigoberto Martínez, Daniel Lorias, Arturo Minor

Abstract:

This paper presents a system for tracking the movement of laparoscopic instruments which is based on an orthogonal system of webcams and video image processing. The movements are captured with two webcams placed orthogonally inside of the physical trainer. On the image, the instruments were detected by using color markers placed on the distal tip of each instrument. The 3D position of the tip of the instrument within the work space was obtained by linear triangulation method. Preliminary results showed linearity and repeatability in the motion tracking with a resolution of 0.616 mm in each axis; the accuracy of the system showed a 3D instrument positioning error of 1.009 ± 0.101 mm. This tool is a portable and low-cost alternative to traditional tracking devices and a trustable method for the objective evaluation of the surgeon’s surgical skills.

Keywords: Laparoscopic Surgery, Orthogonal Vision, Tracking Instruments, Triangulation.

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Authors: K. Thulasimani, K. G. Srinivasagan

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Driver fatigue is an important factor in the increasing number of road accidents. Dynamic template matching method was proposed to address the problem of real-time driver fatigue detection system based on eye-tracking. An effective vision based approach was used to analyze the driver’s eye state to detect fatigue. The driver fatigue system consists of Face detection, Eye detection, Eye tracking, and Fatigue detection. Initially frames are captured from a color video in a car dashboard and transformed from RGB into YCbCr color space to detect the driver’s face. Canny edge operator was used to estimating the eye region and the locations of eyes are extracted. The extracted eyes were considered as a template matching for eye tracking. Edge Map Overlapping (EMO) and Edge Pixel Count (EPC) matching function were used for eye tracking which is used to improve the matching accuracy. The pixel of eyeball was tracked from the eye regions which are used to determine the fatigue state of the driver.

Keywords: Driver fatigue detection, Driving safety, Eye tracking, Intelligent transportation system, Template matching.

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Authors: Janet Holland

Abstract:

Eye tracking is a great way to triangulate multiple data sources for deeper, more complete knowledge of how instructional materials are really being used and emotional connections made. Using sensor based biometrics provides a detailed local analysis in real time expanding our ability to collect science based data for a more comprehensive level of understanding, not previously possible, for teaching and learning. The knowledge gained will be used to make future improvements to instructional materials, tools, and interactions. The literature has been examined and a preliminary pilot test was implemented to develop a methodology for research in Instructional Design and Technology. Eye tracking now offers the addition of objective metrics obtained from eye tracking and other biometric data collection with analysis for a fresh perspective.

Keywords: Area of interest, eye tracking, biometrics, fixation, fixation count, fixation sequence, fixation time, gaze points, heat map, saccades, time to first fixation.

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Authors: Jean-Pierre Dubois, Jihad S. Daba, M. Nader, C. El Ferkh

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GSM has undoubtedly become the most widespread cellular technology and has established itself as one of the most promising technology in wireless communication. The next generation of mobile telephones had also become more powerful and innovative in a way that new services related to the user-s location will arise. Other than the 911 requirements for emergency location initiated by the Federal Communication Commission (FCC) of the United States, GSM positioning can be highly integrated in cellular communication technology for commercial use. However, GSM positioning is facing many challenges. Issues like accuracy, availability, reliability and suitable cost render the development and implementation of GSM positioning a challenging task. In this paper, we investigate the optimal mobile position tracking means. We employ an innovative scheme by integrating the Kalman filter in the localization process especially that it has great tracking characteristics. When tracking in two dimensions, Kalman filter is very powerful due to its reliable performance as it supports estimation of past, present, and future states, even when performing in unknown environments. We show that enhanced position tracking results is achieved when implementing the Kalman filter for GSM tracking.

Keywords: Cellular communication, estimation, GSM, Kalman filter, positioning

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Authors: Yu-Sheng Lu, Chung-Hsin Cheng, Shuen-Shing Jan

Abstract:

This paper presents the design and implementation of a sliding-mod controller for tracking servo of optical disk drives. The tracking servo is majorly subject to two disturbance sources: radial run-out and shock. The lateral run-out disturbance is mostly repeatable, and a model of such disturbance is incorporated into the controller design to effectively compensate for it. Meanwhile, as a shock disturbance is usually non-repeatable and unpredictable, the sliding-mode controller is employed for its robustness to abrupt perturbations. As a result, a sliding-mode controller design based on the internal model principle is tailored for tracking servo of optical disk drives in order to deal with these two major disturbances. Experimental comparative studies are conducted to investigate the effectiveness of the specially designed controller.

Keywords: Mechatronics, optical disk drive, sliding-mode control, servo systems.

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Authors: B. Baigzadeh, V.Nazarzehi, H.Khaloozadeh

Abstract:

The two cart inverted pendulum system is a good bench mark for testing the performance of system dynamics and control engineering principles. Devasia introduced this system to study the asymptotic tracking problem for nonlinear systems. In this paper the problem of asymptotic tracking of the two-cart with an inverted-pendulum system to a sinusoidal reference inputs via introducing a novel method for solving finite-horizon nonlinear optimal control problems is presented. In this method, an iterative method applied to state dependent Riccati equation (SDRE) to obtain a reliable algorithm. The superiority of this technique has been shown by simulation and comparison with the nonlinear approach.

Keywords: Nonlinear optimal control, State dependent Riccatiequation, Asymptotic tracking, inverted pendulum

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

Abstract:

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: T. Kusuma, K. Ashwini

Abstract:

This paper presents a real time video surveillance system which is capable of tracking multiple real time objects using Polar Vector Median (PVM) and Block Coding Modes (BCM) with Global Motion Compensation (GMC). This strategy works in the packed area and furthermore utilizes the movement vectors and BCM from the compressed bit stream to perform real time object tracking. We propose to do this in view of the neighboring Motion Vectors (MVs) using a method called PVM. Since GM adds to the object’s native motion, for accurate tracking, it is important to remove GM from the MV field prior to further processing. The proposed method is tested on a number of standard sequences and the results show its advantages over some of the current modern methods.

Keywords: Block coding mode, global motion compensation, object tracking, polar vector median, video surveillance.

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Authors: Dennis L. Owuor, Okuthe P. Kogeda, Johnson I. Agbinya

Abstract:

Mobile localization has attracted a great deal of attention recently due to the introduction of wireless networks. Although several localization algorithms and systems have been implemented and discussed in the literature, very few researchers have exploited the gap that exists between indoor localization, tracking, external storage of location information and outdoor localization for the purpose of digital forensics during and after a disaster. The contribution of this paper lies in the implementation of a robust system that is capable of locating, tracking mobile device users and store location information for both indoor and partially outdoor the cloud. The system can be used during disaster to track and locate mobile phone users. The developed system is a mobile application built based on Android, Hypertext Preprocessor (PHP), Cascading Style Sheets (CSS), JavaScript and MATLAB for the Android mobile users. Using Waterfall model of software development, we have implemented a three level system that is able to track, locate and store mobile device information in secure database (cloud) on almost a real time basis. The outcome of the study showed that the developed system is efficient with regard to the tracking and locating mobile devices. The system is also flexible, i.e. can be used in any building with fewer adjustments. Finally, the system is accurate for both indoor and outdoor in terms of locating and tracking mobile devices.

Keywords: Indoor localization, waterfall, digital forensics, tracking and cloud.

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

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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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Authors: Mohamed Amine Haraoubia, Abdelaziz Hamzaoui, Najib Essounbouli

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The pursuit of the MPPT has led to the development of many kinds of controllers, one of which is the Fuzzy Logic controller, which has proven its worth. To further tune this controller this paper will discuss and analyze the use of Genetic Algorithms to tune the Fuzzy Logic Controller. It will provide an introduction to both systems, and test their compatibility and performance.

Keywords: Fuzzy logic controller (FLC), fuzzy logic (FL), genetic algorithm (GA), maximum power point (MPP), maximum power point tracking (MPPT).

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Authors: Santhakumar M., Asokan T.

Abstract:

This paper addresses the problem of trajectory tracking control of an underactuated autonomous underwater vehicle (AUV) in the horizontal plane. The underwater vehicle under consideration is not actuated in the sway direction, and the system matrices are not assumed to be diagonal and linear, as often found in the literature. In addition, the effect of constant bias of environmental disturbances is considered. Using backstepping techniques and the tracking error dynamics, the system states are stabilized by forcing the tracking errors to an arbitrarily small neighborhood of zero. The effectiveness of the proposed control method is demonstrated through numerical simulations. Simulations are carried out for an experimental vehicle for smooth, inertial, two dimensional (2D) reference trajectories such as constant velocity trajectory (a circle maneuver – constant yaw rate), and time varying velocity trajectory (a sinusoidal path – sinusoidal yaw rate).

Keywords: autonomous underwater vehicle, system matrices, tracking control, time – varying feed back, underactuated control.

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