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Bir endüstriyel robotun modelleme, simülasyon ve kontrolü

Modeling simulation control of an industrial robot

  1. Tez No: 21855
  2. Yazar: OSMAN CANBERİ
  3. Danışmanlar: PROF. DR. AHMET KUZUCU
  4. Tez Türü: Yüksek Lisans
  5. Konular: Makine Mühendisliği, Mechanical Engineering
  6. Anahtar Kelimeler: Belirtilmemiş.
  7. Yıl: 1992
  8. Dil: Türkçe
  9. Üniversite: İstanbul Teknik Üniversitesi
  10. Enstitü: Fen Bilimleri Enstitüsü
  11. Ana Bilim Dalı: Belirtilmemiş.
  12. Bilim Dalı: Belirtilmemiş.
  13. Sayfa Sayısı: 66

Özet

ÖZET Bu çalışmada N serbestlik dereceli, dönel eklemli robotların dinamik analizini ve kontrol simülasyonunu yapmak için genel amaçlı bir program geliştirilmiştir. Simülasyon sırasında konumların, hızların ve motor faz akımlarının grafik animasyonları gerçek zamanda yapılmatadır. Program yardımıyla eklemlerin ve uzuv ağırlık merkezlerinin açısal ve lineer hızlan gibi kinematik özellikleri inceleyebilmek de mümkündür. Programda kullanılan dinamik modelleme Newton-Euler formülasyonuna dayalı olarak elde edilmiş ve koordinat dönüşümlerinin getirdiği işlem karmaşıklığını azaltabilmek için robotu oluşturan açık kinematik zincir elemanlarının herbirinin kinematik ve dinamik özellikleri kendi koordinat sistemlerinde incelenmiştir. TÜBİTAK Marmara Araştırma Merkezi'nde tasarlanıp imal edilmekte olan 6 serbestlik dereceli ve roll-pitch-roll tipi bilek yapışma sahip ER-15 endüstriyel robotu tanıtılmıştır. Robotta kullanılan kalıcı mıknatıslı senkron motorlar hakkında bilgi verilmiş ve motor modellenmiştir. Orantı-diferansiyel (PD) ve hesaplanmış moment tekniğine (HMT) dayalı kontrolörler tanıtılmış ve bu tekniklerle, geliştirilen program kullanılarak ER-15'in simülasyonu iki ayrı senaryo altoda yapılmıştır. Simülasyon sonuçlan gözönüne alınarak kontrol teknikleri karşılaştırılmıştır. ix

Özet (Çeviri)

SUMMARY MODELING, SIMULATION & CONTROL OF AN INDUSTRIAL ROBOT Robotic systems are extensively used in industrial applications. On the basis of task specifications, the planner determines the desired trajectory for the manipulator motion. The controller must be so designed that the manipulator will track the desired trajectory as closely as possible. The actual trajectory values of the manipulator are feedback through feedback loops to determine possible tracking errors, and the controller will then react to compensate for the observed errors. Thus the basic operations of a manipulator are controlled by computers that implement the designed algorithms. The construction of the control algorithms requires a thorough knowledge of manipulator dynamics as well as control theory. In this study a computer simulation programme has developed for six revolute joint robot which has roll-pitch-roll wrist mechanism. For modelling the robot the method has been used is the Newton-Euler formulation using recurence relations for velocities, accelerations and generalized forces. This is based on numerical efficiecy and intermediate results. A general algorithm which solves both the direct and inverse problem of dynamics for an open- chained spatial mechanism of an arbitrary mechanical configuration is used. The algorithm which has been used in this study designed for dynamic analysis of mechanical configuration, control synthesis, and evolution of different control laws by simulation should solve the direct and inverse problem of dynamics. A mechanical manipulator can be modeled as an open-loop articulated chain with several rigid bodies (links) connected in series by either revolute or prismatic joints driven by actuators. One end of the chain is attached to a supporting base while the other end is free and attached with a tool (the end- effector) to manipulate objects or perform assemby tasks. The relative motion of the joints results in the motion of the links that positions the hand in a desired orientation. In most robotic applications, one is interested in the spatial description of the end-effector of the manipulator with respect to a fixed refernce coordinate system. Each joint-link pair of a mechanical manipulator constitues 1 degree of freedom. Hence, for an N degree of freedom manipulator, there are N joint-link pairs with link 0 (not considered part of the robot). To describe the translational and rotational relationship between adjacentlinks, Denawit and Hartenberg [1955] proposed a matrix method of systematically estabilishing a coordinate system (body-attached frame) to each link of an articulated chain. The Denavit-Hartenberg representation results in a 4x4 homogeneous transformation matrix representing each link's coordinate system at the joint with respect to the previous link's coordinate system. Thus, through sequential transformations, the end-effector expressed in the“hand coordinates”can be transformed and expressed in the“base coordinates”which make up the inertial frame of this dynamic system. Joint control produces the desired position and orientation of the end effector. The position and orientation of the end effector with respect to the world coordinate system is expressed by means of the H transformation matrix: rf- n s a p 0 0 0 1 -AiAiy..J\f. V / where the (3x3) submatrix tn s a1 indicates wrist orientation, P the end effector position in world coordinates, and the A's are the link transformation matrices.Solution of this equation to obtain the angle of rotation of rotary joints or displacement distance of prismatic joints as functions of the end effector position and orientation is commonly referred to as the“inverse kinematics problem.”There are various recursive algorithms proposed in the literature for dynamic modelling of manipulators. They generally calculate the velocities and accelerations of each link by a forward recursion starting from the base of the manipulator to the end link. Then the generalized forces are obtained by a backward recursion from the end link to the base of the manipulator. In this section a general algorithm for dynamic modelling of a six degree of freedom manipulator is developed using Newton-Euler's formulation. Rather than calculating the velocities and accelerations directly, their corresponding coefficients are calculated. Thus a dynamic model of the system is obtained which can be used for the solution of both direct and inverse problem of mechanichs. Also the velocities and accelerations or corresponding coefficients are calculated in each link's internal coordinate system. Thus eliminated the need for a great deal of coordinate transformations. The dynamic model of an n degree of freedom manipulator is represented by a set of n non-linear differential equations which describes the motion of the system in the space of inertial coordinates. The equations of XImotion can be generated in various forms depending on whether the information on dynamics is necessary for dynamic analysis of the system or for synthesis of control algorithms and the simulation of particular control laws. The equation of motion for an n degree of freedom manipulator can be written in a general form as: ^jm+vf+ftf^jS+m+ft.® (2) H : nxl vector of joint variables, : nxn symmetric, nonsingular moment of inertia matrix, P" : nxn diagonal viscous friction matrix, f(4i»4j>n), ğ(s) : nxl vector specifying the effects due to gravity, h(4) : nxl vector specifying the effects due to external forces and moments exerted on link n, T : nxl vector of input generalized forces. Such equations of motion are useful for computer simulation of robot arm motion, the design of suitable control equations for a robot arm, and the evaluation of the kinematic design and structure of a robot arm. Second chapter of this study deals with formulation, characteristics, and properties of the dynamic equations of motion that are suitable for control purposes. The purpose of manipulator control is to maintain the dynamic response of a computer-based manipulator in accordance with some prespecified system performance and desired goals. In general, the dynamic performance of a manipulator directly depends on the efficiency of the control algorithms and the dynamic model of the manipulator. The control problem consists of obtaining dynamic models of the physical robot arm system and then specifying corresponding control laws or strategies to achieve the desired system response and performance. Chapter three deals mainly with the former part of the manipulator control problem; that is, modelling and evaluating the dynamical properties and behaviour of computer-controlled robot. An industrial robot can be defined, using automatic control terminology, as a non-lineer coupled, multiple-input / multiple-output system. A majority of xiiindustrial robots are driven by ac or dc servo motors. In that case, the inputs are the armature voltages or current of the motors driving the joints and the outputs are the positions of the joints. Coupling results from the undesired motion of one joint when other joint is driven. Nonlinearities result from the effects of gravitational loading, coriolis and centrifugal torques, friction, etc. The control laws that govern system behaviour are of almost importance since they not only determine the accuracy of the desired motion, but also the speed with which a desired task is performed. Computer simulation of a robot manipulator provides inside into manipulator operation and control law effectiveness. In this study a accurate simulation model for the dynamics of ER- 15 is used to evaluate the performance of two control schemes. The ER-15 robot used for simulation was designed in TÜBİTAK Marmara Research Center for scientific and commercial purposes thus all necessary robot parameters has taken from ER-15. The dynamic equations are developed via the Newton-Euler formulation and used in a state space based simulation program. A P.D. (proportional & diferential) and a computed torque controller are simulated in order to compare their performance. It is hoped this will provide clear and useful information on the robot's transient and steady-state behaviour. Torque equation on motor level can be written as, t =(J +-)Q +(£ +- )4 +- (3) where N is reduction rate. Using PD control law motor phase current can be written as control vector, Im=kp(£lmref V^W

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