Robot kolların geleneksel ve dinamik kontrolu
Başlık çevirisi mevcut değil.
- Tez No: 19320
- Danışmanlar: PROF.DR. KEMAL SARIOĞLU
- Tez Türü: Yüksek Lisans
- Konular: Elektrik ve Elektronik Mühendisliği, Electrical and Electronics Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1991
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 124
Özet
ÖZET Robotikde yüksek performanslı robot kontrolörlerin geliştirilmesi önemli bir araştırma dalıdır. Bu çalışmada robot kolların kontroluna ilişkin geleneksel ve dinamik kontrolü incelenmiştir. Geleneksel kontrol şeması olarak Bağımsız Eklem kontrolörleri ele alınırken, dinamik kontrol şeması olarak ileri yol dinamik kompenzasyonu ve hesaplanmış moment tekniği ele alınmıştır. Endüstride kullanım alanları kaynak yapma, boyama ve bir cismi alıp yerine koyma işlemleri gibi basit işlerle sınırlı robotların kontrol sistemleri genel olarak eklem konumlarını ayrı ayrı kontrol eden birbirinden bağımsız konum kontrol çevrimleri içermektedirler. Önceden hesaplanmış parametreleri içeren bu konum kontrol sistemleri robotun uygulama alanını, işlem hızını ve değişik yükler altında istenen dinamik davranışını göstermesini sınırlar. Robotların montaj, önceden verilen bir yörüngeyi izleme, hızlı ve seri işlemler yapma gibi daha karmaşık işlerde kullanmak için kullanılan kontrol sistemini geliştirmek gerekir. Bu tip kontrol sistemleri geliştirilirken, eklemler arasındaki dinamik etkileşimler gözönüne alınmalıdır. Gelişmiş dinamik kontrol teknikleri, geri beslemeli nonlineer bir kontrolör yardımı ile robot dinamiğindeki nonlineerliklerin iptal edilmesi esasına dayanır. Model esaslı bu kontrol tekniklerinde dinamik modelin, manipülatör parametrelerinin ve yükün tam olarak bilinmesine ihtiyaç vardır. -v-
Özet (Çeviri)
SUMMARY What is a Robot The Robotics Institute of America (RIA) defines the robot as a reprogrammable, multi-functional manipulator designed to move material, parts, tools, or specialized devices through variable programmed motions for the performance of a variety of tasks. This is a widely accepted definition of an industrial robot. The emphasis is on the programmable facilities by which the robot can perform simple tasks without human assistance. Robot arm consists of several rigid links which are connected to each other in series by revaluate or prismatic joints. One end of the chain is attached to a supporting base, while the other end is free and equipped with a tool to perform various tasks. The motion of the robot arm is accomplished by driving the joints with actuators. Classification of Robots Robot classification may be considered on the following basis: (1) Structural configuration and robot motion. (2) Trajectories based on motion control Classification based on structural configuration and robot motion (i) Revaluate (jointed arm) robot (ii) Polar (spherical) robot (iii) Cartesian (rectangular) robot (iv) Cylindrical robot Classification based on path control (i) Point-to-point (PTP) control (ii) Continuous path (CP) controlRobot Arm Kinematics Robot arm kinematics deals with the analytical study of the geometry of motion of a robot arm with respect to a fixed reference coordinate system without regard to the forces / moments that cause the motion. Thus, kinematics deals with the analytical description of the spatial displacement of the robot as a function of time, in particular the relations between the joint-variable space and the position and orientation of the end-effector of a robot arm. There are fundamental problems in robot arm kinematics. The first problem is usually referred to as the direct (or forward) kinematics problem, while the second problem is the inverse kinematics problem. The direct kinematics problem is to find the position and orientation of the end effector of a manipulator with respect to a reference coordinate system, given the Joint-angle vector q= (q1f q2, q3 q6 ) T of the robot arm. The inverse kinematics problem (or arm solution) is to calculate the joint-angle vector q given the position and orientation of the end effector with respect to the reference coordinate system. Since the independent variables in a robot arm are the joint angles, and a task is generally stated in terms of the base or world coordinate system, the inverse kinematics solution is used more frequently in control of robot arm. The homogeneous matrix To', which specifies the position and orientation of the end point of link i with respect to the base coordinate system, is the chain product of successive coordinate transformation matrices of A'm, expressed as i T0i = Aol V. Ai.1i=riAL1i ; fori =1,2, M 0) where Zi 0 0 0 1 R0i 0 Poj [ Xj, yj, Zj ] = orientation matrix of the i th coordinate system established at link i with respect to the base coordinate system. Pi = position vector which points from the origin of the base coordinate system to the origin of the i th coordinate system. Specifically for i=6, we obtain the T matrix, T = A06, which specifies the position an orientation of the end point of a manipulator with respect to the base coordinate system. This T matrix is used so frequently in robot arm kinematics that it is called the“arm matrix”. Consider the T matrix as -VII-“x6 y6 ze Pe 0 0 0 1 0 (2) where n = the normal vector of the hand s = the sliding vector of the hand a = the approach vector of the hand p = the position vector of the hand Robot Arm Dynamics The dynamic behavior of robot arm is described in terms of the time rate of change of the arm configuration in relation to the joint torques exerted by the actuators. This relations can be expressed by a set of differential equations that govern the dynamic response of the arm linkage to input joint torques. Two dynamic models that are widely used to describe the dynamic behavior of a manipulator are the Lagrange - Euler (LE) formulation and the Newton - Euler (NE) formulation. The LE formulation generates a set of closed form differential equations to describe the motion. However, the LE formulation is computationally very inefficient with an order 0 (n4 ) relationship to the number of degrees of freedom of a manipulator. For a PUMA robot arm, where n=6, this corresponds to approximately 78000 addition and 102000 multiplications, In general, the LE equations of motion can be written in a compact vector matrix notation as T (I) - D (q) q (t) + h (q,q) + G (q) (3) where T (t) is an nx1 applied torque vector for joint actuators; q (t) is an nx1 joint position vector; q (t) is an nx1 joint velocity vector; q (t) is an n x 1 joint acceleration vector; G (q) is an n x 1 gravitational force vector; h (q, q) is an n x 1 coriolis and centrifugal force vektör; and D (q) is an n x n acceleration - related matrix. Studies have shown that, with current hardware, implementation of this algorithm would be prohibitively expensive for real-time control. The NE formulation yields a computationally efficient set of forward and backward recursive equations of motion (Table- 4.2.). The forward equations propagate linear velocity, linear acceleration, angular velocity, angular acceleration, and total link forces and moments at each link's center of mass from the base coordinate frame to the end effector coordinate frame of the manipulator. The backward equations propagate the forces and moments exerted on each link from the end effector -VIII-coordinate frame to the base coordinate frame of the manipulator. To compute the joint torques, the NE equations of motion have an order 0(n) relationship to the number of degrees of freedom of the manipulator. Solving for all torques using the NE formulation requires 666 additions and 804 multiplications for n=6 (as in the case of a PUMA robot arm). Robot Arm Control Given the motion equations of a manipulator, the purpose of robot arm control is to maintain a prescribed motion for the arm along a desired arm trajectory by applying corrective compensation torques to the actuators to adjust for any deviations of the arm from the trajectory. The dynamics of a manipulator are described by a set of highly nonlinear and coupled differential equations. This complex description of the system makes the design of controllers a difficult task. To circumvent the difficulties, the control engineer often assumes a simplified model to proceed with the controller design. Industrial manipulators are usually controlled by conventional PID-type independent joint control structures designed under the assumption the dynamics of the link are uncoupled and linear. The controllers based on such an overly simplified dynamics model result in low speeds of operation and overshoot of the end-effector. Independent Joint controllers can be designed by conventional methods based on two factors: damping factor and structural resonant frequency. To improve the performance of the PID controllers, researchers have investigated model-based control schemes which attempt to compensate for the nonlinearities and the mismatch in the dynamical description of the robot. One of the model-based techniques is the ”feedforward dynamics compensation“ method which computes the desired torques from the given trajectory and injects these torques as feedforward control signals. Independent joint feedback controllers are then added with the intention of compensating for the small coupling torques arising out of the mismatch in the dynamics of the model and the real arm. For a single-joint controller, it is possible to reduce the steady-state position error and to eliminate the velocity and acceleration errors by feedforward compensations. For multiple-joint controllers, further feedforward compensation is necessary to encounter the force interactions between joints. However, this introduces computational difficulties so that methods of approximation, simplification, or parallel computation are needed. More through compensation can be achieved by the ”computed-torque" technique based on the LE or the NE equations of motion. Basically, the computed torque technique is a feedforward control with feedforward and feedback components. The feedforward component computes the nominal joint torques along the desired -K-trajectory to compensate for the interaction forces among all the various joints; the feedback component computes the necessary correction torques to compensate any deviations from the desired trajectory. It assumes that one can accurately compute the counter parts of D (q), h (q,q) an G (q) in (3) in order to minimize their non linear effects and use a proportional plus derivative control to servo the joint motors. Controlling the manipulator reduces to computing the control equation in every sampling period of time. If one can compute joint torques as fast as possible, this will greatly reduce the degradation of the controller and make the system more robust to parameter variation. The computation of joint torques based on the complete LE equations of motion is very inefficient. Real-time closed-loop digital control is very difficult. For this reason, simplified and approximate models are being used for controlling the manipulator. These models confine the manipulators to moving at reduced speeds where the effects of the coupling terms are negligible. Another approach is to compute inverse plant dynamics using the NE equations. The control law is computed recursively using the NE equations of motion. From the experimental results, the computed-torque scheme performs better trajectory tracking than the independent joint control scheme. -x-
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