Paletli mobil manipülatör tasarımı ve modellenmesi
Tracked mobile manipulator design and dynamical modelling
Yazar: MUSTAFA TOLGA YAVUZ
Danışman: PROF. DR. HAKAN TEMELTAŞ
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Mekatronik Mühendisliği Ana Bilim Dalı / Mekatronik Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2014
Konu: Makine Mühendisliği = Mechanical Engineering ; Mekatronik Mühendisliği = Mechatronics Engineering

Özet:
Bu çalışmada, dış ortamlarda kullanılmak üzere paletli mobil manipülatör tasarımının yapılması, aracın dinamik modelinin sistematik bir şekilde uzaysal operatör cebrinden faydalanılarak çıkarılması ele alınmıştır. Tasarlanan aracın mobil platformu üzerinde konstrüktif açıdan hareket kabileyetini yani mobilitesini mevcut mobil robotlara göre artıracak bir takım iyileştirmeler yapılmış ve üzerine yerleştirilen algılayıcılar ile de çevresiyle olan etkileşimine karşı yarı otonom özellik kazandırılmış böylece üzerine gömülü olarak yerleştirilen manipülatörün sonsuz bir çalışma uzayında çeşitli görevleri yerine getirirken manipülasyon potansiyeli artırılmıştır. Lakin aracın artan karmaşık yapısı, dinamik platformla manipülatör arasındaki dinamik etkileşimden ve holonomik olmayan kısıtlardan kaynaklanan bir takım problemleri doğurmakta, bunun neticesinde de aracın dinamiğini açıklayacak yeni dinamik ifadelere başvurulmasına zorunlu kılmaktadır. Bundan ötürü tasarlanan aracın dinamik modeli, robot dinamiğinde yeni bir yöntem sayılabilecek primitif olarak sunduğu çözüm ile paralel veya seri uzuvlu açık zincirli mekanizmalar ile kapalı çevrimli veyahut ağaç topolojisine sahip karmaşık  mekanizmaların ifadelerini temel dinamik prensiplere göre uzaysal olarak etkili bir şekilde kolayca çıkarmayı sağlayan uzaysal operatör cebri ile açıklanmaktadır. Bu yöntem basitçe, birbirine bir eklemle bir noktadan bağlanmış bağıl hareket etmekte olan uzuvların bağıl hız denklemlerindeki vektörel çarpım ifadelerini matematiksel ara bir işlemle, doğrusal bir operatör ile, iki matrisin skaler çarpımına dönüştürmekte; bulunan ifadenin n-uzuvdan oluşan sistemler üzerinde uygulanmasıyla da tüm sistemin hareketi açıklayan uzaysal ifadelerin elde edilmesi şeklinde açıklanabilir. Bulunan bu ifadelerin basit matematiksel deyimlerle ifade edilişi ve sade fiziksel anlatımından dolayı n-uzuvdan oluşan sistemlerde uzaysal olarak kendini tekrar eden  ifadelerden faydalanılarak uzaysal operatör cebri için etkili döngüsel algoritmalar geliştirilebilir. Bu döngülerin hesaplanma karmaşıklığı da serbestlik derecesi ile doğrusal olarak artmakta olduğundan düşük serbestlik dereceli sistemlerde daha etkili gerçek zamanlı benzetimler olasıdır. Elde edilen ifadeler aracılığıyla aracın verilen bir yörüngeyi takip etmesi problemi, mobil platform üzerindeki holonomik olmayan kısıtların korunduğu durumdaki kısıtlar ve ani dönme merkezine göre oluşturulan kinematik tabanlı modelin PID kontrolünün yapılması ile çözülmekte olup matematiksel ifadelerden hareketi açıklayan algoritmaların simülasyon programında tanımlanan araç modeli üzerine kontrol bloğuyla birlikte etkitilmesiyle bu  çalışma tamamlanmaktadır.

Abstract:
Etymologically, the word robot is used for autonomous or manual mechatronic systems having sensors,controller, motors and drivers which are creating  body links moving wanted objects at the present time, while firstly used for human effort serving in factory instead of artificial people in Karel Capek's play named as Rossum's Universal Robots. Advancing technology up to developing semiconductor technology cause an acceleration in the robotic field and  beginning the trip of robot B.C. 2500 in Egypt becomes an indispensable part of our lives due to operating ability in a hazardous environment, providing high precision and yield, low producing costs in manufacturing, continuity and endurance. They can be classified fixed and mobile according to locomotion ability of base platform, also they can be classified industrial, medical, social, specialist according to usage fields. In this study, mobile specialist robots are examined, which are not fixed to a physical point or location, and  can move freely in a defined enviroment as serving predefined duties. Meanwhile, they vary according to locomotions such undulated, tracked, biped etc. and wheel and locomotion type under the ground robots title. If wheel type classification is discussed, there are to be fixed, centered oriented, swedish, offset centered oriented and screw as wheel type. Similarly, there are few different locomotion mechanism used in ground wheeled robots which are diferential, omni-directional, ackerman, steered wheels, synchronous. In the past two decades, there has been observed a growing research in the mobile robotics due to various reasons which some of them told above. Some of these reasons can be ordered as urban search and rescue, explosive ordnance disposal, military missions, hazardous environment exploration such as nuclear areas or collecting datas in planet exploration missions etc. Up to these facts focus on this field, it is compulsory to consider new design and methods for modelling of mobile platforms with manipulator. Therefore, many academic and industrial mobile robots were designed and demonstrated until now and will continue from now on. For these reasons described, design and modelling of domestic mobile robot with domestic labor  and capital is the inevitable need for every nation. In this graduation study, presentation of tracked skid-steered mobile manipulator operating on various rough terrains and dynamical modelling in a systematic way by using spatial operator algebra is aimed and realized by the help of various computer aided designing and simulation softwares which are Dassault Catia and Solidworks, Siemens Nx Unigraphics, Ansys, Msc Adams and Functionbay Recurdyn used to complete this study virtually in design and modelling steps before manufacturing first prototype. After that, algorithm of spatial operator algebra tested over the virtual prototype running realistic virtual environment by the help of Matlab/Simulink software communicating computer aided design and simulation softwares mentioned above. 
Before starting to tell design process and modelling algorithm, some facts have to be clarified, one of them is electrical and electronic components. During this study, stock parts were used instead of redesign circuits which are used to control trajectory, actuators and include classical unmodelled based control algorithms with dynamical model of skid steered tracked mobile manipulator. Also, current and voltage consumed via actuators are controlled by these stock subelectronic components (arduino mega 2560) containing avr microcontroller working in the service of main computer circuit (raspberry pi model b) containing arm microprocessor. In mechanical design process, attention has been paid to some cases related to arm and track system mechanism, manipulability, maneuverability that is combination of steerability and mobility. Mobility of the platform is combined with manipulability of embeded manipulator mounted on the platform. Hence, the mobile platform provides mobility while the 5 dof manipulator provides manipulation. In this way, manipulability of embeded manipulator mounted on platform increases while performing a various tasks in an unlimited working space. To increase maneuverability in tough zones, which thoroughly depends on robot's locomotion and dimensions, various locomotion modes were defined such as climbing, flipper, obstacle overcoming etc.by dividing track systems into two part which is consisting of two sub-arm and dimensions of platform were optimized as much as no empty volume in the body of platform. Meanwhile, differential steering system was preferred due to simple and robust structure under  variable loads. In fact, working zone terrain is efficient on this choice due to soft and rough structure. The other case paid attention is place of mass center which determines instantaneous center of rotation, consumed energy by track arm actuators and stability during a motion. Therefore,  power pack and various actuotars driving arm links and tracks were placed specific positions in the platform  inner body to obtain the center of mass at the middle of platform. The final design consideration is structure of track system in which smooth motion ability of bi-wheel type mobile robots and robust stucture to slipping  are combined. Also, added suspension system contaning torsinal and pressure spring with aeral damper between platform and track arms provides robustness towards to disturbance effects due to terrain conditions. At the end of mechanical design process, strength of overall structure of mobile manipulator were controlled by finite elements software and inner polyamid supports were reguired to increase endurance of manipulator and track arms manufactured from a thin sheet metal. In dynamical modelling step, increased complexity of robot causes some problems due to interaction between manipulator and platform, and  nonholonomic constraints, so applying new solution methods governing robot dynamics is necessary to obtain dynamical model of robot. Also, nonlinear, coupled  equations of dynamics and diffuculties to meet the requirements of real time simulation obligates that. Therefore, dynamical model of designed robot can be expressed more effecient and  a simplified way by help of  spatial operator algebra which is an almost new method based on basic fundamental dynamic principles between two relatively moving rigid links. In this method, relative velocity relation between links attached to each other via a joint is presented with scalar product instead of vectoral product by using operator called as spatial operator and applied over whole system to explain spatial velocity equation in matrix form. In other words, dynamical equation of motion for complex system is expressed in a concise and systematic formulation via spatial operators. Also, spatial operator algebra provides high level frameworks for describing the dynamic behaviour of robot and for control and trajectory design algorithms.The only drawback of this method is singulariy problem of jacobian matrix if jacobian is not square. In these cases, jacobian matrix transform into pseudo jacobian matrix via additional calculation to obtain square matrix. However, fast solution algorithm for real time systems and easily modelling abstract expressions of high level structures via link and rotation vectors and ease of implementing are some advantages of this recursive method. Furthermore, distribution of velocity, acceleration and forces through rigid links are shown via propagation matrix which can present an obvious physical interpretations. As a final step,this study based on spatial operator algebra method algorithm were simulated via both Msc Adams and Matlab/Simulink by communicating them each other and results were discussed with Euler Lagrange based algorithms. Also, trajectory control of platform  was observed and compared under PID controller and without controller in the light of kinematic equations by assuming conserved nonholonomic constraints and this study was concluded via implementing control algorithm to mobile robot simulink block. Briefly, maneuverability on the mobile platform is increased by improving  it structurally when compared existing mobile robots in this area. So, new design based on this fact were realized and almost new dynamical modelling method, spatial operator algebra, were used over the system to make quick calculations for real-time operating. Therefore, fast decisions can be taken for collecting datas from environment via sensors. In these fast decisions, working frequency of main electronic circuits is efficient, so raspberry pi providing interface between user and robot was preferred to other ones. In addition to mentioned above, some problems were come accross due to singularity of jacobian matrix which causes faulty resuts and so decomposition of matrix applied to overcome this problems.