İnsansı robotlarda yürüme
Humanoid walking
Yazar: SABRİ YILMAZ
Danışman: PROF. DR. METİN GÖKAŞAN
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Kontrol ve Otomasyon Mühendisliği Ana Bilim Dalı / Kontrol ve Otomasyon Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2013
Konu: Bilgisayar Mühendisliği Bilimleri-Bilgisayar ve Kontrol = Computer Engineering and Computer Science and Control ; Makine Mühendisliği = Mechanical Engineering ; Mekatronik Mühendisliği = Mechatronics Engineering

Özet:
İnsansı robotlar insanlara benzerlikleri ve insanlar için uygun olan ortamlarda hareket edebilme kabiliyetleri nedeniyle mobil robotlar içinde dikkat çekici bir yere sahiptirler. Tekerlekli robotlarla kıyaslanacak olursa, insansı robotlar iç ortam ve dış ortam koşullarında daha özgürce hareket edebilirler. Merdiven çıkabilirler veya engellerin üzerinden adım atabilirler. Robotik ve otonom sistemler açısından bakılırsa, hareket-yörünge planlaması daha yoğun ilgilenilen bir çalışma alanıdır, çünkü bu tarz sistemlerin kinematik yapıları oldukça karışık ve serbestlik dereceleri yüksek sayılardır.
İnsan yürüyüşünün teknik adı iki bacaklı yürümedir, humanoid robotların da yer değiştirme sistemleri bu iki bacaklı yürümeye dayanmaktadır. İnsansı bacağa çalışmalarda kullanılabilecek en yakın model altı serbestlik dereceli modeldir.
Robotiğin tarihi antik çağlara dayanmaktadır. Endüstride kullanılan günümüz robotlarından daha önce Yunan Tanrısı Hephaestus atölyesinde kendisi için çalışacak bir robot üzerinde çalışmaktaydı, bu tarz çalışmalar başarısız olmuştur.
Son yıllarda otonom makinalara ilgi artmaktadır. Robotların kullanım alanları hizmet ve endüstriyel robotlar olarak ikiye ayrılabilir. Hizmet alanında kullanılan robotlar; askeri alanlarda kullanılabilir, tıp alanında kullanılabilir ya da astronomi alanında kullanılabilir. Endüstriyel robotlarsa üretim sürecinin hatalarının minimize edilmesi, üretimin hızlanması ve insan gücünün yetersiz kalacağı yerlerde kullanılabilir.
Robot hareketi parçaları uzayda hareket ettirmek olarak isimlendirilebilir. Uzayda çalışabilmek için eksen takımlarının tanımlanması ve bu eksen takımlarının kendi içlerinde konumları ve oryantasyonlarının tanımlanması gereklidir. Robot eyleyiciler eklemler ve uzuvların kombinasyonlarından oluşur. Robotlarda kullanılabilecek altı farklı eklem tanımlanabilir, bunlar; dairesel, prizmatik, silindirik, düzlemsel, küresel ve vida tipinde olabilir.
Bir insan bacağı altı dairesel eklem ve ara uzuvlarla tanımlanabilir ve bu altı serbestlik dereceli robot manipulatör olarak isimlendirilebilir. Çünkü insan bacağında kalçada üç eksen etrafında dönme, dizde bir eksen etrafında dönme ve bilekte iki eksen etrafında dönme hareketleri söz konusudur, bu durum kinematik modelin çıkartılması sırasında kolaylık sağlayacaktır.
Kinematik analizin ardından modelin dinamik analizi yapılmıştır. Dinamik analiz ile harekete sebep olan kuvvetler ve torklar incelenecektir, kinematik analizde ise hareketin geometrik yorumu yaratılmaya çalışılmışıtır. Dinamik analiz ile amaçlanan, tasarım kriterlerinin bacak adım hareketini gerçekleştirirken eklemler
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üzerindeki tepki kuvvetlerini ve eklemlerin üretmesi gereken tork değerleri kullanılarak belirlenmesidir.
Bu çözümleme sırasında hiçbir kontrolör sistemi kontrol etmediğinden, iterasyon sayısının hızlı çözümleme adına düşük olması ve gerek matris tersi alma işleminde Jacobien matrisinin kare matris olmaması nedeniyle yarattığı hatadan dolayı planlanan hareket ile elde edilen hareket arasında belli bir fark oluşmaktadır, yani sistem sürekli hal hatası yapmaktadır.

Abstract:
Humanoid robots are a particularly interesting group of mobile robots because of their resemblance to humans and their potential ability to operate in environments created for humans. In comparison to wheeled robots, humanoid robots can move more freely in indoor and outdoor environments. They can climb stairs, step over or onto obstacles. In robotics and autonomous systems however, motion planning for a biped walking robot is a rather demanding task because of the complex kinematics of such machines and the many degrees of freedom involved.
Man walking named as biped walking, biped means having two legs. Humanoid robots? locomotion system is based on biped walking. The most similar model to a human leg should have six degrees of freedom.
The projected leg with six degrees of freedom is drawn in Solid Works. Solid Works is 3D drawing program. This leg has three degrees of freedom in hip, one degree of freedom in knee and two degrees of freedom in wrist. For this purpose six servo motors will be used, every servo motor has one degree of freedom.
Robot, a mechanism that can move automatically explained in thesaurus. Robot has different meanings in literature. Robot is defined as any automated machine programmed to perform specific mechanical functions in the manner of a man in, or not controlled by man and a person who works, or behaves like a machine; automaton in dictionaries. From these meanings it can be understood that robot is an autonomous thing. But in 1921 the word robot was introduced the world by Czech writer Karel ?apeK.
A reference by Professor Chudoba, to the Oxford Dictionary account of the word Robot's origin and its entry into the English language, reminds me of an old debt. The author of the play R.U.R. did not, in fact, invent that word; he merely ushered it into existence. It was like this: the idea for the play came to said author in a single, unguarded moment. And while it was still warm he rushed immediately to his brother Josef, the painter, who was standing before an easel and painting away at a canvas till it rustled. "Listen, Josef," the author began, "I think I have an idea for a play."
"What kind," the painter mumbled (he really did mumble, because at the moment he was holding a brush in his mouth). The author told him as briefly as he could. "Then write it," the painter remarked, without taking the brush from his mouth or halting work on the canvas. The indifference was quite insulting. "But," the author said, "I don't know what to call these artificial workers. I could call them Labori, but that strikes me as a bit bookish." "Then call them Robots," the
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painter muttered, brush in mouth, and went on painting. And that's how it was. Thus was the word Robot born; let this acknowledge its true creator.
Robot manipulation is moving parts and tools in space. Because of working in space there must be coordinate systems and positions and orientation of these systems with respect to other defined systems, naturally. The manipulators are the combination of joints and links. There are six possible joints, revolute, prismatic, cylindrical, planar, screw and spherical joints.
In this study for working on two legs, half of the length of the hip is added to the legs so that the legs are not on the same plane, there is a hip offset between the legs, naturally. First of all the kinematics models of the legs are derived, for this purpose joints and the links have to be defined. Firstly the axes must be defined on the joints. In Denavit-Hartenberg approach the z-axes are found on the joints with respect to their degrees of freedom, the moving direction. This model leg has six revolute joints so that these joints are rotating around an axis. The rotation axes are the z-axes.
The joint parameters are written with a mark above themselves. With this approach, transformation matrix will be found. Transformation matrix is a matrix that gives the translation and the rotation of the target joint with respect to another joint. Transformation matrix includes a translation and a rotation matrix in itself. Rotation matrix gives the rotation of the target joint around the defined axes with respect to another joint.
After implementing forward kinematics with respect to Denavit-Hartenberg, the inverse kinematics will be studied. Inverse kinematics is needed because when robot manipulator is moving, there must be a path that is followed. In this path joints will be in different positions and orientations, inverse kinematic gives the results of unsolved joint parameters across this path. In this work Jacobian matrix is used to find the inverse kinematics solution.
Manipulator arm must have at least six degrees of freedom in order to locate its end-effector at an arbitrary point with an arbitrary orientation in space. Manipulator arms with less than six degrees of freedom are not able to perform such arbitrary positioning. On the other hand, if a manipulator arm has more than six degrees of freedom, there exist an infinite number of solutions to the kinematic equation. So the humanoid legs are modeled by six degrees of freedom for each other.
For path planning, this study aims walking across linear path so yaw axis has no effect on walking. Legs are modeled by six degrees of freedom but their homogenous transformation matrices are suitable for multiplication so that biped can be considered by twelve degrees of freedom. So that the kinematics models can be used separately or together, this gives the chance of controlling Jacobian matrices with respect to each other. And also each leg has two different Jacobian matrixes. One is for the leg?s support position, other one is for swing position. When right leg is the support leg, the base frame of Jacobian matrix will be on right foot, and the first tip will be on center of gravity. Second Jacobian matrix will take center of gravity as the base frame and will take left foot as tip point. At this configuration again one part of the partial function will be used as path.
After defining kinematic side of the walking, dynamic modeling is derived. There are two widely used models available. Zero-Moment Point (ZMP) and Inverted
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Pendulum (IP). ZMP is based on controlling the motion of the ZMP where movement and body dynamics do not cause any moments. IP uses pendulum model and controls the leg as a pendulum. In this study, instead of these models another path is defined for center of gravity, where is accepted between two legs. The path that is defined for center of gravity is another half circular path but width and period of this sinusoidal function is different from path that is defined for legs.
When support leg and swing leg change the kinematic models change. Biped modeled by four different models and every configuration has two models. By this division biped uses two different kinematic models for one step. By using two different models, center of gravity and swing leg can be controlled separately. Support leg can be taken as a robot arm, and swing leg can be taken as robot arm that is on the moving platform. Defining sinusoidal paths makes solution very fast and simple. Controlling bipeds swing leg and center of gravity by simple sinusoidal functions gives chance to consider dynamic model by kinematic solution.
After defining models dynamic analysis of the walking is done, for this purpose forces on the joints and torques of the joints are found by Matlab SimMechanics Toolbox. The motion of the real center of gravity is found and analyised. Projected biped is built and for the future works all this simulation work must be implemented onto the real robot and the success of this study must be inspected. After having results this open loop path planning must be controlled with proper controllers, control theory must be studied.