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EN
This work proposes a convex cooperative control scheme for a multiagent system of differential mobile robots in a leader-follower formation. First, the kinematic model of the differential robots is obtained in a linear parameter varying representation. Next, a reference model approach is considered to track the desired trajectory. The paper’s contribution is then to derive conditions to guarantee the convergence of the convex controller, which is achieved using a non-quadratic Lyapunov function. Subsequently, this control law is integrated into the agent that leads a distributed control protocol based on graph theory designed to reach the consensus of the followers. Simulations of five mobile robots are performed to illustrate the effectiveness of the proposed method.
EN
This paper proposes an autonomous obstacle avoidance method combining improved A-star (A*) and improved artificial potential field (APF) to solve the planning and tracking problems of autonomous vehicles in a road environment. The A*APF algorithm to perform path planning tasks, and based on the longitudinal braking distance model, a dynamically changing obstacle influence range is designed. When there is no obstacle affecting the controlled vehicle, the improved A* algorithm with angle constraint combined with steering cost can quickly generate the optimal route and reduce turning points. If the controlled vehicle enters the influence domain of obstacle, the improved artificial potential field algorithm will generate lane changing paths and optimize the local optimal locations based on simulated annealing. Pondering the influence of surrounding participants, the four-mode obstacle avoidance process is established, and the corresponding safe distance condition is analyzed. A particular index is introduced to comprehensively evaluate speed, risk warning, and safe distance factors, so the proposed method is designed based on the fuzzy control theory. In the tracking task, a model predictive controller in the light of the kinematics model is devised to make the longitudinal and lateral process of lane changing meet comfort requirements, generating a feasible autonomous lane-change path. Finally, the simulation was performed in the Matlab/Simulink and Carsim combined environment. The proposed fusion path generation algorithm can overcome the shortcomings of the traditional single method and better adapt to the dynamic environment. The feasibility of the obstacle avoidance algorithm is verified in the three-lane simulation scenario to meet safety and comfort requirements.
EN
This paper focuses on trajectory tracking control for ro‐ bot manipulators. While much research has been done on this issue, many other aspects of this field have not been fully addressed. Here, we present a new solution using feedforward controller to eliminate parametric uncer‐ tainties and unknown disturbances. The Takagi‐Sugeno fuzzy descriptor system (TSFDS) is chosen to describe the dynamic characteristics of the robot. The combination of this fuzzy system and the robust H∞ performance makes the system almost isolated from external factors. The li‐ near matrix inequalities based on the theory of Lyapunov stability is considered for control design. The proposed method has proven its effectiveness through simulation results.
4
Content available remote Porównanie wybranych algorytmów sterowania napędem PMSM w sterowaniu nadążnym
PL
W niniejszym artykule przedstawiono porównanie czterech regulatorów podczas zadania nadążania za zadaną trajektorią. Obiektem symulacji jest napęd z silnikiem PMSM, na którego wale umieszczono dodatkowo masę bezwładną oraz masę skupioną, poruszającą się promieniście. Regulator w żaden sposób nie jest informowany o położeniu masy skupionej. Dodatkowo na układ oddziałuje tarcie, które również nie zostało zamodelowane. Porównano ze sobą regulator PID, regulator ślizgowy w postaci klasycznej, quasi-ślizgowy oraz supertwisting. Na końcu wyniki przedstawiono w tabeli.
EN
This paper presents comparison of four selected tracking control algorithms. The simulated plant is a PMSM drive with additional well-balanced inertia load and a point mass, which is moving radially. The controller has no information about position of the point mass. Moreover, friction is present in the plant, but it is unmodelled in the controller. PID, classical sliding mode, quasi-sliding mode and super-twisting controllers are compared. The paper ends with the table of advantages and disadvantages of investigated control algorithms.
PL
W artykule zaprezentowano hierarchiczny układ sterowania ruchem mobilnego robota kołowego w nieznanym środowisku ze statycznymi przeszkodami. Układ sterowania składa się z dwóch warstw, warstwy planowania trajektorii ruchu oraz warstwy realizacji ruchu. Warstwa planowania trajektorii generuje bezkolizyjną trajektorię ruchu robota w złożonym zadaniu typu „podążaj do celu z omijaniem przeszkód”. W warstwie planowania trajektorii ruchu zastosowano metody sztucznej inteligencji w formie układów z logiką rozmytą. Warstwę podrzędną hierarchicznego układu sterowania stanowi neuronowy algorytm sterowania ruchem nadążnym, w którym zastosowano algorytm aproksymacyjnego programowania dynamicznego w konfiguracji dualnego heurystycznego programowania dynamicznego, zrealizowany w formie dwóch struktur: aktora i krytyka. W strukturach aktora i krytyka zastosowano sztuczne sieci neuronowe z wagami warstwy wejściowej dobieranymi w sposób losowy w procesie inicjalizacji sieci i sigmoidalnymi bipolarnymi funkcjami aktywacji neuronów. Poprawności procesu generowania i realizacji trajektorii ruchu zweryfikowano poprzez serię testów numerycznych przeprowadzonych w środowisku obliczeniowym Matlab/Simulink z zastosowaniem emulatora mobilnego robota kołowego oraz toru pomiarowego.
EN
In the article the hierarchical control system of the wheeled mobile robot movement in the unknown environment with static obstacles was presented. The control system consists of two layers, the path planning layer and the tracking control layer. The path planning layer generates the collision-free trajectory of the robot in the complex “goal seeking and obstacle avoiding” task. In the path planning layer fuzzy logic systems were used. The subordinate layer of the hierarchical control system was the neural tracking control algorithm. In that layer the approximate dynamic programming algorithm in the dual heuristic dynamic programming configuration was used. It was realised in a form of two structures: the actor and the critic. In both the actor and the critic structures artificial neural networks with input layer weights chosen randomly in the network initialization process and sigmoidal bipolar neuron activation functions were used. Performance evaluation of the trajectory of generating and realisation processes was verified by the series of numerical tests performed in the Matlab/Simulink computational environment, using the wheeled mobile robot emulator and the laboratory environment emulator.
PL
Przedstawiono hierarchiczny układ sterowania ruchem mobilnego robota kołowego (MRK) Pioneer 2-DX w nieznanym środowisku. Układ ten składa się z: warstwy generowania trajektorii z zastosowaniem układów z logiką rozmytą oraz warstwy realizacji ruchu. W warstwie generowania trajektorii wykorzystano sterowanie behawioralne typu „omijaj przeszkody”. Do detekcji przeszkód posłużył skaner laserowy przestrzeni Hokuyo.
EN
The article presents hierarchical control system of a wheeled mobile robot in the unknown environment. The system consists of two layers: trajectory generating layer using fuzzy logic systems, and tracking control layer. Behavioral control concept arranged for the “avoid obstacles” instruction is employed in trajectory generator, but for detection of obstacles the Hokuyo scanning laser range finder is applied.
7
Content available remote Rozmyte sterowanie behawioralne mobilnym robotem kołowym w nieznanym środowisku
PL
W artykule zaprezentowano hierarchiczny układ sterowania ruchem mobilnego robota kołowego w nieznanym środowisku ze statycznymi przeszkodami. Układ sterowania składa się z generatora trajektorii realizującego sterowanie behawioralne z zastosowaniem układów z logiką rozmytą oraz neuronowego algorytmu sterowania ruchem nadążnym, w którym zastosowano algorytm aproksymacyjnego programowania dynamicznego. W warstwie planowania trajektorii ruchu zrealizowano sterowania behawioralne typu „podążaj do celu” oraz „omijaj przeszkody”. W prezentowanym hierarchicznym układzie sterowania sygnały sterowania warstwy planowania trajektorii są generowane przez dwa układy z logiką rozmytą, w których zastosowano model Takagi-Sugeno. W warstwie realizacji ruchu zastosowano algorytm aproksymacyjnego programowania dynamicznego w konfiguracji dualnego heurystycznego programowania dynamicznego, zbudowany z dwóch struktur: aktora i krytyka. Struktury aktora i krytyka zostały zrealizowane z zastosowaniem sztucznych sieci neuronowych. Poprawność zaproponowanych rozwiązań zweryfikowano numerycznie, stosując emulator mobilnego robota kołowego oraz laboratoryjnego toru pomiarowego, zrealizowane w środowisku obliczeniowym Matlab/Simulink.
EN
In the article the hierarchical control system of the wheeled mobile robot movement in the unknown environment with static obstacles was presented. The control system consists of the trajectory generator that realises the behavioural control using fuzzy logic system, and the neural tracking control system in which approximate dynamic programming algorithm is implemented. In the planning layer of movement trajectory the behavioural control tasks of the „goal-seeking” type and the „obstacle avoiding” type were realised. In the presented hierarchical control system the control signals of the trajectory planning layer were generated using two fuzzy logic systems in which Takagi-Sugeno model was utilized. In the movement control layer the approximate dynamic programming algorithm in the dual heuristic dynamic programming configuration was applied. It consists of two structures: the actor and the critic. Both the actor and the critic structures were realised using artificial neural networks. Performance of the proposed control algorithm was verified numerically using emulator of the wheeled mobile robot and the laboratory measuring track in the Matlab/Simulink computational environment.
PL
W artykule zaprezentowano hierarchiczny układ sterowania ruchem mobilnego robota kołowego Pionier 2-DX w nieznanym środowisku ze statycznymi przeszkodami. Układ sterowania składa się z dwóch warstw: warstwy planowania trajektorii i warstwy realizacji ruchu. Zadaniem warstwy planowania trajektorii jest generowanie parametrów ruchu kół robota w czasie rzeczywistym na podstawie sygnałów z układu sensorycznego. W warstwie tej zastosowano koncepcję sterowania behawioralnego, zrealizowanego z zastosowaniem układów z logiką rozmytą. Warstwa realizacji ruchu generuje sygnały sterowania modułami napędowymi robota, w warstwie tej zastosowano algorytmy aproksymacyjnego programowania dynamicznego. Weryfikację algorytmu sterowania przeprowadzono z zastosowaniem robota Pioneer 2-DX, wyposażonego w skaner laserowy przestrzeni.
EN
In the article a hierarchical control system of the Wheeled Mobile Robot Pioneer 2-DX movement in the unknown environment with static obstacles is presented. The control system consists of two layers: the path planning layer and the tracking control layer. On the basis of the sensory system signals the path planning layer generates the desired trajectory in real time. In this layer of the hierarchical control system, the conception of behavioural control was used. It was realised using Fuzzy Logic systems. The tracking control system is the lower layer of the hierarchical control system. It generates control signals for the WMR’s motors and is realised using Approximate Dynamic Programming algorithms. Using the WMR Pioneer 2-DX verification of the proposed hierarchical control system was performed. The WMR was equipped with the scanning laser range finder for obstacles detection.
PL
W pracy zaprezentowano hierarchiczny układ sterowania ruchem formacji mobilnych robotów kołowych, w którym zastosowano koncepcję wirtualnej struktury. W algorytmie tym każdy z agentów podąża za zadanym punktem wirtualnej struktury, realizując trajektorię formacji wygenerowaną przez najwyższą warstwę hierarchicznego układu sterowania. Środkowa warstwa algorytmu sterowania wyznacza trajektorie ruchu poszczególnych agentów, które następnie są realizowane przez warstwę sterowania ruchem nadążnym. W prezentowanej pracy zastosowano nowe podejście, w którym jedna struktura warstwy generowania trajektorii, zbudowana z zastosowaniem dwóch układów z logiką rozmytą, generuje sygnały sterowania umożliwiające realizację złożonego zadania typu „podążaj do celu i omijaj przeszkody”.
EN
In the article a hierarchical control system of the wheeled mobile robots formation is presented, where the virtual structure conception is applied. In the proposed control algorithm every agent tracks a desired point of the virtual structure and realises trajectory of the wheeled mobile robots formation generated by the highest layer of the hierarchical control system. The middle layer of the control system is the formation control layer. It generates desired trajectories for particular agents. These trajectories are realized by the tracking control layer. In the presented article a new approach is applied, where one structure of the highest layer of the hierarchical control system generates control signals that make realisation of the complex task of “goal seeking with obstacle avoiding” possible. In this layer two fuzzy logic systems were used.
PL
W pracy przedstawiono nowe podejście do generowania i realizacji ruchu mobilnego robota kołowego z zastosowaniem algorytmów aproksymacyjnego programowania dynamicznego (APD). Zaproponowano hierarchiczny układ sterowania ruchem robota w nieznanym środowisku ze statycznymi przeszkodami, składający się z warstwy generowania trajektorii oraz warstwy realizacji ruchu. W warstwie generowania trajektorii zrealizowano dwa podstawowe zadania: „podążaj do celu”, oraz „omijaj przeszkody”, stosując algorytmy APD w konfiguracji zależnego od sterowania heurystycznego programowania dynamicznego. Wygenerowana trajektoria ruchu jest realizowana przez układ sterowania ruchem nadążnym, w którym zastosowano algorytm dualnego heurystycznego programowania dynamicznego. Weryfikację algorytmu sterowania przeprowadzono z zastosowaniem robota Pioneer 2-DX.
EN
In the article a new approach to generating and realisation of the trajectory of the Wheeled Mobile Robot is presented. In this approach Approximate Dynamic Programming (APD) algorithms were used. The hierarchical control system of the WMR movement in the unknown environment with static obstacles was proposed. It consists of two layers: the trajectory generating layer and the tracking control layer. In the trajectory generating layer two basic tasks: the goal seeking task and the obstacle avoiding task, were realised. APD algorithms in the Action Dependant Heuristic Dynamic Programming configuration were used. Using the tracking control system the trajectory is realised. In the tracking control system APD algorithm in the Dual Heuristic Dynamic Programming configuration was used. Using the WMR Pioneer 2-DX verification of the proposed hierarchical control system was performed.
EN
The paper presents a sequential neural network (NN) identification scheme for the four-wheeled mobile robot subject to wheel slip. The sequential identification scheme, different from conventional methods of optimization of a cost function, attempts to ensure stability of the overall system while the neural network learns the nonlinearities of the mobile robot. An on-line weight learning algorithm is developed to adjust the weights so that the identified model can adapt to variations of the characteristics and operating points in the four-wheeled mobile robot. The proposed identification system that can guarantee stability is derived from the Lyapunov stability theory. Computer simulations have been conducted to illustrate the performance of the proposed solution by a series of experiments on the emulator of the wheeled mobile robot.
EN
This paper presents a control concept for a single-axle mobile robot moving on the horizontal plane. A mathematical model of the nonholonomic mechanical system is derived using Hamel's equations of motion. Subsequently, a concept for a tracking controller is described in detail. This controller keeps the mobile robot on a given reference trajectory while maintaining it in an upright position. The control objective is reached by a cascade control structure. By an appropriate input transformation, we are able to utilize an input-output linearization of a subsystem. For the remaining dynamics a linear set-point control law is presented. Finally, the performance of the implemented control law is illustrated by simulation results.
PL
W artykule przedstawiono koncepcję sterowania ruchem jednoosiowego robota poruszającego się po płaszczyźnie poziomej. Model matematyczny nieholonomicznego systemu mechanicznego wyprowadzono korzystając z równań ruchu Hamela. Opisano następnie szczegółowo koncepcję sterownika śledzącego. Sterownik prowadzi poruszający się robot po zadanej trajektorii utrzymując go jednocześnie w pozycji pionowej. Cel sterowania jest osiągnięty przy zastosowaniu kaskadowej struktury sterowania. Dzięki odpowiedniej transformacji danych wejściowych, w podsystemie istnieje możliwość linearyzacji wejście-wyjście. Dla dynamiki pozostałej części zaprezentowano prawo liniowego sterowania stałowartościowego. Ostatecznie, jakość działania zastosowanych praw sterowania zilustrowano wynikami symulacji.
13
Content available remote Adaptive hybrid position/force control of manipulator
EN
The problem of the manipulators hybrid position/force control is not trivial because manipulators are objects with nonlinear and uncertain dynamics, unknown and variable parameters, and which operate in changeable conditions. Therefore the hybrid position/force control problem requires application of advanced control techniques for compensation of manipulator nonlinearities. The adaptive control system enables the manipulator to behave correctly, even if parameters of the mathematical model of the control object are unknown. In this paper, the hybrid position/force controller with an adaptive compensation of nonlinearities for the SCORBOT-ER 4pc robotic manipulator is presented. The control law and adaptive law presented herein guarantee practical stability of the closed-loop control system in the sense of Lyapunov. The results of a numerical simulation are presented.
14
Content available remote Adaptive dynamic programming methods in control of wheeled mobile robot
EN
The control problem of nonlinear systems is a demanding task that requires application of complex methods. The development of artificial intelligence methods in recent years has made it possible to design control systems able to adapt parameters to changing or unknown parameters of the controlled object or process. In the article, a new approach to the tracking control problem of a wheeled mobile robot is presented. It uses the newest methods of artificial intelligence, such as adaptive dynamic programming algorithms, in the tracking control task. The proposed tracking control system is compared to the neural control system and the PD controller in a problem of the mobile robot tracking control. Laboratory tests of the proposed control systems were advances performed using the wheeled mobile robot Pioneer 2-DX and the computational environment that makes real time control and data acquisition possible. The proposed tracking control systems are stable and do not require the stage of preliminary learning of neural networks.
15
Content available remote Design of a path following controller for an underactuated AUV
EN
This paper describes a tracking control strategy for an underactuated autonomous underwater vehicle (AUV) on a two dimensional plane (ℜ²). Based on a smooth, inertial, 2D reference trajectory curve, the proposed algorithm uses vehicle dynamics to generate the reference orientation and body-fixed velocities. Following these, required error dynamics are developed. Error dynamics are then stabilized using inverse dynamics control strategy, forcing the tracking error to an arbitrarily small neighborhood of zero. Circular path, as a constant velocity reference trajectory, has been chosen for simulation studies. Simulation results are included to demonstrate the tracking performance of the controller.
16
EN
The work describes an automatically on-line Self-Tunnable Fuzzy Interference Systems (STFIS) of a new configuration of mini-flying called XSF (X4 Stationary Flyer) drone. A Fuzzy controller based on-line optimization of a zero order Takagi-Sugeno fuzzy interference system (FIS) by a back propagation like algorithm is successfully applied. It is used to minimize a cost function that is made up of a quadratic error term and a weight decay term that prevents an excessive growth of parameters. Thus, we carried out control for helical trajectories by using the STFIS technique. This permits to prove the effectiveness of the proposed control law. Simulation results and a comparison with a Static Feedback Linearization controller (SFL) are presented and discussed. We studied the robustness of the two used controllers in the presence of disturbances. We presented the case of an engine breakdown as well as a gust of wind and taking into account white noise disturbances.
17
Content available remote Modeling and tracking control of wheeled mobile robots
EN
The problem of tracking control of wheeled mobile robots (WMRs) using neural network is analyzed in this paper. The synthesis of control systems using the second Lapunov method was carried out. As a result of the synthesis, the stability of the designed systems was proven. A large number of computer simulations for these control systems using Matlab/Simulink package were executed. The results of the theoretical tests were verified by the rapid prototypical method. The rapid prototyping environment for the Pioneer robot was based on the Matlab/Simulink package and dSPACE board.
18
Content available remote A variable structure observer for the control of robot manipulators
EN
This paper deals with the application of a variable structure observer developed for a class of nonlinear systems to solve the trajectory tracking problem for rigid robot manipulators. The analyzed approach to observer design proposes a simple design methodology for systems having completely observable linear parts and bounded nonlinearities and/or uncertainties. This observer is basically the conventional Luenberger observer with an additional switching term that is used to guarantee robustness against modeling errors and system uncertainties. To solve the tracking problem, we use a control law developed for robot manipulators in the full information case. The closed loop system is shown to be globally asymptotically stable based on Lyapunov arguments. Simulation results on a 3-DOF robot manipulator show the asymptotic convergence of the vectors of observation and tracking errors.
EN
In this paper we propose a sensor-based navigation method for navigation of wheeled mobile robot, based on the Kohonen self-organising map (SOM). We discuss a sensor-based approach to path design and control of wheeled mobile robot in an unknown 2-D environment with static obstacles. A strategy of reactive navigation is developed including two main behaviours: a reaching the middle of a collision-free space behaviour, and a goal-seeking behaviour. Each low-level behaviour has been designed at design stage and then fused to determine a proper actions acting on the environment at running stage. The combiner can fuse low-level behaviours so that the mobile robot can go for the goal position without colliding with obstacles one for the convex obstacles and one for the concave ones. The combiner is a softswitch, based on the idea of artificial potential fields, that chooses more then one action to be active with different degrees at each time step. The output of the navigation level is fed into a neural tracking controller that takes into account the dynamics of the mobile robot. The purpose of the neural controller is to generate the commands for the servo-systems of the robot so it may choose its way to its goal autonomously, while reacting in real-time to unexpected events. Computer simulation has been conducted to illustrate the performance of the proposed solution by a series of experiments on the emulator of wheeled mobile robot Pioneer-2DX.
20
Content available remote Tracking Control Algorithms for a Laboratory Aerodynamical System
EN
The tracking control problem of a strongly nonlinear MIMO system is presented. The system shares some features with a helicopter, such as important interactions between the vertical and horizontal motions. The dedicated I/O board allows for control, measurements and communication with a PC. The RTWT toolbox in the MATLAB environment is used to perform real-time experiments. The control task is to track a predefined reference trajectory. A mathematical model of the system, containing experimental characteristics, is used to design the controllers: a multidimensional PD, a suboptimal controller in the sense of a quadratic performance index and a variable gain controller.
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