İki ve üç boyutlu farklı robotik sistemler arasında kinematik dönüşüm analizleri

Abstract

Günümüzde teknoloji alanında en büyük gelişme kaydeden alanlardan birisi robotik sistemlerdir. Tarihi milattan öncesine kadar dayanan robotların günümüzde yapay zekaya sahip olmaya başladıklarını göz önüne alırsak, bu yapay zekaya katkı sağlayacak en önemli unsurlardan birisi de robotların hareketidir. Robotların hareketinin belirli bir konuma bağlı olması, bu konumun doğruluğu ve robot hareketlerinin istenen düzeyde, kesin çözümler sunması bir robot tasarımındaki en önemli gereksinimlerdendir. Bu tezde öncelikle düzlemde ve uzayda koordinat sistemlerinden bahsedilmiş ve ardından bu tez çalışmasına altlık sağlayacak olan jeodezik koordinat sistemlerine ve koordinat sistemleri arasındaki dönüşüm yöntemlerine yer verilmiştir. Bu tez çalışmasında ayrıca robotların tarihçesine kısaca değinilmiş olup farklı çeşitlerde robotların çalışma alanlarından ve amaçlarından bahsedilmiştir. Robotların hareketlerini incelemek amacıyla ileri ve geri kinematik yöntemlere değinilmiş ve bu kinematik analizlerinin yapılabilmesi için gerekli olan jeodezik dönüşüm matrislerinin oluşturulma aşaması anlatılmıştır. Dönüşüm matrisleri oluşturulurken kullanılan üç boyutlu kartezyen koordinat sistemine değinilmiştir. Tez çalışmasının örnek uygulama kısımlarında ilk olarak iki boyutlu düzlemde hareketi gerçekleşebilen bir robot düşünülmüştür. Bu robota ait başlangıç noktasının koordinatlarına, robotun eklem ve bağ parametrelerine değerler atanarak ileri ve ters kinematik dönüşümleri gerçekleştirilmiştir. Aynı şekilde başlangıç noktası belirli olan bir rotational-rotational-prismatic (RRP) yani iki dönel bir prizmatik eklem yapılı robot için ileri ve ters kinematik denklemler dönüşüm matrisleri yardımıyla çıkarılmış ve robot eklem-bağ parametrelerine değerler atanarak değişken parametreler de hesaplanmıştır. Son uygulamada ise yeni bir robot tasarlanmıştır. Tasarlanan robotun çizimi SketchUp yazılımı ile sağlanmıştır. Başlangıç koordinatları belirli olan ve bir düzlemde bir konuma sabitlendirilmiş şekilde yer alan bu robota bir dönel, iki prizmatik eklem yerleştirilip, bu eklemler ve robot uç işlevcisi arasında ileri ve ters kinematik analizler gerçekleştirilmiştir. Bu analizlerin yapılması için robot eklemleri arasında üç boyutlu kartezyen koordinatların dönüşümü gerçekleştirilmiştir. Robotun eklem parametreleri Denavit-Hertanberg yöntemine göre belirlenmiş ve ters kinematik analizinde analitik çözüm yöntemi uygulanmıştır. Yapılan ileri ve ters kinematik analizleri sonucunda robotun alabileceği minimum ve maksimum parametre değerleri de tespit edilmiş ve robot uç işlevcisinin varacağı koordinatlar bulunmuştur.

Recently, we've been witnessing that robotic systems has been improved in technology sites fabulously. We can see the history of robots date to before common era if we need to research. If we consider that robots now have artificial intelligence, one of the most important factors that contribute to this artificial intelligence is capability of the movement of robots. There are significant requirements in a robot design such motions of the robots depends on a specific position and correctness of their positions.In this thesis, firstly coordinate systems on a plane and space are mentioned and after that geodetic coordinate systems and transformations between those coordinate systems which provide a base for the study of this thesis are explained. Three dimensional cartesian coordinate systems which are an example of terrestrial coordinate systems from geodesic coordinate systems and the transformations in three dimensions which these coordinate systems can perform between them can be named as the basis of this thesis work. Terrestrial coordinate systems are one-, two-, or three-dimensional coordinate systems that are difficult to identify due to reasons attributable to physical properties of the earth. The three-dimensional cartesian coordinate systems are coordinate systems consisting of three mono-parametric surfaces with a fixed center in space. In a three-dimensional cartesian coordinate system, the center of gravity is the center point (starting point) of this coordinate system, Z axis coincides with the rotation axis of the surface, the direction passing through the Greenwich meridian with the X axis within the equatorial plane, the Y axis on the equatorial plane and perpendicular to the X and Z axes which are assigned by right hand rule. In this thesis study, the history of robots is briefly mentioned, and work areas and purposes of different kinds of robots are mentioned. In this thesis, the robot that is designed is considered as a kind of industrial robot. Industrial robots usually consist of an articulated (multi-link manipulator) and an end effect attached to a fixed surface. In addition to industrial robots in the thesis, mobile robots, service robots, general purpose autonomous robots and humanoid robots are briefly mentioned.The forward and backward kinematic methods have been referred to in order to examine the movements of the robots. In robotic systems, movements of joints belonging to all arms and other parts of the robot are defined by robot kinematics. A robot comes from joints that can provide translational and rotational movements and links that connect these joints. The movement of a joint determines the position and orientation of the joint which follows it. In the robot kinematics section of this thesis, the Denavit-Hartenberg method which describes the relationships of robot joints and links and 4x4 homogeneous transformation matrices formed by Maxwell is mentioned. A systematic technique has been proposed by Denavit and Hertanberg for establishing the translation and translation relationship for each adjacent connection. This approach is also known as D-H. After coordinate systems which are connected links have been assigned, the transformation between adjacent coordinate systems is represented by a [4 × 4] homogeneous transformation matrix.In the sample application part of the thesis study, firstly a robot which can move in two dimensional plane is considered. For a planar robot with two rotational (RR) joints, the forward kinematics are first solved to determine the position of the end-effector the robot, and then the variable D-H parameters of the robot are calculated by using the inverse kinematic method.For a rotational-rotational-prismatic (RRP) robot with the same first example application, forward and inverse kinematic equations are derived by using transformation matrices and variable parameters are calculated by assigning values to robot joint-link parameters.In the final application, a new robot is designed. The design of the robot is provided by SketchUp software. Designed to be able to move in all directions in a three-dimensional plane, this robot has three degrees of freedom. It has only one rotational joint and two prismatic joints. By adding two prismatic joints to the robot, the solution of the inverse kinematic problem is also facilitated. This also is the reason why the rotational joint is kept as single and not increased. The more the number of rotational joints is increased, the more physically the solution will be so difficult so a single rotational joint is given. The position of the starting point of this designed RPP robot is known. In this study, after the design of the robot, the parameter values that the robot can take to arrive at a certain position are found and then the position at which these parameters can be reached is determined. Forward and inverse kinematic analyzes were performed between these joints and end function of the robot. In order to perform these analyzes, three-dimensional cartesian coordinates were transformed between robot joints. Parameters of the joints of the robot were determined by being used Denavit-Hartenberg method and analytical solution method was applied in inverse kinematic analysis and analytical solution method was applied in inverse kinematic analysis. As a result of the analyzes of both direct and inverse kinematics, minimum and maximum parameter values belongs to the robot are determined. Correspondingly the coordinates are found for the end-effector.The inverse kinematics problems of the robot have been solved by analytical solution and exact results have been produced. More than one using of prismatic joints also physically reduced the number of solutions. The robot in this thesis study was transformed into two and three dimensions by considering that it would not be exposed to any problems after any movement. But for future studies, it is thought that the transformations can be done by affine transformation model. Depending on the time, if the robot is deemed to be subjected to deformation due to the exposure of a joint to any external influences, or if endurance is taken into account, depending on the robot design, since there will be a scale difference between the axes in the robota joints, it will be necessary to apply the affine transformation model. The transformation will be performed so that the scale difference before the transformation is preserved after the transformation. The robot design in the thesis study corresponds more to the industrial robot class. It is thought that various fields can do certain tasks needed for human power. Since the last two joints are prismatic, any work can be done with a robot on a surface perpendicular to the end-effector of the robot. It is also anticipated that robot joints and link lengths are adjusted to each other and that they can perform a task of lifting and placing a material if necessary works are done on the carrying capacity. Once again, if we think about what kind of works can be done on the same robot design and how to develop the robot, a laser meter, a GPS device or such measurement tools can be added to any joint of the robot in order to facilitate convenience in construction and cartography, and the robot can be brought to the capacity to measure between certain points or to assist in making certain point markings.