A Comparative Study of Three Inverse Kinematic Methods of Serial Industrial Robot Manipulators in the Screw Theory Framework

In this paper, we compare three inverse kinematic formulation methods for the serial industrial robot manipulators. All formulation methods are based on screw theory. Screw theory is an effective way to establish a global description of rigid body and avoids singularities due to the use of the local coordinates. In these three formulation methods, the first one is based on quaternion algebra, the second one is based on dual-quaternions, and the last one that is called exponential mapping method is based on matrix algebra. Compared with the matrix algebra, quaternion algebra based solutions are more computationally efficient and they need less storage area. The method which is based on dual-quaternion gives the most compact and computationally efficient solution. Paden-Kahan sub-problems are used to derive inverse kinematic solutions. 6-DOF industrial robot manipulator\u27s forward and inverse kinematic equations are derived using these formulation methods. Simulation and experimental results are given

Canonical Subproblems for Robot Inverse Kinematics

The inverse kinematics (IK) problem for many common robot manipulators may be decomposed into canonical subproblems which are solved by finding the angles on circles where they intersect with other geometric objects. We present new algebraic solutions and geometric interpretations for six subproblems using a linear algebra approach, and we demonstrate significant computational performance improvements over existing IK methods. We show that IK for any 6-dof all revolute (6R) robot with three intersecting or parallel joint axes may be solved in closed form using subproblem decomposition. For any other 6R robot, subproblem decomposition reduces finding all IK solutions to a search over one or two joint angles. The first three subproblems, called the Paden-Kahan subproblems, are Subproblem 1: Circle and Point, Subproblem 2: Two Circles, and Subproblem 3: Circle and Sphere. The other three subproblems, which have not been extensively covered in the literature, are Subproblem 4: Circle and Plane, Subproblem 5: Three Circles, and Subproblem 6: Four Circles. Our approach also finds the least-squares solutions for Subproblems 1-4 when the exact solution does not exist.Comment: 14 pages, 8 figures. Updated with new solution methods and timing result

Stable locomotion of humanoid robots based on mass concentrated model

El estudio de la locomoción de robots humanoides es actualmente un área muy activa, en el campo de la robótica. Partiendo del principio que el hombre esta construyendo robots para trabajar juntos cooperando en ambientes humanos. La estabilidad durante la caminata es un factor crítico que prevee la caída del robot, la cual puede causar deterioros al mismo y a las personas en su entorno. De esta manera, el presente trabajo pretende resolver una parte del problema de la locomoción bípeda, esto es los métodos empleados para “La generación del paso” (“Gait generation”) y asi obtener la caminata estable. Para obtener una marcha estable se utilizan modelos de masa concentrada. De esta manera el modelo del “pendulo invertido simple” y el modelo del “carro sobre la mesa” se han utilizado para conseguir la marcha estable de robots humanoides. En el modelo del pendulo invertido, la masa el pendulo conduce el movimiento del centro de gravedad (CDG) del robot humanoide durante la marcha. Se detallara que el CDG se mueve como una bola libre sobre un plano bajo las leyes del pendulo en el campo de gravedad. Mientras que en el modelo del “carro sobre la mesa”, el carro conduce el movimiento del CDG durante la marcha. En este caso, el movimiento del carro es tratado como un sistema servocontrolado, y el movimiento del CDG es obtenido con los actuales y futuros estados de referencia del Zero Moment Point (ZMP). El método para generar el paso propuesto esta compuesto de varias capas como son Movimiento global, movimiento local, generación de patrones de movimiento, cinemática inversa y dinámica inversa y finalmente una corrección off-line. Donde la entrada en este método es la meta global (es decir la configuración final del robot, en el entorno de marcha) y las salidas son los patrones de movimiento de las articulaciones junto con el patrón de referencia del ZMP. Por otro lado, se ha propuesto el método para generar el “Paso acíclico”. Este método abarca el movimiento del paso dinámico incluyendo todo el cuerpo del robot humanoide, desde desde cuaquier postura genérica estáticamente estable hasta otra; donde las entradas son los estados inicial y final del robot (esto es los ángulos iniciales y finales de las articulaciones) y las salidas son las trayectorias de referencia de cada articulación y del ZMP. Se han obtenido resultados satisfactorios en las simulaciones y en el robot humanoide real Rh-1 desarrollado en el Robotics lab de la Universidad Carlos III de Madrid. De igual manera el movimiento innovador llamado “Paso acíclico” se ha implemenado exitosamente en el robot humanoide HRP-2 (desarrollado por el AIST e Industrias Kawada Inc., Japon). Finalmente los resultados, contribuciones y trabajos futuros se expondran y discutirán. _______________________________________________The study of humanoid robot locomotion is currently a very active area in robotics, since humans build robots to work their environments in common cooperation and in harmony. Stability during walking motion is a critical fact in preventing the robot from falling down and causing the human or itself damages. This work tries to solve a part of the locomotion problem, which is, the “Gait Generation” methods used to obtain stable walking. Mass concentrated models are used to obtain stable walking motion. Thus the inverted pendulum model and the cart-table model are used to obtain stable walking motion in humanoid robots. In the inverted pendulum model, the mass of the pendulum drives the center of gravity (COG) motion of the humanoid robot while it is walking. It will be detailed that the COG moves like a free ball on a plane under the laws of the pendulum in the field of gravity. While in the cart-table model, the cart drives the COG motion during walking motion. In this case, the cart motion is treated as a servo control system, obtaining its motion from future reference states of the ZMP. The gait generation method proposed has many layers like Global motion, local motion, motion patterns generation, inverse kinematics and inverse dynamics and finally off-line correction. When the input in the gait generation method is the global goal (that is the final configuration of the robot in walking environment), and the output is the joint patterns and ZMP reference patterns. Otherwise, the “Acyclic gait” method is proposed. This method deals with the whole body humanoid robot dynamic step motion from any generic posture to another one when the input is the initial and goal robot states (that is the initial and goal joint angles) and the output is the joint and ZMP reference patterns. Successful simulation and actual results have been obtained with the Rh- 1 humanoid robot developed in the Robotics lab (Universidad Carlos III de Madrid, Spain) and the innovative motion called “Acyclic gait” implemented in the HRP-2 humanoid robot platform (developed by the AIST and Kawada Industries Inc., Japan). Furthermore, the results, contributions and future works will be discussed

A New Approach To Inverse Kinematic Solutions Of Serial Robot Arms Based On Quaterninons In The Screw Theory Framework

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2009Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 2009Screw teori, üç boyutlu uzayda dönme ve öteleme hareketlerinin birleşimi ile oluşan, genel hareket, hız, kuvvet ve torkların ifade edilmesini sağlayan bir yöntemdir. Genel olarak screw hareketi bir doğru etrafında dönme ve yine aynı doğru boyunca öteleme hareketlerinin bir birleşimidir. Katı cisimlerin tüm hareketleri bu yaklaşımla ifade edilebilir. Genel olarak üç boyutlu uzayda screw hareketi bir doğru ve bir oran (pitch) kullanılarak ifade edilir. (Burada kullanılan oran (pitch), dönme başına meydana gelen öteleme miktarıdır). Genel screw hareketi toplamda dört eleman kullanılarak tanımlanabilir. Bunlardan üç tanesi dönme ve ötelemenin meydana geldiği doğruyu, bir tanesi de doğru etrafında meydana gelen dönme miktarını ifade etmek için kullanılır. Katı cisimlerin hareketinde kullanılan en geleneksel yöntem Euler açılarıdır. Euler açıları bir katı cismin hareketini 6 eleman kullanarak ifade eder. Bunlardan üç tanesi kartezyen koordinatlarda öteleme hareketinin ifadesinde kullanılırken, diğer üç tanesi de bu koordinat sistemlerinde meydana gelen dönmelerin ifadesinde kullanılır. Screw teorinin robot kinematiğinde çeşitli uygulamaları vardır. Diğer yöntemlere kıyasla screw teorinin robot kinematiğinde şu üstünlükleri vardır; yalnız iki koordinat sistemiyle kinematik analiz yapılır, geometrik olarak çok anlaşılırdır ve ters kinematik çözümlemede tekil nokta probleminden etkilenmez. Bu nedenlerden dolayı screw teorinin robot kinematiğinde çok önemli bir yeri vardır. En genel anlamda bu tezin amaçlarını iki temel başlık altında toplayabiliriz. Bunlardan birincisi seri robotların ters kinematiğinde tekil nokta problemlerinden etkilenmeden çözümlerin elde edilmesidir. Bunun için önerilen yöntemler screw teori tabanlı olarak seçilmiştir. İkinci temel amaç ise kinematik problemin etkin bir cebir kullanılarak ifade edilmesidir. Bunun içinde önerilen yöntemlerde kuaterniyon cebiri kullanılmıştır. Kuaterniyonlar rankı dört olan hiper-kompleks sayılardır. Kuaterniyon cebirinde bu dört eleman kullanılarak bir doğru tanımlanır ve bu doğru etrafında herhangi bir dönme temsil edilebilir. Fakat genel katı cisim hareketi tek bir kuaterniyon ile ifade edilemez. Bunun için ya iki kuaterniyon (bunlardan bir tanesi “birim kuaternion” dönmeyi ifade etmede, diğeri ötelemeyi ifade etmede kullanılır) ya da dual kuaterniyonlar kullanılmalıdır. Dual operatörler screw hareketi ifade etmede kullanılabilecek en iyi operatörlerdir. Aynı zamanda dual operatörlerin içinde de dual kuaterniyon operatörü screw hareketin temsilinde kullanılabilecek en verimli ve en az parametreli dual operatördür. Bu tezde seri robot kollarının ters kinematik çözümlerine yönelik screw teori tabanlı yöntemler incelenmiştir. Bunlardan ilki ekponensiyel haritalama yöntemidir. Bu yöntemde screw teori ve matris cebiri kullanılır. Bu nedenle tekil nokta problemi olmamasına karşın denklemler çok fazla parametre ile ifade edilmiştir. Bu durumu ortadan kaldırmaya yönelik iki farklı ters kinematik çözümü önerilmiştir. Bunlardan birincisi birim kuaterniyon (dönme operatörü) ve bir kuaterniyon (öteleme oerpatörü) kullanılarak elde edilmiştir. İkinci çözüm ise dual kuaterniyonlar kullanılarak elde edilmiştir. Bu üç yöntem ve robot kinematiğinde en çok kullanılan yöntem olan D-H yöntemi tekil nokta problemleri, hesaplama verimi, dizayn zorluğu ve çözüm doğruluğu açısından karşılaştırılmışlardır. Simulasyon çalışmaları Matlab ortamında geçekleştirilmiştir. Animasyon uygulamaları ise Matlabın sanal gerçeklik araç kutusu kullanılarak gerçekleştirilmiştir (VRML). Simulasyon denemelerinde Staubli TXL60 seri robotunun tek ve kooperatif çalışma örnekleri yapılmıştır.Screw theory is a way to express displacements, velocities, forces and torques in three dimensional space combining both rotational and translational parts. Any motion along a screw can be decomposed into a rotation about an axis followed by a translation along that axis. Any general displacement of a rigid body can therefore be described by a screw. In general, a three dimensional motion can be defined using a screw with a given direction and pitch. Four parameters are required to fully define a screw motion, the 3 components of a direction vector and the angle rotated about that line. In contrast, the traditional method of characterizing 3-D motion using Euler Angles requires 6 parameters, 3 rotation angles and a 3x1 translation vector. Several application of screw theory has been introduced in robot kinematic. Compared with other methods, screws theory method just establish two coordinates, its geometrical meaning is obvious and it avoids singularities due to the use of the local coordinates. Therefore, screw theory has regained importance and has become an important method in robot kinematic. The major intents of this thesis are to formulize inverse kinematic problem in a compact closed form and to avoid singularity problem. Non-singular inverse kinematic solutions are obtained by using screw theory. Quaternion algebra is used to formulize kinematic problem in a compact closed form. Quaternions are hyper-complex numbers of rank 4, constituting a four dimensional vector space over the field of real numbers. Any rotation can be represented by unit-quaternion and also any screw motion can be defined by unit dual-quaternion. Screw motion can also be defined by using two quaternions however dual operators are the best way to describe screw motion and also the dual-quaternion is the most compact and efficient dual operator to express screw displacement. In this thesis, three inverse kinematic solution methods of 6-DOF serial robot manipulator, which are based on screw theory is presented. The first one is exponential mapping method. This method uses matrices as a screw operator. There are 16 parameters to describe screw motion in matrix operators while just 6 parameters are needed. Thus, however this method is singularity avoding, it is not compact closed. And also two new formulations of the inverse kinematic solution of the 6-DOF serial robot manipulator are proposed by using quaternion algebra. In these two new formulation methods, one of them uses quaternions as a screw operator which combines a unit quaternion plus pure quaternion and the other one uses dual-quaternions as a screw operator. These three methods and also the D-H convantion, which is the most common method in robot kinematic are compared with respect to singularity, computation efficiency, design complexity and accuracy. Simulation results are obtained by using Matlab and animation applications are obtained by using the virtual reality toolbox of MATLAB (VRML). Simulation experiments are made for single and cooperative working of Staubli TXL60 serial robot arm.Yüksek LisansM.Sc

Kinematics of continuum robots with constant curvature bending and extension capabilities

Continuum robots are becoming increasingly popular due to the capabilities they offer, especially when operating in cluttered environments, where their dexterity, maneuverability, and compliance represent a significant advantage. The subset of continuum robots that also belong to the soft robots category has seen rapid development in recent years, showing great promise. However, despite the significant attention received by these devices, various aspects of their kinematics remain unresolved, limiting their adoption and obscuring their potential. In this paper, the kinematics of continuum robots with the ability to bend and extend are studied, and analytical, closed-form solutions to both the direct and inverse kinematics are presented. The results obtained expose the redundancies of these devices, which are subsequently explored. The solution to the inverse kinematics derived here is shown to provide an analytical, closed-form expression describing the curve associated with these redundancies, which is also presented and analyzed. A condition on the reachable end-effector poses for robots with six actuation degrees-of-freedom (DOFs) is then distilled. The kinematics of robot layouts with over six actuation DOFs are subsequently considered. Finally, simulated results of the inverse kinematics are provided, verifying the study

Image Guided Robots for Urology

This dissertation addresses the development of medical image-guided robots and their applications in urology. Image-guided robots integrate medical image information with robotic precision to assist the planning and execution of the image-guided interventions. Robots guided by two different image modalities, ultrasound and MR image, were developed. Ultrasound image-guided robots manipulate an ultrasound probe and a needle-guide that are calibrated with respect to the robot for image-guided targeting. A method for calibration was developed and verified through the image-guided targeting experiments. Robotic manipulation of the calibrated probe allows acquisition of image slices at precise location, which can be combined to generate a 3D ultrasound image. Software for 3D ultrasound image acquisition, processing, and segmentation was developed as a part of the image-guided robot system. The feasibility of several image-guided intervention procedures using the ultrasound image-guided robot system was tested. The robot was used in a clinical trial of intraoperative transrectal ultrasound (TRUS) guided prostatectomy. The accuracy of TRUS-guided prostate biopsy using the robot was evaluated in a comparative study versus the classic human operation of the probe. Robot controlled palpation and image processing methods were developed for ultrasound elastography imaging of the prostate. An ultrasound to CT image-fusion method using the robot as a common reference was developed for percutaneous access of the kidney. MRI-guided robots were developed for transrectal and transperineal prostate biopsy. Extensive in-vitro tests were performed to ensure MRI compatibility and image-guided accuracy of the robots. The transrectal robot was evaluated in an animal study and the transperineal robot is undergoing a clinical trial. The collection of methods and algorithms presented in this dissertation can contribute to the development of image-guided robots that may provide less invasive and more precise interventions in urology, interventional radiology, and other fields

Image-Guided Robot-Assisted Needle Intervention Devices and Methods to Improve Targeting Accuracy

This dissertation addresses the development of medical devices, image-guided robots, and their application in needle-based interventions, as well as methods to improve accuracy and safety in clinical procedures. Needle access is an essential component of minimally invasive diagnostic and therapeutic procedures. Image-guiding devices are often required to help physicians handle the needle based on the images. Integrating robotic accuracy and precision with digital medical imaging has the potential to improve the clinical outcomes. The dissertation presents two robotic devices for interventions under Magnetic Resonance Imaging (MRI) respectively Computed Tomography (CT) – Ultrasound(US) cross modality guidance. The MRI robot is a MR Safe Remote Center of Motion (RCM) robot for direct image-guided needle interventions such as brain surgery. The dissertation also presents the integration of the robot with an intraoperative MRI scanner, and preclinical tests for deep brain needle access. The CT-Ultrasound guidance uses a robotic manipulator to handle an US probe within a CT scanner. The dissertation presents methods related to the co-registration of multi-image spaces with an intermediary frame, experiments for needle targeting. The dissertation also presents method on using optical tracking measurements specifically for medical robots. The method was derived to test the robots presented above. With advanced image-guidance, such as the robotic approaches, needle targeting accuracy may still be deteriorated by errors related to needle defections. Methods and associated devices for needle steering on the straight path are presented. These are a robotic approach that uses real-time ultrasound guidance to steer the needle; Modeling and testing of a method to markedly reduce targeting errors with bevel-point needles; Dynamic design, manufacturing, and testing of a novel core biopsy needle with straighter path, power assistance, reduced noise, and safer operation. Overall, the dissertation presents several developments that contribute to the field of medical devices, image-guided robots, and needle interventions. These include robot testing methods that can be used by other researchers, needle steering methods that can be used directly by physicians or for robotic devices, as well as several methods to improve the accuracy in image-guided interventions. Collectively, these contribute to the field and may have a significant clinical impact

Climbing and Walking Robots

Nowadays robotics is one of the most dynamic fields of scientific researches. The shift of robotics researches from manufacturing to services applications is clear. During the last decades interest in studying climbing and walking robots has been increased. This increasing interest has been in many areas that most important ones of them are: mechanics, electronics, medical engineering, cybernetics, controls, and computers. Today’s climbing and walking robots are a combination of manipulative, perceptive, communicative, and cognitive abilities and they are capable of performing many tasks in industrial and non- industrial environments. Surveillance, planetary exploration, emergence rescue operations, reconnaissance, petrochemical applications, construction, entertainment, personal services, intervention in severe environments, transportation, medical and etc are some applications from a very diverse application fields of climbing and walking robots. By great progress in this area of robotics it is anticipated that next generation climbing and walking robots will enhance lives and will change the way the human works, thinks and makes decisions. This book presents the state of the art achievments, recent developments, applications and future challenges of climbing and walking robots. These are presented in 24 chapters by authors throughtot the world The book serves as a reference especially for the researchers who are interested in mobile robots. It also is useful for industrial engineers and graduate students in advanced study

Human pose estimation from video and inertial sensors

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