4 Serbestlik Dereceli Robot Kolu Kinematik Denklemlerinin Destek Vektör Makinası İle Çözümü

Abstract

Kinematik problemin çözülmesi robot manipülatörlerinin yörünge takibi açısından büyük önem taşımaktadır. Kinematik modelleme için kullanılan analitik, geometrik ve numerik yöntemlerin her birinin değişik açılardan dezavantajı bulunmaktadır. Analitik ve geometrik yöntemler basit yapılı ve belirli bi geometrik dizilime sahip robot kollarında etkili olabilirken, çok serbestlik dereceli ve karmaşık yapıdaki robot kollarına çözüm sağlayan numerik yöntemlerin hesaplama zorluğu bulunmaktadır. Ayrıca bu yöntemler robot kol çalışma uzayındaki tekil noktalarda cevap verememektedir. Yapay sinir ağları bu problemlere çözüm olabilecek alternatif bir yöntemdir. Robot koldan alınan giriş-çıkış verileri ile sistem eğitililerek kinematik denklemler modellenebilmektedir. Ancak model kestirimi yapılırken yerel minimum noktalara takılması yapay sinir ağlarının bir dezavantajıdır. Tezde, bu probleme çözüm olarak destek vektör makineleri algoritmasının kullanılması önerilmiştir. Doğrudan global minimum noktasına ulaşmayı öngören bu yöntem, kinematik model kestiriminin en az hatayla yapılmasını sağlamaktadır. Bu tez çalışmasında, kinematik model çözümlemesine örnek olarak Gelecek Robotik Makine ve Tıp Teknolojileri Ar. Ge. Tic. Ltd. Şti. firmasının T.C. Bilim Sanayi ve Teknoloji Bakanlık’ ı desteğiyle yürütmekte olduğu “Robotik Tekerlekli Sandalye” adlı projesinde kullanılan rehabilitasyon robot kolu ele alınmıştır. 4 serbestlik dereceli olan bu rehabilitasyon robot kolu, paralel 2 parmaklı bir tutucuya sahiptir. Maksimum erişim mesafesi 400-500 mm’dir. Bu çalışmanın amacı, ileri ve ters kinematik modeli, destek vektör makinası regresyonu ile tahmin ederek analitik, geometrik ve numerik çözümlemenin neden olduğu tekillik sorunu ortadan kaldırmak ve yörünge takibi problemine kinematik tabanlı hızlı ve güvenilir bir çözüm sunmaktır. Analitik yöntemle elde edilen eğitim verileri kullanılarak, 4 eksenli rehabilitasyon robot kolunun ileri ve ters kinematik modelleri destek vektör makinesi yöntemi ile oluşturulmuştur.

Solving kinematic problems has a great importance in terms of trajectory tracking of robot manipulators. Every analitic, geometric and numerical methods for solving this problem, caused differently disadvantages. Analytical and geometric methods may be effective in specific geometric arrangements and basic structures, numerical calculations is used for robot arms that have complex structure and many degrees of freedom. In addition, this method can not be answered in the singular point on the robot arm workspace. Artificial neural networks is an alternative method that may be a solution to kinematic problem. In addition to this, using neural network is becoming very coming due to solve inverse kinematic problem. Neural networks can be used in every configuration of manipulators. Kinematic equations could be modeled with training data that is obtained from system input-output data. On the other hand, a disadvantage of artificial neural networks is that the model is fitted to estimating the local minimum point. In this thesis, an algorithm using support vector machines is proposed as a solution to this problem. This direct method foresees to reach the global minimum point so kinematic model estimation could be done with minimum error. Applications of support vector machines have many areas from health to agriculture. In control engineering, support vector machine algorythm has an important place. Flight control, robust control , system identification are some of the application topics. Furthermore; in automative , support vector machine can be used in engine control. In our topic-robotics- forward and inverse kinematics, trajectory planning and positioning problems have various solutions with support vector machine regression. Especially, support vector machine regression provides an efficient solution to inverse kinematic problem. In this study, kinematics analysis as an example of "Gelecek Robotik Makine ve Tıp Teknolojileri Ar. Ge. Tic. Ltd. Şti. firm . C. Science, Industry and Technology Ministry 's, which are executed with the support of "Robotic Wheelchair" rehabilitation robot arm used in his project were discussed. The aim of this project is helping disabled people with their daily activities. The rehabilitation robotic arm has four degree of freedom and a parallel two-fingered holder. Maximum access distance is 400-500 mm. At the end of the project, the final product will be consist a robotic arm which is entegrated on a electric wheelchair, camera, laser scanner , proximity sensors, touchscreen and an embedded PC. Links of the robot arm is placed vertical to each other. Construction of the links can be seperated two types – vertical and horizontal. Apart from this, there are two types of links according to their torque values. Rehabilitation robot arm project’s aim is helping elder or diasbled people who have to use wheelchair for their basic daily activities. The project process is 18 months and the resultin product is a robotic manipulator prototype which can be controllede by a touchscreen.Another feature of this robot manipulator is that link numbers and kinematic structure are adjustable for users’ needs. This feature adds an extra advantage to manipulator. With adjustablr kinematic structure, robotic arm can be used for industrial purposes. Controlling the robot manipulator with inverse kinematic can be possible with learning the forward kinematic model by the help of the support vector machine algorithym. While learning forward kinematic model, optimum parameters of support vector machine regression must be used. In this study, optimum parameter research is accomplished by grid search algorithym. The same learning process is aplied inverse kinematic model. At the end of these processes , forward and inverse kinematic model of the robot arm is obtained. The kinematic model, that is predicted by support vector machine algorythm, can be used in adaption of a computed torque PD controller’s parameters. Computed torque controllers provide a dyanmic based solution to trajectory planning problem. By this method , controller performans can be reduced and trajectory planning can be done with minimum error. The aim of this study is that elimination of the singularity problem that is caused by geometric and analytic solutions with the estimation of forward and inverse kinematic models by using support vector machine regression. 4-axis rehabilitation robot arm forward and inverse kinematics model is created with support vector machine method by using the training data obtained from analytical solution.