İki uzuvlu bir robot kolunun hesaplanmış moment metoduyla kontrolü

Abstract

ÖZET Anahtar kelimeler: Robot, Robot dinamiği, Hesaplanmış moment algoritması. Yakın zamana kadar robot kontrol metodlarının bir çok tipi üzerinde durulmuş fakat son yıllarda hesaplanmış moment kontrolörlerinin kullanımı ağırlık kazanmıştır. Hesaplanmış moment aynı zamanda nonlineer sistemlerin geri beslemeli lineerleştirme işleminin özel bir uygulamasıdır. Bu metodda eklemlere uygulanacak T momenti, her eklem için ayrı olarak hesaplanır. Hesaplanmış moment metodu kumanda sinyali olarak eklem ivmesini alır. T = M(qd -u) + N. Bu kanundan yola çıkılarak robot kolu kontrolünün simülasyonu yapılmıştır. Robot kolundan değişik yörüngeler takip etmesi istenerek değişik çalışma periyotları seçilmiş, böylelikle eklem açılarının, torklarının, hızlarının ve izleme hatasının öngörülen ve gerçekleşen değerleri eğriler yardımıyla mukayese edilmiştir. Sonuç olarak bu kontrol metodunun hassasiyeti sınanmıştır.

Keywords: Robot, Robot dynamics, Computed torque control algoritm. The robot as a programmable.multi-functionaJ manipülatör designed to move material, parts, tools, ör specialized devices trough variable programmed motions for the performance of a variety of tasks. This is a widely accepted definition of an indusrial robot. The emphasis is on the programmable facilıties by which the robot can perform simple tasks without human assistance. Robot arm consists of several rigid links \vhich are connected to each other in seriesby revaluate ör prismatic joints. Öne 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 joint with actuators. Robot classification may be considered on the following basics: 1l)Structural configuration and robot motion (2)Trajectories based on motion control Classification based on structural configuration and robot motion -Revaluate (jointed arm) robot -Polar (spherical) robot -Cartesian (rectangular) robot -Cylindirical robot Classification based on path control -Point to point control -Continuous path control. Robot 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 forces/moments that cause the motion. Thus, kinematic deals wıth the analytical description of the spatıal displacement of the robot as a funcn'on of time, in particular the relations between the joint vanablespace and the pozitıon and orientation of the end-effector of a robot arm. There are fimdamental problems in robot arm kinematics. The first problem is usually referred to as the direct (ör fonvard) kinematics problem,while the second problem is the invers kinematik problem, while the second problem is the invers kinematics viproblem. The direct kinematics problem is to find the position and orientation of the end effector of a manipülatör vvith respect to a reference coordinate system, given the Joint-angle vector q=(qı,q:,q3,....,q6)7of the robot arm. The inverse kinematics problem (ör 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 ör world coordinate system, the inverse kmematics solution ıs used more frquently in control of robot arm. The homogenıus matrix T0ı, 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 succesive coordinate transformation matrices of A,1.,, expressed as Tâ = AXA;, = f]Arlj ; fort= 1,2n )-> -IX y, z- P.I.FR; pJ ~Lo o o ıj-[o ıj(1) where; [x,.y,'zJ= Orientation matrix of the i th coordinate system established at link i with respect to the base coordinate system. P, = Position vector which points from the origin of the base coordinate system. Specifically for i=6, we obtain the T matnx, T= A*, which specifies the position an orientation of the end point of a manipülatör vvith respect to the base coordinate system. This T matrix is used so frequentiy in robot arm kinematics that it is called the "arm matrix". Consider the T matrix as T=[X> y< Z< P