Parallel Manipulators

In recent years, parallel kinematics mechanisms have attracted a lot of attention from the academic and industrial communities due to potential applications not only as robot manipulators but also as machine tools. Generally, the criteria used to compare the performance of traditional serial robots and parallel robots are the workspace, the ratio between the payload and the robot mass, accuracy, and dynamic behaviour. In addition to the reduced coupling effect between joints, parallel robots bring the benefits of much higher payload-robot mass ratios, superior accuracy and greater stiffness; qualities which lead to better dynamic performance. The main drawback with parallel robots is the relatively small workspace. A great deal of research on parallel robots has been carried out worldwide, and a large number of parallel mechanism systems have been built for various applications, such as remote handling, machine tools, medical robots, simulators, micro-robots, and humanoid robots. This book opens a window to exceptional research and development work on parallel mechanisms contributed by authors from around the world. Through this window the reader can get a good view of current parallel robot research and applications

Penyelesaian Kinematika Langsung Manipulator Paralel Bidang 3-RRR Secara Eksak Menggunakan Open Source Computer Algebra Software: SymPy

Penentuan jawab kinematika langsung manipulator paralel merupakan hal yang menarik untuk dikaji karena kompleksitas matematisnya. Artikel ini menyajikan penyelesaian eksak permasalahan kinematika langsung manipulator paralel bidang 3-RRR melalui pemanfaatan perangkat lunak aljabar komputer dengan kode terbuka: SymPy. Prosedur penyelesaian secara simbolik diimplementasikan ke dalam sebuah fungsi python melalui penggunaan pustaka SymPy secara ekstensif. Melalui fungsi ini akan dikalkulasi jawab kinematika langsung manipulator secara numerik untuk nilai konstanta kinematik dan besar sudut input pada sambungan aktif. Hasil pengujian untuk suatu dimensi konstanta kinematika manipulator ini menunjukkan bahwa terdapat dua akar-akar ril penyelesaian kinematika langsungya. Dua akar ril ini mengindikasikan bahwa manipulator memiliki dua modus rakitan kinematika langsung yang berbeda dengan modus rakitan untuk jawab kinematika invers

Position analysis based on multi-affine formulations

Aplicat embargament des de la data de defensa fins el 31/5/2022The position analysis problem is a fundamental issue that underlies many problems in Robotics such as the inverse kinematics of serial robots, the forward kinematics of parallel robots, the coordinated manipulation of objects, the generation of valid grasps, the constraint-based object positioning, the simultaneous localization and map building, and the analysis of complex deployable structures. It also arises in other fields, such as in computer aided design, when the location of objects in a design is given in terms of geometric constrains, or in the conformational analysis of biomolecules. The ubiquity of this problem, has motivated an intense quest for methods able of tackling it. Up to now, efficient algorithms for the general problem have remained elusive and they are only available for particular cases. Moreover, the complexity of the problem has typically led to methods difficult to be implemented. Position analysis can be decomposed into two equally important steps: obtaining a set of closure equations, and solving them. This thesis deals with both of them to obtain a general, simple, and yet efficient solution method that we call the trapezoid method. The first step is addressed relying on dual quaternions. Although it has not been properly highlighted in the past, the use of dual quaternions permits expressing the closure condition of a kinematic loop involving only lower pairs as a system of multi-affine equations. In this thesis, this property is leveraged to introduce an interval-based method specially tailored for solving multi-affine systems. The proposed method is objectively simpler (in the sense that it is easier to understand and to implement) than previous methods based on general techniques such as interval Newton methods, conversions to Bernstein basis, or linear relaxations. Moreover, it relies on two simple operations, namely, linear interpolations and projections on coordinate planes, which can be executed with a high performance. The result is a method that accurately and efficiently bounds the valid solutions of the problem at hand. To further improve the accuracy, we propose the use of redundant, multi affine equations that are derived from the minimal set of equations describing the problem. To improve the efficiency, we introduce a variable elimination methodology that preserves the multi-affinity of the system of equations. The generality and the performance of the proposed trapezoid method are extensively evaluated on different kind of mechanisms, including spherical mechanisms, generic 6R and 7R loops, over-constrained systems, and multi-loop mechanisms. The proposed method is, in all cases, significantly faster than state of the art alternatives.El problema de l'anàlisi de posició és un tema fonamental que subjau a molts problemes de la robòtica, com ara la cinemàtica inversa de robots sèrie, la cinemàtica directa de robots paral·lels, la manipulació coordinada d'objectes, la generació de prensions vàlides amb mans robòtiques, el posicionament d'objectes basat en restriccions, la localització i la creació de mapes de forma simultània, i l'anàlisi d'estructures desplegables complexes. També sorgeix en altres camps, com ara en el disseny assistit per ordinador, quan la ubicació dels objectes en un disseny es dóna en termes de restriccions geomètriques o en l'anàlisi conformacional de biomolècules. La omnipresència d'aquest problema ha motivat una intensa recerca de mètodes capaços d'afrontar-lo. Fins al moment, els algoritmes eficients per al problema general han estat esquius i només estan disponibles per a casos particulars. A més, la complexitat del problema normalment ha conduït a mètodes difícils d'implementar. L'anàlisi de posició es pot descompondre en dos passos igualment importants: l'obtenció d'un sistema d'equacions de tancament i la resolució d'aquest sistema. Aquesta tesi tracta de tots dos passos per tal d'obtenir un mètode de solució general, senzill i alhora eficient que anomenem el mètode del trapezoide. El primer pas s'aborda utilitzant quaternions duals. Tot i que no ha estat suficientment destacat en el passat, l'ús de quaternions duals permet expressar la condició de tancament d'un bucle cinemàtic que impliqui només parells inferiors com a un sistema d'equacions multi-afins. En aquesta tesi s'aprofita aquesta propietat per introduir un mètode especialment dissenyat per resoldre sistemes multi-afins. El mètode proposat és objectivament més senzill (en el sentit que és més fàcil d'entendre i d'implementar) que els mètodes anteriors que utilitzen tècniques generals com ara els mètodes de Newton basats en intervals, les conversions a la base de Bernstein o les relaxacions lineals. A més, el mètode es basa en dues operacions simples, a saber, les interpolacions lineals i les projeccions en plans de coordenades, que es poden executar de forma molt eficient. El resultat és un mètode que acota amb precisió i eficiència les solucions vàlides del problema. Per millorar encara més la precisió, proposem l'ús d'equacions multi-afins redundants derivades del conjunt mínim d'equacions que descriuen el problema. Per altra banda, per millorar l'eficiència, introduïm un metodologia d'eliminació de variables que preserva la multi-afinitat del sistema d'equacions. La generalitat i el rendiment del mètode del trapezoide s'avalua extensivament en diferents tipus de mecanismes, inclosos els mecanismes esfèrics, bucles 6R i 7R genèrics, sistemes sobre-restringits i mecanismes de múltiples bucles. El mètode proposat és, en tots els casos, significativament més ràpid que els mètodes alternatius descrits en la literatura fins al moment.Postprint (published version

Development of Alternative Methods for Robot Kinematics

The problem of finding mathematical tools to represent rigid body motions in space has long been on the agenda of physicists and mathematicians and is considered to be a well-researched and well-understood problem. Robotics, computer vision, graphics, and other engineering disciplines require concise and efficient means of representing and applying generalized coordinate transformations in three dimensions. Robotics requires systematic ways to represent the relative position or orientation of a manipulator rigid links and objects. However, with the advent of high-speed computers and their application to the generation of animated graphical images and control of robot manipulators, new interest arose in identifying compact and computationally efficient representations of spatial transformations. The traditional methods for representing forward kinematics of manipulators have been the homogeneous matrix in line with the D-H algorithm. In robotics, this matrix is used to describe one coordinate system with respect to another one. However for online operation and manipulation of the robotic manipulator in a flexible manner the computational time plays an important role. Although this method is used extensively in kinematic analysis but it is relatively neglected in practical robotic systems due to some complications in dealing with the problem of orientation representation. On the other hand, such matrices are highly redundant to represent six independent degrees of freedom. This redundancy can introduce numerical problems in calculations, wastes storage, and often increases the computational cost of algorithms. Keeping these drawbacks in mind, alternative methods are being sought by various researchers for representing the same and reducing the computational time to make the system fast responsive in a flexible environment. Researchers in robot kinematics tried alternative methods in order to represent rigid body transformations based on concepts introduced by mathematicians and physicists such as Euler angle or Epsilon algebra. In the present work alternative representations, using quaternion algebra and lie algebra are proposed, tried and compared

Inverse Kinematic Analysis of Robot Manipulators

An important part of industrial robot manipulators is to achieve desired position and orientation of end effector or tool so as to complete the pre-specified task. To achieve the above stated goal one should have the sound knowledge of inverse kinematic problem. The problem of getting inverse kinematic solution has been on the outline of various researchers and is deliberated as thorough researched and mature problem. There are many fields of applications of robot manipulators to execute the given tasks such as material handling, pick-n-place, planetary and undersea explorations, space manipulation, and hazardous field etc. Moreover, medical field robotics catches applications in rehabilitation and surgery that involve kinematic, dynamic and control operations. Therefore, industrial robot manipulators are required to have proper knowledge of its joint variables as well as understanding of kinematic parameters. The motion of the end effector or manipulator is controlled by their joint actuator and this produces the required motion in each joints. Therefore, the controller should always supply an accurate value of joint variables analogous to the end effector position. Even though industrial robots are in the advanced stage, some of the basic problems in kinematics are still unsolved and constitute an active focus for research. Among these unsolved problems, the direct kinematics problem for parallel mechanism and inverse kinematics for serial chains constitute a decent share of research domain. The forward kinematics of robot manipulator is simpler problem and it has unique or closed form solution. The forward kinematics can be given by the conversion of joint space to Cartesian space of the manipulator. On the other hand inverse kinematics can be determined by the conversion of Cartesian space to joint space. The inverse kinematic of the robot manipulator does not provide the closed form solution. Hence, industrial manipulator can achieve a desired task or end effector position in more than one configuration. Therefore, to achieve exact solution of the joint variables has been the main concern to the researchers. A brief introduction of industrial robot manipulators, evolution and classification is presented. The basic configurations of robot manipulator are demonstrated and their benefits and drawbacks are deliberated along with the applications. The difficulties to solve forward and inverse kinematics of robot manipulator are discussed and solution of inverse kinematic is introduced through conventional methods. In order to accomplish the desired objective of the work and attain the solution of inverse kinematic problem an efficient study of the existing tools and techniques has been done. A review of literature survey and various tools used to solve inverse kinematic problem on different aspects is discussed. The various approaches of inverse kinematic solution is categorized in four sections namely structural analysis of mechanism, conventional approaches, intelligence or soft computing approaches and optimization based approaches. A portion of important and more significant literatures are thoroughly discussed and brief investigation is made on conclusions and gaps with respect to the inverse kinematic solution of industrial robot manipulators. Based on the survey of tools and techniques used for the kinematic analysis the broad objective of the present research work is presented as; to carry out the kinematic analyses of different configurations of industrial robot manipulators. The mathematical modelling of selected robot manipulator using existing tools and techniques has to be made for the comparative study of proposed method. On the other hand, development of new algorithm and their mathematical modelling for the solution of inverse kinematic problem has to be made for the analysis of quality and efficiency of the obtained solutions. Therefore, the study of appropriate tools and techniques used for the solution of inverse kinematic problems and comparison with proposed method is considered. Moreover, recommendation of the appropriate method for the solution of inverse kinematic problem is presented in the work. Apart from the forward kinematic analysis, the inverse kinematic analysis is quite complex, due to its non-linear formulations and having multiple solutions. There is no unique solution for the inverse kinematics thus necessitating application of appropriate predictive models from the soft computing domain. Artificial neural network (ANN) can be gainfully used to yield the desired results. Therefore, in the present work several models of artificial neural network (ANN) are used for the solution of the inverse kinematic problem. This model of ANN does not rely on higher mathematical formulations and are adept to solve NP-hard, non-linear and higher degree of polynomial equations. Although intelligent approaches are not new in this field but some selected models of ANN and their hybridization has been presented for the comparative evaluation of inverse kinematic. The hybridization scheme of ANN and an investigation has been made on accuracies of adopted algorithms. On the other hand, any Optimization algorithms which are capable of solving various multimodal functions can be implemented to solve the inverse kinematic problem. To overcome the problem of conventional tool and intelligent based method the optimization based approach can be implemented. In general, the optimization based approaches are more stable and often converge to the global solution. The major problem of ANN based approaches are its slow convergence and often stuck in local optimum point. Therefore, in present work different optimization based approaches are considered. The formulation of the objective function and associated constrained are discussed thoroughly. The comparison of all adopted algorithms on the basis of number of solutions, mathematical operations and computational time has been presented. The thesis concludes the summary with contributions and scope of the future research work

Real-time Dynamic Simulation of Constrained Multibody Systems using Symbolic Computation

The main objective of this research is the development of a framework for the automatic generation of systems of kinematic and dynamic equations that are suitable for real-time applications. In particular, the efficient simulation of constrained multibody systems is addressed. When modelled with ideal joints, many mechanical systems of practical interest contain closed kinematic chains, or kinematic loops, and are most conveniently modelled using a set of generalized coordinates of cardinality exceeding the degrees-of-freedom of the system. Dependent generalized coordinates add nonlinear algebraic constraint equations to the ordinary differential equations of motion, thereby producing a set of differential-algebraic equations that may be difficult to solve in an efficient yet precise manner. Several methods have been proposed for simulating such systems in real time, including index reduction, model simplification, and constraint stabilization techniques. In this work, the equations of motion are formulated symbolically using linear graph theory. The embedding technique is applied to eliminate the Lagrange multipliers from the dynamic equations and obtain one ordinary differential equation for each independent acceleration. The theory of Gröbner bases is then used to triangularize the kinematic constraint equations, thereby producing recursively solvable systems for calculating the dependent generalized coordinates given values of the independent coordinates. For systems that can be fully triangularized, the kinematic constraints are always satisfied exactly and in a fixed amount of time. Where full triangularization is not possible, a block-triangular form can be obtained that still results in more efficient simulations than existing iterative and constraint stabilization techniques. The proposed approach is applied to the kinematic and dynamic simulation of several mechanical systems, including six-bar mechanisms, parallel robots, and two vehicle suspensions: a five-link and a double-wishbone. The efficient kinematic solution generated for the latter is used in the real-time simulation of a vehicle with double-wishbone suspensions on both axles, which is implemented in a hardware- and operator-in-the-loop driving simulator. The Gröbner basis approach is particularly suitable for situations requiring very efficient simulations of multibody systems whose parameters are constant, such as the plant models in model-predictive control strategies and the vehicle models in driving simulators

MUSME 2011 4 th International Symposium on Multibody Systems and Mechatronics

El libro de actas recoge las aportaciones de los autores a través de los correspondientes artículos a la Dinámica de Sistemas Multicuerpo y la Mecatrónica (Musme). Estas disciplinas se han convertido en una importante herramienta para diseñar máquinas, analizar prototipos virtuales y realizar análisis CAD sobre complejos sistemas mecánicos articulados multicuerpo. La dinámica de sistemas multicuerpo comprende un gran número de aspectos que incluyen la mecánica, dinámica estructural, matemáticas aplicadas, métodos de control, ciencia de los ordenadores y mecatrónica. Los artículos recogidos en el libro de actas están relacionados con alguno de los siguientes tópicos del congreso: Análisis y síntesis de mecanismos ; Diseño de algoritmos para sistemas mecatrónicos ; Procedimientos de simulación y resultados ; Prototipos y rendimiento ; Robots y micromáquinas ; Validaciones experimentales ; Teoría de simulación mecatrónica ; Sistemas mecatrónicos ; Control de sistemas mecatrónicosUniversitat Politècnica de València (2011). MUSME 2011 4 th International Symposium on Multibody Systems and Mechatronics. Editorial Universitat Politècnica de València. http://hdl.handle.net/10251/13224Archivo delegad

Advances in Robot Kinematics : Proceedings of the 15th international conference on Advances in Robot Kinematics

International audienceThe motion of mechanisms, kinematics, is one of the most fundamental aspect of robot design, analysis and control but is also relevant to other scientific domains such as biome- chanics, molecular biology, . . . . The series of books on Advances in Robot Kinematics (ARK) report the latest achievement in this field. ARK has a long history as the first book was published in 1991 and since then new issues have been published every 2 years. Each book is the follow-up of a single-track symposium in which the participants exchange their results and opinions in a meeting that bring together the best of world’s researchers and scientists together with young students. Since 1992 the ARK symposia have come under the patronage of the International Federation for the Promotion of Machine Science-IFToMM.This book is the 13th in the series and is the result of peer-review process intended to select the newest and most original achievements in this field. For the first time the articles of this symposium will be published in a green open-access archive to favor free dissemination of the results. However the book will also be o↵ered as a on-demand printed book.The papers proposed in this book show that robot kinematics is an exciting domain with an immense number of research challenges that go well beyond the field of robotics.The last symposium related with this book was organized by the French National Re- search Institute in Computer Science and Control Theory (INRIA) in Grasse, France

Grasp plannind under task-specific contact constraints

Several aspects have to be addressed before realizing the dream of a robotic hand-arm system with human-like capabilities, ranging from the consolidation of a proper mechatronic design, to the development of precise, lightweight sensors and actuators, to the efficient planning and control of the articular forces and motions required for interaction with the environment. This thesis provides solution algorithms for a main problem within the latter aspect, known as the {\em grasp planning} problem: Given a robotic system formed by a multifinger hand attached to an arm, and an object to be grasped, both with a known geometry and location in 3-space, determine how the hand-arm system should be moved without colliding with itself or with the environment, in order to firmly grasp the object in a suitable way. Central to our algorithms is the explicit consideration of a given set of hand-object contact constraints to be satisfied in the final grasp configuration, imposed by the particular manipulation task to be performed with the object. This is a distinguishing feature from other grasp planning algorithms given in the literature, where a means of ensuring precise hand-object contact locations in the resulting grasp is usually not provided. These conventional algorithms are fast, and nicely suited for planning grasps for pick-an-place operations with the object, but not for planning grasps required for a specific manipulation of the object, like those necessary for holding a pen, a pair of scissors, or a jeweler's screwdriver, for instance, when writing, cutting a paper, or turning a screw, respectively. To be able to generate such highly-selective grasps, we assume that a number of surface regions on the hand are to be placed in contact with a number of corresponding regions on the object, and enforce the fulfilment of such constraints on the obtained solutions from the very beginning, in addition to the usual constraints of grasp restrainability, manipulability and collision avoidance. The proposed algorithms can be applied to robotic hands of arbitrary structure, possibly considering compliance in the joints and the contacts if desired, and they can accommodate general patch-patch contact constraints, instead of more restrictive contact types occasionally considered in the literature. It is worth noting, also, that while common force-closure or manipulability indices are used to asses the quality of grasps, no particular assumption is made on the mathematical properties of the quality index to be used, so that any quality criterion can be accommodated in principle. The algorithms have been tested and validated on numerous situations involving real mechanical hands and typical objects, and find applications in classical or emerging contexts like service robotics, telemedicine, space exploration, prosthetics, manipulation in hazardous environments, or human-robot interaction in general