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Abstract - In this paper, an optimal trajectory planning method is presented for robot manipulators with multiple degrees of freedom in 3D space using a new analytical technique for collision avoidance in the presence of ellipsoidal obstacles. To generate the robot’s trajectory, a genetic algorithm with a fuzzy mutation rate is introduced to have a quick access to optimal solutions in a complex workspace. A cubic spline interpolation polynomial is applied to approximate trajectories in the joint space. In order to optimize the objective function, the genetic algorithm determines a number of interior points for curve fitting using interpolation polynomials. The performance of the proposed technique is demonstrated by simulations.

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This paper presents a parameterization method to optimal trajectory planning and dynamic obstacle avoidance for Omni-directional robots. The aim of trajectory planning is minimizing a quadratic cost function while a maximum limitation on velocity and acceleration of robot is considered. First, we parameterize the trajectory using polynomial functions with unknown coefficients which transforms trajectory planning to an optimization problem. Then we use a novel method to solving the optimization problem and obtaining the unknown parameters. Finally, the efficiency of proposed approach is confirmed by simulation.  

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In this paper, optimal trajectory planning of flexible joint manipulator in point-to-point motion is presented in which besides the determining the maximum load carrying capacity, the vibration amplitude is also reduced. The solution method is on the base of the indirect solution of optimal control problem. For this purpose, an appropriate objective function is defined, dynamic equations are derived in state space form, Hamiltonian function is developed and necessary optimality conditions are obtained by using the Pontryagin maximum principle. In order to reduce the vibration of the end effector during the path, an appropriate state variables are defined and the control law is improved to omit the suddenly variation in applied torque. Then, in order to illustrate the power and efficiency of the proposed method, a number of simulation tests are performed for a two-link manipulator. To this end, after deriving the equation in details, two simulations are performed. In the first case, determining the maximum load without considering the vibration is solved, in the second simulation, optimal trajectory with maximum load and minimum vibration is obtained. Finally discussions on the obtained results are presented.

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The present research explores the trajectory of changing emotions throughout the lifelong experience of English language learning and language use among English-as-an-Additional-Language (EAL) students at a Vietnamese university. It employs a qualitatively-driven mixed methods research design with two phases of data collection using initial and exploratory self-designed questionnaires, followed by semi-structured interviews and reflective journals. The quantitative data, collected from English majored students aimed to capture the range of emotions the participants experienced in speaking English. The qualitative data, collected from the students recruited from the questionnaire phase, revealed the complexity and dynamism of their emotions in the process of language learning and use. The findings show that the participants experienced shifting emotions across the different contexts of language learning, including school, out-of-school, and tertiary contexts. The emotions were seen to be dynamic, socially and contextually constructed, emerging from their social circumstances and interaction with others. They were interwoven with self-concept, language learning success, perceived standing in different communities, and relationships with others. The results also provide theoretical and practical implications for emotion research and pedagogies of EAL teaching and learning.
 

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Tractor-trailer wheeled mobile robot (TTWMR) is a robotic system that consists of a tractor module towing a trailer. Trajectory tracking is one of the challenging problems which is focused in the context of wheeled mobile robots (WMRs) that has been discussed in this paper. First, kinematic equations of TTWMR are obtained. Then, reference trajectories for tracking problem are produced. Subsequently, an output feedback kinematic control law and a dynamic Fuzzy Sliding Mode Control (FSMC) are designed for the TTWMR. The proposed controller steer the TTWMR asymptotically follow reference trajectories. Finally, experimental results of the designed controller on an experimental setup and comparison results are presented. Obtained results show the effectiveness of the proposed controller.

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در این مقاله، طراحی مسیر بازگشت به جو یک کپسول فضایی از لحظه خروج از مدار اولیه تا رسیدن به شرایط عملکرد سیستم بازیابی مورد بررسی قرار می گیرد. برای این منظور دو روش حل عددی مسائل کنترل بهینه با رویکرد چند بازه ای توسعه داده شده و مورد استفاده و مقایسه قرار گرفته است. روش اول در دسته روشهای پرتاب (شوتینگ متد) قرار دارد که بهینه سازی در آن با استفاده از الگوریتم ژنتیک صورت می پذیرد. در این روش با بهره گیری از مدل جامعی برای توصیف تاریخچه کنترلی، به طور همزمان تعداد و چینش بازه ها و نوع تاریخچه کنترلی در هر بازه بهینه می شود. روش دوم موسوم به روش شبه طیفی می باشد که در آن متغیرهای حالت و کنترل برای ارضای همزمان قیود و شرایط بهینگی در نقاطی موسوم به گره ها تعیین می شوند. این روش هم با رویکرد چند بازه ای حل شده و با روش اول مقایسه گشته است. روشهای توسعه داده شده که در انتها عملکرد آنها مورد مقایسه و تحلیل قرار گرفته، قابل استفاده برای حل کلیه مسائل کنترل بهینه و طراحی مسیر می باشند.

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In this paper, the problem of the navigation error effect for the optimal and constraint Trajectory of the UAVs that are required to fly at low altitude over terrains has been discussed. Due to the increasing deviation problem of inertial navigation systems in terms of time, having a safe flight and collision avoidance with terrain at low altitude is the main point in the trajectory design of this type of the vehicles. On the other hand, some of these vehicles use Terrain Contour Matching (TERCOM) as a navigation aiding system. This system is more efficient in rough terrains, and providing the requirements of this system beside other constraints is a complex task. In this paper is tried to meet these constraints in the trajectory design process. For this purpose, an algorithm based on the layered network flow on the digital terrain maps used in a manner that has a high potential in adoption of various constraints and optimal trajectory is generated. Then, using equations of motion on a terrain digital data in 3D space with the dynamical constraints and different optimality criteria, a complete model of navigation error and also parameters affecting TERCOM has been developed to generate feasible path reducing terrain collision probability to zero.. Numerical results show validity of this issue.

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In this paper, trajectory tracking control of a wheeled mobile robot is analyzed. Wheeled mobile robot is a nonlinear system. This system including three generalized coordinates (x,y,ϕ), and a nonholonomic constraint. First, system kinematic and dynamic equations are obtained. A non-model-based control algorithm using PD-action filtered errors has been used in order to control the wheeled mobile robot. Non-model-based controllers are always more appropriate than model-based algorithms due to independency from dynamic models, lower computational costs and also robustness to uncertainties. Asymptotic stability of the closed loop system for trajectory tracking control of wheeled mobile robot has been investigated using appropriate Lyapunov function and also Barbalat’s lemma method. Finally, in order to show the effectiveness of the proposed approach simulation and experimental results have been presented. Obtained results show that without requiring a priori knowledge of plant dynamics, and with reduced computational burden, the tracking performance of the presented algorithm is quite satisfactory. Therefore, the proposed control algorithm is well suited to most industrial applications where simple efficient algorithms are more appropriate than complicated theoretical ones with massive computational burden.

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Trajectory tracking is one of the main control problems in the context of Wheeled Mobile Robots (WMRs). Besides, control of underactuated systems possesses a particular complexity and importance; so it has been focused by many researchers in recent years. In this paper, these two important control subjects are discussed regarding a Tractor-Trailer Wheeled Mobile Robot (TTWMR); which includes a differential drive wheeled mobile robot towing a passive spherical wheeled trailer. The use of spherical wheels instead of standard wheels in trailer makes the robot highly underactuated with severe nonlinearities. Spherical wheels are used for the trailer to increase robots’ maneuverability. In fact, standard wheels create nonholonomic constraints by means of pure rolling and nonslip conditions, and reduce robot maneuverability. In this paper, after introducing the robot, kinematics and kinetics models are obtained, and combined as the dynamics model. Then, based on physical intuition a new controller is developed for the robot, named as Lyapaunov-PID control algorithm. Then, singularity avoidance of the proposed algorithm is discussed and the stability of the algorithm is discussed. Simulation results reveal the suitable performance of the proposed algorithm. Finally, experimental implementation results are presented which verify the simulation results.

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Time optimal trajectory planning of closed chain mechanisms has not been done by indirect method yet. In this paper, this problem is considered for a four bar mechanism and its solution is presented on the base of the indirect solution of optimal control problem. To this end, the additional coordinates are omitted using the holonomic constraints, so the dynamic equation is obtained with respect to only one generalized coordinate. Then the necessary conditions for optimality are derived using Pontryagin's minimum principle by considering the constraint on the applied torque. The obtained equations lead to a two-point boundary value problem (BVP) that its solution is the optimum answer. Unlike the direct methods that result in approximate solution, indirect method leads to an exact solution. But the main challenge in indirect method is solving the BVP. Solving this problem is sensitive to the initial guess. This problem is much more severe for time optimal problem which has a high nonlinear answer in bang-bang form. To overcome this problem an algorithm is proposed to solve the time optimal problem with any desired accuracy, and the initial solution can simply be zero at the start of the algorithm. But in the time optimal trajectory the large jerk is occurred, due to control signals switching. In order to overcome this problem, another algorithm is presented to calculate the minimum time with bounded jerk. Finally, the simulation results show the performance of the proposed method in time optimal trajectory planning.

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Different reasons cause traffic oscillation such as: sudden speed drop of leader vehicle. Stop and go traffic commonly observed in congested freeway traffic result in traffic oscillation. When follower driver of platoon receives the last released wave of downstream to upstream in the traffic oscillation, driver makes different reactions proportional to released wave. They result in forming different behavioral patterns and behavior diversion from equilibrium driver. Follower vehicle drivers of platoon make different reactions to receiving wave based on behavior patterns. In this paper, this study employs vehicle trajectory data from Next Generation Simulation (NGSIM) program. Platoons of vehicles identified through a traffic disturbance classify in deceleration and acceleration phase based on driver behavior and hysteresis in traffic oscillation. Driver behavior in deceleration phase lead to congestion classify into four behavioral patterns: under reaction, under constant reaction, over reaction, over constant reaction based on maneuvering errors of follower driver. And also, in acceleration phase based on traffic hysteresis it classifies into two categories: aggressive and timid behavior. In this search, we can study only three driver behaviors: Over Reaction-Timid, Over Constant Reaction-Timid, Under Reaction-Timid because of vehicle trajectories data failure. When follower vehicle in traffic oscillation receives the last deceleration wave lead to congestion, follower vehicle deviates with equilibrium behavior, Newell trajectory, based on driver behavioral patterns. Every car-following model is used to explain the dependency of the follower vehicle trajectory, and its position at time t, to leader vehicle. According to fig.4, if leader vehicle (n-1), moves with constant speed (v), the follower vehicle must move with constant speed (v), too. Spacing between follower and leader vehicles at the time (t) can be changed, but if the freeway was homogenous, the spacing must be constant at approximately Sn; however, it can be varied for different types of vehicles. In this case, all the vehicles are considered as the same type. According to fig 5.a, in the Newell`s model, when a leader vehicle changes its speed from v to v`, the disturbance wave by speed of d^i/τ^i , will be sent to follower vehicle. This process results in an increase in acceleration of follower vehicle. In this model, di, τi are considered constant and independent of speed. According to fig.5.b, these characteristics result in linear relationship between speed and spacing s^i=d^i+τ^iv. Next, neural network models are developed to analyze the relationship between the microscopic parameters and time of two phases. Neural Networks are kinds of mathematical models characterized by a huge parametric space and flexible structure, and also, inspired by human brain neurons. In this article Multi-Layer Perception (MLP) related to free-Forward neural network is used by following the backward error propagation regulation, including 3 different Layers, namely, input layer, hidden layer and output layer. In comparison to more complex neural network structures, the advantage of Multi-Layer perception is its procedure according to universal function approximation. Although by choosing the suitable active Multi-Layer perception function, the direct relationship with the statistical equal model is available, Multi-Layer perception with the active mathematical function may be considered as a general sample of mathematical regression model. There is some progress in different methods that enable the neural network to identify the impacts of input on the changes of output, more precisely, i.e., information measurement theory, partial derivative and etc. Based on three behavior patterns, analysis results present that are most effective two parameters: deceleration wave lead to congestion and stop phase time. increasing deceleration wave results in reducing time between two phases based on over reaction-timid, and results in increasing it based on under reaction-timid and pattern and over constant up reaction – timid. And also, results of stop phase lead to congestion present based on three behavior patterns that increasing stop phase results in increasing time between two phases.

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An Aerial Robot or Unmanned Aerial Vehicle (UAV) is an aerial vehicle that provides its flight condition using aerodynamic forces. Also, this vehicle can be named as an autonomous robot. This robot is an under-actuated system and it is inherently unstable. Thus, the control of this nonlinear system is a problem for both practical and theoretical interest. So, the goal of this research is to contrast with highly nonlinear dynamic system of Octorotor that its control is difficult in many cases and it causes existence of instability in this Unmanned Aerial Vehicle (UAV). At the first, the structure of Octorotor is studied in this paper in order to increasing power, more carrying and increment of resistance into changing and distribution. Also, the electronic and mechanic of this robot is studied in some sections. Then, in the following, in order to attitude control of robot with introduction of dynamic system, one of the most common implemented controllers is applied on this robot. Initially, this process is done on the dynamic model of robot by Matlab/Simulink software and finally, implementation of this controller is applied on a fabricated Octorotor during a real flight in autonomous trajectory tracking in outdoor environment. At last, the study of sensors results is also shown.

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In this article, trajectory generation, control and hardware development of a knee exoskeleton robot is provided. The robot aims to help the individuals with lower extremity weakness or disability during the sit-to-stand movement. In the trajectory generation phase, a new method is proposed which uses a library of sample trajectories to predict the sit-to-stand movement trajectory based on the initial sitting conditions of the user. This method utilizes the theory of "dynamic movement primitives" to estimate the sit-to-stand trajectory. The trajectory generation method is tested on a library of human motion data which has been obtained in a laboratory of motion analysis. In the next step, an exponential sliding mode controller is used to guide the robot along the predicted trajectory. The controller and the trajectory generator are implemented on the exoskeleton robot. For the hardware development, the xPC Target toolbox of MATLAB software and a data acquisition card was used. Finally, the robot was tested on a male adult. The subjects were asked to wear the robot while doing several sit-to-stand movements from various sitting positions. According to the results, the average power which is required to be applied by the user’s knee, is less when the exoskeletons assists him.

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The major purpose of this paper is to illustarte of statistical design accuracy using trajectory simulation for launch vehicles design in conceptual design phase and also sensitivity analysis of velocity relative to effective external forces. Considering the advantages of statistical design to prevent the time and cost losses, system specification of sample launch vehicle calculated based on statistical data of the studied population. Then, by solving the equations of motion, design parameters are calculated in such a way that difference of the final velocity of trajectory simulation and needed orbital speed is less than 1 percent. Studied launch vehicles are two-stage liquid propellant vehicles, with Portability 2.5-3.5 tons mass to the low earth orbit. To validate, curves of speed, altitude and angle of path of launch vehicle designed with statistical method, compared with curves of Tsiklon launch vehicle, therefore correct operation the mission and accuracy of the statistical design algorithm is proved. By comparing ideal speed and speed of simulation, speed changes of any effective force obtained. Eventually speed loss factor at each stage and sensitive percent of each stage speed relative to the force, for both launch vehicles, statistical design and tsiklon, is analyzed.

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In this paper, online manual guidance of industrial robots using impedance control with singularity avoidance is studied. In this method, operator enters the robot workspace, physically holds the end-effector equipped with force sensor and manually guides the robot. In doing so, the operator generates the desired trajectory for applications like welding or painting. Robot singular configuration is possible during the process which makes it unsafe due to unexpected high velocity robot joints and the physical human-robot interaction. Therefore, real-time identification of singularity position and orientation must be evaluated during trajectory generation. The use of manipulability ellipsoid is suggested as a simple method for the singularity identification. By combining the manipulability ellipsoid and impedance control, a simple and new approach is proposed to warn operator before reaching singularity. Based on the proposed approach, effect of opposite force is exerted on the human hand in the predefined distance to singularity. Real-time implementation is the main advantage of the proposed approach because it keeps robot away from reaching singularity. Real-time experiments are performed using a SCARA robot. In the first experiment, the operator stops the trajectory generation process when an opposite force is produced. In the second experiment, the operator insists on entering the singular points. Experimental results show the effectiveness of the proposed approach in dealing with singularity problem during the trajectory generation by an operator for industrial robots.

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In this paper, a single bubble free ascending in a vertical channel was studied experimentally. Five different Newtonian fluids were used where the surface tension force is dominant. The bubble trajectory was considered in water, glycerin 30 and 50 Vol% that is zigzag, however, linear behavior is observed while the weight concentration of the glycerin reaches to 80 and 100 percent. The bubble rise velocity and aspect ratio coefficient are calculated by image analysis via MATLAB software. The results are in a very good agreement with the literature for the bubble velocity. The effect of magnetic field (perpendicular to the bubble flow) on the hydrodynamic characteristics of the bubble for each of the working fluids has been scrutinized. Although the presence of the magnetic field does not affect the bubble trajectory type or change the flow pattern from zigzag to linear, but it reduces the flow domain where this descending trend decreases with the increase in viscosity. It should be also noted that the magnetic field causes the bubble rise velocity to increase while this enhancement increases with higher viscosity. The magnetic field effect on the bubble aspect ratio was also considered and it was found that as viscosity increases the aspect ratio change is decreases.

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One of the main topics in the field of robotics is the formation control of the group of robots in trajectory tracking problem. Using organized robots has many advantages compared to using them individually. Among them the efficiency of using resources, the possibility of robots' cooperation, increasing reliability and resistance to defects can be pointed out. Therefore, formation control of multi-body robotic systems and intelligent vehicles attracted considerable attention that is discussed in this paper. First, kinematic and kinetic equations of a differential drive wheeled robot are obtained. Then, reference trajectories for tracking problem of the leader robot are produced. Next, a kinematic control law is designed for trajectory tracking of the leader robot. The proposed controller steer the leader robot asymptotically follow reference trajectories. Subsequently, a dynamic control algorithm for generating system actuator toques is designed based on feedback linearization method. Afterwards, formation control of the robots has been considered and an appropriate algorithm is designed in order to organize the follower robots in the desired configurations, meanwhile tracking control of the wheeled robot. Furthermore the stability of the presented algorithms for kinematic, dynamic and formation control laws is analyzed using Lyapunov method. Finally, obtained results for different reference paths are presented which represents the effectiveness of the proposed controller.

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In this paper, using both linear and nonlinear identification methods based on iterative and recursive least-square, the performance of a backstepping control system of a quadrotor in the presence of uncertainties is improved. At first, the dynamic model of a quadrotor is introduced and descriptive equations are presented in an appropriate state-space in order to design a controller based on backstepping method. Then the backstepping controller is designed using virtual controller for trajectory tracking. In this control system, the control performance is not satisfying because of the physical uncertainties existed in quadrotor. Consequently, an online identification method is introduced and used to improve the performance of the controller. In this regard, some parameters, which are linear in the model structure, are identified by least square error technique and iterative least square method is used for identifying other parameters.The results indicate that the steady-state error is decreased and the ability of tracking of a desired trajectory in the presence of uncertainties is increased. Furthermore, the result demonstrate the stabilization of roll and pitch angles, while, the method prevents the vibration of control forces.

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In this paper a controller has been presented based on the predictive control to drive and control the bipedal Nao robot. One of the challenges in the practical applying of these types of controllers is their high computational loading and the time-consuming control operations in each time step, in which it is suggested to use Laguerre Functions to reduce the computational loading of the predictive controller. In this study, at first using the conventional methods for the identification, and via the real data obtained from the Nao robot in Mechatronics research center of Qazvin Azad University, a proper model is proposed for walking the Nao robot which is considered as a two-dimensional motion in the plane. Then a controller will be designed to control the robot motion using the model based predictive controller. The purpose of this control approach in the first place is to stabilize the walking of the robot and then to guide and keep it on the desired trajectory, so that this trajectory tracking can be performed well as much as possible. Moreover, in order to evaluate the efficiency of the proposed controller, this controller has been compared with a proportional-integral-derivative controller and will be studied. The simulation results show the effectiveness of the proposed controller performance in the robot trajectory tracking, which finally comparing the obtained results from both of the control approaches, indicates the efficiency and different capabilities of the proposed method in this study.

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In this paper, according to flight devices categories, advantages and features of quadrotors and its performances are investigated. Then, the main challenges in quadrotors control and stability in the presence of obstacles have been considered in such a way that the system crosses the maximum number of obstacles in the best distance and time. For this purpose, the equations of motion of the system are derived and a controller for command tracking is designed without obstacles based on sliding mode method. The simulation results of the controller performances are given in the paper. In continuous, trajectory planning for crossing the system from the obstacles in alternative positions is presented and the quadrotor with the designed control system are simulated using the designed trajectory. The preference of the proposed trajectory planning is that the system can cross the number of obstacles in alternative positions in minimum time and using fewer sensors. Because of free shape of designing method and alternative initial velocity, the proposed method are applicable for piecewise trajectories. As a result of considering the drag force, the proposed approach is more successful in the various problems.