Design And Comparison Of Controller Performance On Four Mecanum Wheeled Mobile Robot

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2016Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 2016Bu tez çalışmasında çok yönlü hareket edebilen dört tekerlekli mobil robotun tasarımı ve farklı tipteki denetleyicilerin dizayn edilmesi ve bunların sonuçlarının kıyaslanması hedeflenmiştir. Denetim algoritması oluşturmaktaki amaç, gerçek sistem üzerinde oluşabilecek üretim hataları, motorların stabil olmaması ve diğer dış etkenler dolayısıyla meydana gelen hataları kabul edilebilir düzeye indirmektir. Çünkü herhangi bir kontrol algoritması kullanmadan sistemin istenilen stabilitede hareket etmesi ve farklı yüklerin motorlara binmesi durumunda hızların istenilen düzeyde tutulması zor bir durumdur. Gerek dıştan gelen etkiler, gerekse içten kaynaklanan birtakım sebeplerden dolayı sisteme uygulanacak denetleyiciler seçilmiş olup, bunların sonuçları kıyaslanmıştır. Fakat denetleyici tasarlamadan önce sistemin matematik modelinin bilinmesi gerekmektedir. Bunun için sistemin ilk önce ileri ve ters kinematik denklemleri matris şeklinde çıkarılmıştır. Matematiksel modeli oluştururken sistemin hesaplamaları kolaylaştırmak amacıyla bazı kabuller yapılmıştır. Bunlara örnek olarak sistemin rijit olduğu varsayılmış, zemin ile tekerler arasında oluşan yuvarlanma direncinin tekerlerin kaymadan ilerlemesi varsayılmış, tekerlerin zemin ile sürekli temasta olduğu ve diğer sistem bileşenleri modellenirken lineer denklemler kullanılmıştır. Model de tekerlerde üretim hatalarının olmadığı göz önüne alınmıştır. Her tekerin açısı 45° olduğu ve sistem simetrik şekilde dizayn edildiği varsayılmıştır. Oluşturulan matematiksel model ile sistemin istenilen doğrultuda gitmesi için herbir tekerin birbirinden bağımsız olarak hangi hıza sahip olacağı bu model sayesinde hesaplanabilmektedir. İleri kinematik denklemleri sayesinde sistemin kartezyen kordinat üzerindeki hızları ve her bir motorun devir sayısı elde edilebilmektedir. Oluşturulmuş olan ters kinematik denklemleri sayesinde ise sistemin dışarıdan kaynaklanan bozucu etkenlere karşı sistemin istenilen doğrultuda hareket etmesini sağlamak için yeniden motor hızları hesaplanmasına imkan vermektedir. Matematiksel denklemleri elde edilen sistemin sonuçlarını almak için model simulasyon ortamına aktarılmıştır. Bu ortamda sistemin oluşturulan ters ve ileri kinematik denklemleri, dc motor modeli, denetleyici ve input output arasındaki sistemler arası dönüştürücü denklemler yer almaktadır. Oluşturulan model sayesinde simulasyonlar gerçekleştirilmiştir ve alınan sonuçlar neticesinde denetleyici için gerekli olan katsayılar belirlenmiştir. Kontrolcü performansını denetlemek amacıyla ise alınan bu veriler gerçek sistem üzerinde test edilmek amacıyla kullanılmıştır. Gerçek sistem ise dört adet dc motor, dört adet manyetik enkoder, iki adet dc motor sürücü kartı ve mikrodenetleyiciden oluşmaktadır. Sistemde kullanılmış olan dc motor 350 wattlık güce sahip ve bu motorlar 12v luk seri bağlanmış iki adet kuru tip akülerle beslenmektedir. Sistemin istenilen tork değerlerine ulaşması için redüktör kullanılmıştır. Kullanılan iki adet dc motor sürücü kartı kanal başına 30 amper çıkış verebilmektedir ve her kart iki adet motoru sürebilmektedir. Ayrıca kartı kullanmak için üretici firma C++ ve python2.x kütüphanelerini de vermektedir. İstenilen datalar bu kartlar üzerinden bilgisayara seri haberleşme ile aktarılabilmektedir. Kullanılan çokyönlü tekerler 12 adet dış dış tekere sahip olup bunların yanında tekerin hareketini kolaylaştırmak amacıyla da 24 adet küçük yarım tekerleklerde ilave edilmiştir. Amaç tekerlerin dönüşü esnasında süreklilik sağlamak. Montaj sonrası sistemin matematiksel modeli oluşturulması için gerekli ölçümler yapılmıştır. Bunlara örnek olarak dc motor modelinin belirlenmesi ve bu modelde kullanılacak olan parametrelerin saptanması gerekmektedir. Bunları belirlemek için sisteme giriş verilerek çıkışlar gözlenmiş ve Matlab/Simulink system identification toolbox sayesinde sistem belirlenmiş ve parametreler belirlenmiştir. Daha sonra elde edilen bu değerler ile sistem tekrardan doğrulanarak değelerin güvenilirliği ölçülmüştür. Daha sonra sistemin diğer bileşenlerine ait olan tekerleklerin birbirine olan uzaklıkları redüktör oranları, maksimum motor devirleri ve bunun gibi önemli diğer parametrelerin ölçümleri yapılarak matematiksel model oluşturulmuştur. Motor için elde edilen transfer fonksiyonları ve durum uzay modeli denetleyici tasarımında büyük rol oynamaktadır. Denetleyici olarak sisteme uygulanabilir denetleyicilerden lineer quadratic regulator ve model öngörülü kontrolcü kullanılmıştır. LQR denetleyici için sistemde durum geri besleme yapılmaktadır ve bu geri beslemeler için motorların transfer fonksiyonlarına ihtiyaç duyulmuştur. Bu tip denetleyicide optimal geri besleme katsayılarını bulmak için hali hazırda bulunan yöntemler kullanılmıştır ve ayrıca mükemmel sonuçlar için simülasyonlar gerçekleştirilmiştir. Geri besleme katsayıları belirlenirken Matlab’de bulunan fonksiyonlar yardımıyla bulunmuştur. Fakat Q matrisi ve R katsayısı denetleyiciyi tasarlayan kişi tarafından seçilmektedir. Bu katsayılar performansı etkileyen en önemli kriterlerdendir. Kullandığı yazılım ve donanım itibariyle MPC ileri düzey bir denetim yöntemi olarak sınıflanabilir. İleri denetim tekniği olması denetim sinyallerini oluştururken optimizasyon algoritması çalıştırarak ilgilenilen süreç çıkış sinyallerini tasarımcının arzu ettiği optimizasyon ölçütüne uygun olarak sağlayan yapıya sahip olmasındandır. MPC yönteminden daha önce analog kontrol yöntemleri ve nümerik optimizasyonlar kullanılarak kontrol sağlanmıştır. Bugünkü teknolojiye bakarak işlemci teknolojilerini göz önüne aldığımızda bu denetleyicinin başarılı olabilmesini mümkün kılmıştır. Lineer olmayan sistem modelleri için az sayıda MPC algoritması varlığına karşın, lineer sistem modelleri için geliştirilmiş olan hali hazırda çeşitli algoritmalar bulunmaktadır. Model öngörülü kontrolcü ideal çalışma için denetlenmek istenen sistemin kesin modeline gerek duyar; ancak sistem modelindeki belirsizlikler durumunda dahi uygun geri besleme konfigurasyonları kullanılarak MPC algoritması başarılı olarak çalıştırılabilir. Başlangıçtan itibaren T saniyelik süre boyunca arzu edilen süreç çıkış yörüngesini daha önceden kullanıcı tarafından hazırlanabilir. Diğer denetleyici olarak model öngörülü kontrol seçilmiştir bu denetleyicide ki amaç büyük sistemlerin sisteme giriş verilmeden önce kumanda sinyalinin tespit edilmesi amacıyla kullanılmaktadır. Sistemi bir kapalı kutu olarak algılayıp bu sistem ile arka planda çalışan algoritma yardımıyla kullanıcı istekleri doğrultusunda sistem davranışı belirlenmiş olur. Sistem denetleyicisi adım cevabı veya darbe cevabı modeliyle belirlenebilir. Ayrıca Matlab/Simulinkte yer alan toolbox sayesinde denetleyici parametreleri ayarlanabilir. Bunlar kontrol ufku, saniyedeki hesaplama sayısı, tahmin edilen adım sayısı, sistem cevap süreleri gibi parametrelerdir. Bu denetleyiciler belirlenirken amaç motorun farklı senaryolar altında kullanıcı tarafından belirlenen doğrultudaki hızını sabit tutmasıdır. Fakat LQR denetleyicide geri besleme katsayıları sabit olduğundan belli her senaryo için adaptif olarak çalışamamaktadır. Bunun yanında MPC denetleyicide ise sistemin o anki davranışına göre ileride gerçekleşecek olan davranışı tahmin ettiğinden anlık verilerden yeni bir kumanda sinyali hesaplanır. Temelde kullandığı kontrol ufku ve tahmin ufku iterasyon sayılarından dolayı o andaki sistemin durumunu ölçüp gelecekte olabilecek durum hakkında bir kumanda sinyali üretilmektedir. Tahmin ufkunun fazla olması bir kaç adım sonra karşılaşabilecek durum hakkında daha stabil bir kestirim yapılabilmektedir. Ayrıca kumanda sinyallerinde oluşturulan kısıtlamalar sayesinde simulasyonlardan istenilen kumanda çıkışları ve sistem cevapları alınmıştır.In this thesis the main aim is to design and compare controller performance on omnidirectional mobile robot based on mecanum wheels and it can be use for further researches for elemination system errors. On the purpose of to increase orientation capability the system is equipped with four mecanum wheels which have twelve rollers around it. In the scope of this thesis to control dc motor speeds according to user demans and to minimize heading errors in the band of accaptable area. Before start to develop controller for the large scale system experimental test rig has been equipped with system components which are mecanum wheels, dc motors, encoders and controller. Also before start design controller all system elements should have mathematical models to take best controller results. Such as Dc motor model, system forward and backward kinematics, which help to minimize heading errors in real nonlinear environment. For the developing linear quadratic regulator and model predictive controller transfer function of the system is needed. Especially for LQR controller owing to feedback constants. The dc motor model is implemented to the simulation enviroment to see system output according to user inputs. In order to validate designed model, different system scenarios are tested independetly. After validation of system outputs cross validation test is conducted to maximize dependability. Designed model simulated in Matlab/Simulink environment with real dc motor coefficients. To improve controller performance for LQR controller different Q matrixes and R constants are tested and simulated. In the end admissible feedback constants are chosen. For MPC system inputs and outputs are simulated with modelled system. The controller performance is adjusted according to time interval, control horizon, weights of inputs and prediction horizon constants. Based on simulated model the aim is to take smooth response from system without overshoot, minimal oscillation and minimize settling time. Simulated results will be compared to real system results in future.Yüksek LisansM.Sc

Implementation Kinematics Modeling and Odometry of Four Omni Wheel Mobile Robot on The Trajectory Planning and Motion Control Based Microcontroller

The control of kinematic modeling in a four wheel omni-directional robot (FWOR) is very difficult. Because you have to adjust the speed of the four DC motors. The speed of DC motors is controlled so that the FWOR robot can be controlled. This paper will explain the application of kinematic modeling of four wheel omni directional robots as track tracking controllers and microcontroller based movement control. Kinematic is the study of robot motion based on geometric structure analysis of a stationary / moving reference coordinate frame system without considering the force, torque or certain moments that cause movement. By applying kinematic modeling and calculation of the odometric system as feedback, the control of the robot trajectory movement can be controlled with precision in accordance with the path planning that has been made. The robot track control technique is embedded in a 32-bit ARM microcontroller. The path planning system and observing robot movement are carried out using a friendly graphic interface using Processing to facilitate the robot monitoring process. The results of the experiments and tests carried out, the system is able to control the rate of movement of the robot with great precision in accordance with the path planning made

Coordination and Control for a Team of Mobile Robots in an Unknown Dynamic Environment

This research presents a dual-level control structure for controlling a mobile robot or a group of robots to navigate through a dynamic environment (such as an object is moving in the workspace of a robot). The higher-level controller operates in cooperation with robot’s state estimation and mapping algorithm, Extended Kalman Filter – Simultaneous Localization and Mapping (EKFSLAM), and the lower-level controller (PID) controls the motion of the robot when it, encounters an obstacle, i.e., it reorients the robot to a predefined rebound angle and move it straight to maneuver around the obstacle until the robot is out of the obstacle range. The higher-level controller jumps in as soon as the robot is out of the obstacle range and moves the robot to the goal. The obstacle avoidance technique involves a novel approach to calculate the rebound angle. Further, the research implements the aforementioned technique to a Leader-Follower formation. Simulation and Experimental results have verified the effectiveness of the proposed control law

Parameter tuning and cooperative control for automated guided vehicles

For several practical control engineering applications it is desirable that multiple systems can operate independently as well as in cooperation with each other. Especially when the transition between individual and cooperative behavior and vice versa can be carried out easily, this results in ??exible and scalable systems. A subclass is formed by systems that are physically separated during individual operation, and very tightly coupled during cooperative operation. One particular application of multiple systems that can operate independently as well as in concert with each other is the cooperative transportation of a large object by multiple Automated Guided Vehicles (AGVs). AGVs are used in industry to transport all kinds of goods, ranging from small trays of compact and video discs to pallets and 40-tonne coils of steel. Current applications typically comprise a ??eet of AGVs, and the vehicles transport products on an individual basis. Recently there has been an increasing demand to transport very large objects such as sewer pipes, rotor blades of wind turbines and pieces of scenery for theaters, which may reach lengths of over thirty meters. A realistic option is to let several AGVs operate together to handle these types of loads. This Ph.D. thesis describes the development, implementation, and testing of distributed control algorithms for transporting a load by two or more Automated Guided Vehicles in industrial environments. We focused on the situations where the load is connected to the AGVs by means of (semi-)rigid interconnections. Attention was restricted to control on the velocity level, which we regard as an intermediate step for achieving fully automatic operation. In our setup the motion setpoint is provided by an external host. The load is assumed to be already present on the vehicles. Docking and grasping procedures are not considered. The project is a collaboration between the company FROG Navigation Systems (Utrecht, The Netherlands) and the Control Systems group of the Technische Universiteit Eindhoven. FROG provided testing facilities including two omni-directional AGVs. Industrial AGVs are custom made for the transportation tasks at hand and come in a variety of forms. To reduce development times it is desirable to follow a model-based control design approach as this allows generalization to a broad class of vehicles. We have adopted rigid body modeling techniques from the ??eld of robotic manipulators to derive the equations of motion for the AGVs and load in a systematic way. These models are based on physical considerations such as Newton's second law and the positions and dimensions of the wheels, sensors, and actuators. Special emphasis is put on the modeling of the wheel-??oor interaction, for which we have adopted tire models that stem from the ??eld of vehicle dynamics. The resulting models have a clear physical interpretation and capture a large class of vehicles with arbitrary wheel con??gurations. This ensures us that the controllers, which are based on these models, are applicable to a broad class of vehicles. An important prerequisite for achieving smooth cooperative behavior is that the individual AGVs operate at the required accuracy. The performance of an individual AGV is directly related to the precision of the estimates for the odometric parameters, i.e. the effective wheel diameters and the offsets of the encoders that measure the steering angles of the wheels. Cooperative transportation applications will typically require AGVs that are highly maneuverable, which means that all the wheels of an individual AGV ahould be able to steer. Since there will be more than one steering angle encoder, the identi??cation of the odometric parameters is substantially more dif??cult for these omni-directional AGVs than for the mobile wheeled robots that are commonly seen in literature and laboratory settings. In this thesis we present a novel procedure for simultaneously estimating effective wheel diameters and steering angle encoder offsets by driving several pure circle segments. The validity of the tuning procedure is con??rmed by experiments with the two omni-directional test vehicles with varying loads. An interesting result is that the effective wheel diameters of the rubber wheels of our AGVs increase with increasing load. A crucial aspect in all control designs is the reconstruction of the to-be-controlled variables from measurement data. Our to-be-controlled variables are the planar motion of the load and the motions of the AGVs with respect to the load, which have to be reconstruct from the odometric sensor information. The odometric sensor information consists of the drive encoder and steering encoder readings. We analyzed the observability of an individual AGV and proved that it is theoretically possible to reconstruct its complete motion from the odometric measurements. Due to practical considerations, we pursued a more pragmatic least-squares based observer design. We show that the least-squares based motion estimate is independent of the coordinate system that is being used. The motion estimator was subsequently analyzed in a stochastic setting. The relation between the motion estimator and the estimated velocity of an arbitrary point on the vehicle was explored. We derived how the covariance of the velocity estimate of an arbitrary point on the vehicle is related to the covariance of the motion estimate. We proved that there is one unique point on the vehicle for which the covariance of the estimated velocity is minimal. Next, we investigated how the local motion estimates of the individual AGVs can be combined to yield one global estimate. When the load and AGVs are rigidly interconnected, it suf??ces that each AGVs broadcasts its local motion estimate and receives the estimates of the other AGVs. When the load is semi-rigidly interconnected to the AGVs, e.g. by means of revolute or prismatic joints, then generally each AGV needs to broadcasts the corresponding information matrix as well. We showed that the information matrix remains constant when the load is connected to the AGV with a revolute joint that is mounted at the aforementioned unique point with the smallest velocity estimate covariance. This means that the corresponding AGV does not have to broadcast its information matrix for this special situation. The key issue in the control design for cooperative transportation tasks is that the various AGVs must not counteract each others' actions. The decentralized controller that we derived makes the AGVs track an externally provided planar motion setpoint while minimizing the interconnection forces between the load and the vehicles. Although the control design is applicable to cooperative transportation by multiple AGVs with arbitrary semi-rigid AGV-load interconnections, it is noteworthy that a particularly elegant solution arises when all interconnections are completely rigid. Then the derived local controllers have the same structure as the controllers that are normally used for individual operation. As a result, changing a few parameter settings and providing the AGVs with identical setpoints is all that is required to achieve cooperative behavior on the velocity level for this situation. The observer and controller designs for the case that the AGVs are completely rigidly interconnected to the load were successfully implemented on the two test vehicles. Experi ments were carried out with and without a load that consisted of a pallet with 300 kg pave stones. The results were reproducible and illustrated the practical validity of the observer and controller designs. There were no substantial drawbacks when the local observers used only their local sensor information, which means that our setup can also operate satisfactory when the velocity estimates are not shared with the other vehicles

Dynamic Object Tracking Control for a Non-Holonomic Wheeled Autonomous Robot

[[abstract]]This paper is devoted to design and implement a non-holonomic wheeled mobile robot that possesses dynamic object-tracking capability by using real-time image processing. Two motion control laws are proposed using Lyapunov’s direct method and computed-torque method. Simulation results illustrate the effectiveness of the developed schemes. The overall experimental setup of the mobile robot developed in this paper is composed of a Windows based personal computer, Programmable Interface Controllers, a mobile robot, and an omni-directional vision system. Finally, the image-based real-time implementation experiments of the mobile robot demonstrate the feasibility and effectiveness of the proposed schemes.[[incitationindex]]EI[[booktype]]紙本[[booktype]]電子

Design of an adaptive neural predictive nonlinear controller for nonholonomic mobile robot system based on posture identifier in the presence of disturbance

This paper proposes an adaptive neural predictive nonlinear controller to guide a nonholonomic wheeled mobile robot during continuous and non-continuous gradients trajectory tracking. The structure of the controller consists of two models that describe the kinematics and dynamics of the mobile robot system and a feedforward neural controller. The models are modified Elman neural network and feedforward multi-layer perceptron respectively. The modified Elman neural network model is trained off-line and on-line stages to guarantee the outputs of the model accurately represent the actual outputs of the mobile robot system. The trained neural model acts as the position and orientation identifier. The feedforward neural controller is trained off-line and adaptive weights are adapted on-line to find the reference torques, which controls the steady-state outputs of the mobile robot system. The feedback neural controller is based on the posture neural identifier and quadratic performance index optimization algorithm to find the optimal torque action in the transient state for N-step-ahead prediction. General back propagation algorithm is used to learn the feedforward neural controller and the posture neural identifier. Simulation results show the effectiveness of the proposed adaptive neural predictive control algorithm; this is demonstrated by the minimised tracking error and the smoothness of the torque control signal obtained with bounded external disturbances

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This paper presents an intuitively straightforward yet comprehensive approach in developing and controlling a Mecanum-wheeled robot (MWR), with decent path tracking performance by using a simple controller as an end objective. The development starts by implementing two computer ball mice as sensors to realize a simple localization that is immune toward wheel slippage. Then, a linearization method by using open-loop step responses is carried out to linearize the actuations of the robot. Open-loop step response is handy, as it directly portrays the non-linearity of the system, thus achieving effective counteraction. Then, instead of creating a lookup table, polynomial regression is used to generate an equation in which the equation later represents an element of the linearizer. Next, a linear angle-to-gain (LA-G) method is introduced for path tracking control. The method is as easy as just linearly maps the summation of two angles-the angle between immediate and desired positions and the MWR's heading angle, into gains to control the wheels. Unlike the conventional control method which involves inverse kinematics, the LA-G method is directly a displacement-controlled approach and does not require the knowledge of parametric values, such as the robot's dimensions and wheel radius. Finally, all the methods are implemented, and the MWR experimentally demonstrates successfully tracking various paths, by merely using proportional controllers

DESIGN AND DEVELOPMENT OF AN OMNIDIRECTIONAL MOBILE BASE FOR A SOCIAL ROBOT

Master'sMASTER OF ENGINEERIN