Numerical computation and avoidance of manipulator singularities

This thesis develops general solutions to two open problems of robot kinematics: the exhaustive computation of the singularity set of a manipulator, and the synthesis of singularity-free paths between given configurations. Obtaining proper solutions to these problems is crucial, because singularities generally pose problems to the normal operation of a robot and, thus, they should be taken into account before the actual construction of a prototype. The ability to compute the whole singularity set also provides rich information on the global motion capabilities of a manipulator. The projections onto the task and joint spaces delimit the working regions in such spaces, may inform on the various assembly modes of the manipulator, and highlight areas where control or dexterity losses can arise, among other anomalous behaviour. These projections also supply a fair view of the feasible movements of the system, but do not reveal all possible singularity-free motions. Automatic motion planners allowing to circumvent problematic singularities should thus be devised to assist the design and programming stages of a manipulator. The key role played by singular configurations has been thoroughly known for several years, but existing methods for singularity computation or avoidance still concentrate on specific classes of manipulators. The absence of methods able to tackle these problems on a sufficiently large class of manipulators is problematic because it hinders the analysis of more complex manipulators or the development of new robot topologies. A main reason for this absence has been the lack of computational tools suitable to the underlying mathematics that such problems conceal. However, recent advances in the field of numerical methods for polynomial system solving now permit to confront these issues with a very general intention in mind. The purpose of this thesis is to take advantage of this progress and to propose general robust methods for the computation and avoidance of singularities on non-redundant manipulators of arbitrary architecture. Overall, the work seeks to contribute to the general understanding on how the motions of complex multibody systems can be predicted, planned, or controlled in an efficient and reliable way.Aquesta tesi desenvolupa solucions generals per dos problemes oberts de la cinemàtica de robots: el càlcul exhaustiu del conjunt singular d'un manipulador, i la síntesi de camins lliures de singularitats entre configuracions donades. Obtenir solucions adequades per aquests problemes és crucial, ja que les singularitats plantegen problemes al funcionament normal del robot i, per tant, haurien de ser completament identificades abans de la construcció d'un prototipus. La habilitat de computar tot el conjunt singular també proporciona informació rica sobre les capacitats globals de moviment d'un manipulador. Les projeccions cap a l'espai de tasques o d'articulacions delimiten les regions de treball en aquests espais, poden informar sobre les diferents maneres de muntar el manipulador, i remarquen les àrees on poden sorgir pèrdues de control o destresa, entre d'altres comportaments anòmals. Aquestes projeccions també proporcionen una imatge fidel dels moviments factibles del sistema, però no revelen tots els possibles moviments lliures de singularitats. Planificadors de moviment automàtics que permetin evitar les singularitats problemàtiques haurien de ser ideats per tal d'assistir les etapes de disseny i programació d'un manipulador. El paper clau que juguen les configuracions singulars ha estat àmpliament conegut durant anys, però els mètodes existents pel càlcul o evitació de singularitats encara es concentren en classes específiques de manipuladors. L'absència de mètodes capaços de tractar aquests problemes en una classe suficientment gran de manipuladors és problemàtica, ja que dificulta l'anàlisi de manipuladors més complexes o el desenvolupament de noves topologies de robots. Una raó principal d'aquesta absència ha estat la manca d'eines computacionals adequades a les matemàtiques subjacents que aquests problemes amaguen. No obstant, avenços recents en el camp de mètodes numèrics per la solució de sistemes polinòmics permeten ara enfrontar-se a aquests temes amb una intenció molt general en ment. El propòsit d'aquesta tesi és aprofitar aquest progrés i proposar mètodes robustos i generals pel càlcul i evitació de singularitats per manipuladors no redundants d'arquitectura arbitrària. En global, el treball busca contribuir a la comprensió general sobre com els moviments de sistemes multicos complexos es poden predir, planificar o controlar d'una manera eficient i segur

An Overview of Kinematic and Calibration Models Using Internal/External Sensors or Constraints to Improve the Behavior of Spatial Parallel Mechanisms

This paper presents an overview of the literature on kinematic and calibration models of parallel mechanisms, the influence of sensors in the mechanism accuracy and parallel mechanisms used as sensors. The most relevant classifications to obtain and solve kinematic models and to identify geometric and non-geometric parameters in the calibration of parallel robots are discussed, examining the advantages and disadvantages of each method, presenting new trends and identifying unsolved problems. This overview tries to answer and show the solutions developed by the most up-to-date research to some of the most frequent questions that appear in the modelling of a parallel mechanism, such as how to measure, the number of sensors and necessary configurations, the type and influence of errors or the number of necessary parameters

Towards a full higher order AD-based continuation and bifurcation framework

International audienceSome of the theoretical aspects of continuation and bifurcation methods devoted to the solution for nonlinear parametric systems are presented in a higher-order automatic differentiation (HOAD) framework. Besides benefits in terms of generality and ease of use, HOAD is used to assess fold and simple bifurcations points. In particular, the formation of a geometric series in successive Taylor coefficients allows for the implementation of an efficient detection and branch switching method at simple bifurcation points. Some comparisons with the Auto and MatCont continuation software are proposed. Strengths are then exemplified on a classical case study in structural mechanics

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

An Overview of Formulae for the Higher-Order Kinematics of Lower-Pair Chains with Applications in Robotics and Mechanism Theory

The motions of mechanisms can be described in terms of screw coordinates by means of an exponential mapping. The product of exponentials (POE) describes the configuration of a chain of bodies connected by lower pair joints. The kinematics is thus given in terms of joint screws. The POE serves to express loop constraints for mechanisms as well as the forward kinematics of serial manipulators. Besides the compact formulations, the POE gives rise to purely algebraic relations for derivatives wrt. joint variables. It is known that the partial derivatives of the instantaneous joint screws (columns of the geometric Jacobian) are determined by Lie brackets the joint screws. Lesser-known is that derivative of arbitrary order can be compactly expressed by Lie brackets. This has significance for higher-order forward/inverse kinematics and dynamics of robots and multibody systems. Various relations were reported but are scattered in the literature and insufficiently recognized. This paper aims to provide a comprehensive overview of the relevant relations. Its original contributions are closed form and recursive relations for higher-order derivatives and Taylor expansions of various kinematic relations. Their application to kinematic control and dynamics of robotic manipulators and multibody systems is discussed

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

Kinodynamic planning and control of closed-chain robotic systems

Aplicat embargament des de la data de defensa fins el dia 1/6/2022This work proposes a methodology for kinodynamic planning and trajectory control in robots with closed kinematic chains. The ability to plan trajectories is key in a robotic system, as it provides a means to convert high-level task commands¾like “move to that location'', or “throw the object at such a speed''¾into low-level controls to be followed by the actuators. In contrast to purely kinematic planners, which only generate collision-free paths in configuration space, kinodynamic planners compute state-space trajectories that also account for the dynamics and force limits of the robot. In doing so, the resulting motions are more realistic and exploit gravity, inertia, and centripetal forces to the benefit of the task. Existing kinodynamic planners are fairly general and can deal with complex problems, but they require the state coordinates to be independent. Therefore, they are hard to apply to robots with loop-closure constraints whose state space is not globally parameterizable. These constraints define a nonlinear manifold on which the trajectories must be confined, and they appear in many systems, like parallel robots, cooperative arms manipulating an object, or systems that keep multiple contacts with the environment. In this work, we propose three steps to generate optimal trajectories for such systems. In a first step, we determine a trajectory that avoids the collisions with obstacles and satisfies all kinodynamic constraints of the robot, including loop-closure constraints, the equations of motion, or any limits on the velocities or on the motor and constraint forces. This is achieved with a sampling-based planner that constructs local charts of the state space numerically, and with an efficient steering method based on linear quadratic regulators. In a second step, the trajectory is optimized according to a cost function of interest. To this end we introduce two new collocation methods for trajectory optimization. While current methods easily violate the kinematic constraints, those we propose satisfy these constraints along the obtained trajectories. During the execution of a task, however, the trajectory may be affected by unforeseen disturbances or model errors. That is why, in a third step, we propose two trajectory control methods for closed-chain robots. The first method enjoys global stability, but it can only control trajectories that avoid forward singularities. The second method, in contrast, has local stability, but allows these singularities to be traversed robustly. The combination of these three steps expands the range of systems in which motion planning can be successfully applied.Aquest treball proposa una metodologia per a la planificació cinetodinàmica i el control de trajectòries en robots amb cadenes cinemàtiques tancades. La capacitat de planificar trajectòries és clau en un robot, ja que permet traduir instruccions d'alt nivell com ara ¿mou-te cap aquella posició'' o ¿llença l'objecte amb aquesta velocitat'' en senyals de referència que puguin ser seguits pels actuadors. En comparació amb els planificadors purament cinemàtics, que només generen camins lliures de col·lisions a l'espai de configuracions, els planificadors cinetodinàmics obtenen trajectòries a l'espai d'estats que són compatibles amb les restriccions dinàmiques i els límits de força del robot. Els moviments que en resulten són més realistes i aprofiten la gravetat, la inèrcia i les forces centrípetes en benefici de la tasca que es vol realitzar. Els planificadors cinetodinàmics actuals són força generals i poden resoldre problemes complexos, però assumeixen que les coordenades d'estat són independents. Per tant, no es poden aplicar a robots amb restriccions de clausura cinemàtica en els quals l'espai d'estats no admeti una parametrització global. Aquestes restriccions defineixen una varietat diferencial sobre la qual cal mantenir les trajectòries, i apareixen en sistemes com ara els robots paral·lels, els braços que manipulen objectes coordinadament o els sistemes amb extremitats en contacte amb l'entorn. En aquest treball, proposem tres passos per generar trajectòries òptimes per a aquests sistemes. En un primer pas, determinem una trajectòria que evita les col·lisions amb els obstacles i satisfà totes les restriccions cinetodinàmiques, incloses les de clausura cinemàtica, les equacions del moviment o els límits en les velocitats i en les forces d'actuació o d'enllaç. Això s'aconsegueix mitjançant un planificador basat en mostratge aleatori que utilitza cartes locals construïdes numèricament, i amb un mètode eficient de navegació local basat en reguladors quadràtics lineals. En un segon pas, la trajectòria s'optimitza segons una funció de cost donada. A tal efecte, introduïm dos nous mètodes de col·locació per a l'optimització de trajectòries. Mentre els mètodes existents violen fàcilment les restriccions cinemàtiques, els que proposem satisfan aquestes restriccions al llarg de les trajectòries obtingudes. Durant l'execució de la tasca, tanmateix, la trajectòria pot veure's afectada per pertorbacions imprevistes o per errors deguts a incerteses en el model dinàmic. És per això que, en un tercer pas, proposem dos mètodes de control de trajectòries per robots amb cadenes tancades. El primer mètode gaudeix d'estabilitat global, però només permet controlar trajectòries que no travessin singularitats directes del robot. El segon mètode, en canvi, té estabilitat local, però permet travessar aquestes singularitats de manera robusta. La combinació d'aquests tres passos amplia el ventall de sistemes en els quals es pot aplicar amb èxit la planificació cinetodinàmica.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

Robotic Automation of Turning Machines in Fenceless Production: A Planning Toolset for Economic-based Selection Optimization between Collaborative and Classical Industrial Robots

Ursprünglich wurden Industrieroboter hauptsächlich hinter Schutzzäunen betrieben, um den Sicherheitsanforderungen gerecht zu werden. Mit der Flexibilisierung der Produktion wurden diese scharfen Trennbereiche zunehmend aufgeweicht und externe Sicherheitstechnik, wie Abstandssensoren, genutzt, um Industrieroboter schutzzaunlos zu betreiben. Ausgehend vom Gedanken dieser Koexistenz bzw. Kooperation wurde die Sicherheitssensorik in den Roboter integriert, um eine wirkliche Kollaboration zu ermöglichen. Diese sogenannten kollaborierenden Roboter, oder Cobots, eröffnen neue Applikationsfelder und füllen somit die bestehenden Automatisierungslücken. Doch welche Automatisierungsvariante ist aus wirtschaftlichen Gesichtspunkten die geeignetste? Bisherige Forschung untersucht zum Großteil isoliert eine der beiden Technologien, ohne dabei einen Systemvergleich hinsichtlich technologischer Spezifika und Wirtschaftlichkeit anzustellen. Daher widmet sich diese Dissertation einer Methodik zum wirtschaftlichen Vergleich von kollaborierenden Robotern und Industrierobotern in schutzzaunlosen Maschinenbeladungssystemen. Besonderer Fokus liegt dabei auf dem Herausarbeiten der technischen Faktoren, die die Wirtschaftlichkeit maßgeblich beeinflussen, um ein Systemverständnis der wirtschaftlichen Struktur beider Robotertechnologievarianten zu erhalten. Zur Untersuchung werden die Inhalte eines solchen Planungsvorhabens beschrieben, kategorisiert, systematisiert und modularisiert. Auf wirtschaftlicher Seite wird ein geeignetes Optimierungsmodell vorgestellt, während auf technischer Seite vor allem die Machbarkeit hinsichtlich Greifbarkeit, Layoutplanung, Robotergeschwindigkeiten und Zykluszeitbestimmung untersucht wird. Mit deduktiven, simulativen, empirischen und statistischen Methoden wird das Systemverhalten für die einzelnen Planungsinhalte analysiert, um die Gesamtwirtschaftlichkeit mit einem Minimum an Investment,- Produktions,- und Zykluszeitinformationen a priori vorhersagen zu können. Es wird gezeigt, dass durch einen Reverse Engineering Ansatz die notwendigen Planungsdaten, im Sinne von Layoutkomposition, Robotergeschwindigkeiten und Taktzeiten, mithilfe von Frontloading zu Planungsbeginn zur Verfügung gestellt werden können. Dabei dient der Kapitalwert als wirtschaftliche Bewertungsgrundlage, dessen Abhängigkeit vom Mensch-Roboter-Interaktionsgrad in einem Vorteilhaftigkeitsdiagramm für die einzelnen Technologiealternativen dargestellt werden kann. Wirtschaftlich fundierte Entscheidungen können somit auf quantitiativer Basis getroffen werden.:1. Introduction 25 1.1 Research Domain 25 1.2 Research Niche 26 1.3 Research Structure 28 2. State of the Art and Research 31 2.1 Turning Machines and Machine Tending 31 2.1.1 Tooling Machine Market Trends and Machine Tending Systems 31 2.1.2 Workpiece System 34 2.1.3 Machine System 36 2.1.4 Logistics System 39 2.1.5 Handling System 41 2.2 Robotics 43 2.2.1 Robot Installation Development and Application Fields 43 2.2.2 Fenceless Industrial and Collaborative Robots 48 2.2.3 Robot Grippers 55 2.3 Planning and Evaluation Methods 56 2.3.1 Planning of General and Manual Workstations 56 2.3.2 Cell Planning for Fully Automated and Hybrid Robot Systems 59 2.3.3 Robot Safety Planning 61 2.3.4 Economic Evaluation Methods 70 2.4 Synthesis - State of the Art and Research 71 3. Solution Approach 77 3.1 Need for Research and General Solution Approach 77 3.2 Use Case Delineation and Planning Focus 80 3.3 Economic Module – Solution Approach 86 3.4 Gripper Feasibility Module – Solution Approach 89 3.5 Rough Layout Discretization Model – Solution Approach 94 3.6 Cycle Time Estimation Module – Solution Approach 97 3.7 Collaborative Speed Estimation Module – Solution Approach 103 3.7.1 General Approach 103 3.7.2 Case 1: Quasi-static Contact with Hand 107 3.7.3 Case 2: Transient Contact with Hand 109 3.7.4 Case 3: Transient Contact with Shoulder 111 3.8 Synthesis – Solution Approach 114 4. Module Development 117 4.1 Economic Module – Module Development 117 4.1.1 General Approach 117 4.1.2 Calculation Scheme for Manual Operation 117 4.1.3 Calculation Scheme for Collaborative Robots 118 4.1.4 Calculation Scheme for Industrial Robots 120 4.2 Gripper Feasibility Module – Module Development 121 4.3 Rough Layout Discretization Module – Module Development 122 4.3.1 General Approach 122 4.3.2 Two-Dimensional Layout Pattern 123 4.3.3 Three-Dimensional Layout Pattern 125 4.4 Cycle Time Estimation Module – Module Development 126 4.4.1 General Approach 126 4.4.2 Reachability Study 127 4.4.3 Simulation Results 128 4.5 Collaborative Speed Estimation Module – Module Development 135 4.5.1 General Approach 135 4.5.2 Case 1: Quasi-static Contact with Hand 135 4.5.3 Case 2: Transient Contact with Hand 143 4.5.4 Case 3: Transient Contact with Shoulder 145 4.6 Synthesis – Module Development 149 5. Practical Verification 155 5.1 Use Case Overview 155 5.2 Gripper Feasibility 155 5.3 Layout Discretization 156 5.4 Collaborative Speed Estimation 157 5.5 Cycle Time Estimation 158 5.6 Economic Evaluation 160 5.7 Synthesis – Practical Verification 161 6. Results and Conclusions 165 6.1 Scientific Findings and Results 165 6.2 Critical Appraisal and Outlook 173Initially, industrial robots were mainly operated behind safety fences to account for the safety requirements. With production flexibilization, these sharp separation areas have been increasingly softened by utilizing external safety devices, such as distance sensors, to operate industrial robots fenceless. Based on this idea of coexistence or cooperation, safety technology has been integrated into the robot to enable true collaboration. These collaborative robots, or cobots, open up new application fields and fill the existing automation gap. But which automation variant is most suitable from an economic perspective? Present research dealt primarily isolated with one technology without comparing these systems regarding technological and economic specifics. Therefore, this doctoral thesis pursues a methodology to economically compare collaborative and industrial robots in fenceless machine tending systems. A particular focus lies on distilling the technical factors that mainly influence the profitability to receive a system understanding of the economic structure of both robot technology variants. For examination, the contents of such a planning scheme are described, categorized, systematized, and modularized. A suitable optimization model is presented on the economic side, while the feasibility regarding gripping, layout planning, robot velocities, and cycle time determination is assessed on the technical side. With deductive, simulative, empirical, and statistical methods, the system behavior of the single planning entities is analyzed to predict the overall profitability a priori with a minimum of investment,- production,- and cycle time information. It is demonstrated that the necessary planning data, in terms of layout composition, robot velocities, and cycle times, can be frontloaded to the project’s beginning with a reverse engineering approach. The net present value serves as the target figure, whose dependency on the human-robot interaction grade can be illustrated in an advantageousness diagram for the individual technical alternatives. Consequently, sound economic decisions can be made on a quantitative basis.:1. Introduction 25 1.1 Research Domain 25 1.2 Research Niche 26 1.3 Research Structure 28 2. State of the Art and Research 31 2.1 Turning Machines and Machine Tending 31 2.1.1 Tooling Machine Market Trends and Machine Tending Systems 31 2.1.2 Workpiece System 34 2.1.3 Machine System 36 2.1.4 Logistics System 39 2.1.5 Handling System 41 2.2 Robotics 43 2.2.1 Robot Installation Development and Application Fields 43 2.2.2 Fenceless Industrial and Collaborative Robots 48 2.2.3 Robot Grippers 55 2.3 Planning and Evaluation Methods 56 2.3.1 Planning of General and Manual Workstations 56 2.3.2 Cell Planning for Fully Automated and Hybrid Robot Systems 59 2.3.3 Robot Safety Planning 61 2.3.4 Economic Evaluation Methods 70 2.4 Synthesis - State of the Art and Research 71 3. Solution Approach 77 3.1 Need for Research and General Solution Approach 77 3.2 Use Case Delineation and Planning Focus 80 3.3 Economic Module – Solution Approach 86 3.4 Gripper Feasibility Module – Solution Approach 89 3.5 Rough Layout Discretization Model – Solution Approach 94 3.6 Cycle Time Estimation Module – Solution Approach 97 3.7 Collaborative Speed Estimation Module – Solution Approach 103 3.7.1 General Approach 103 3.7.2 Case 1: Quasi-static Contact with Hand 107 3.7.3 Case 2: Transient Contact with Hand 109 3.7.4 Case 3: Transient Contact with Shoulder 111 3.8 Synthesis – Solution Approach 114 4. Module Development 117 4.1 Economic Module – Module Development 117 4.1.1 General Approach 117 4.1.2 Calculation Scheme for Manual Operation 117 4.1.3 Calculation Scheme for Collaborative Robots 118 4.1.4 Calculation Scheme for Industrial Robots 120 4.2 Gripper Feasibility Module – Module Development 121 4.3 Rough Layout Discretization Module – Module Development 122 4.3.1 General Approach 122 4.3.2 Two-Dimensional Layout Pattern 123 4.3.3 Three-Dimensional Layout Pattern 125 4.4 Cycle Time Estimation Module – Module Development 126 4.4.1 General Approach 126 4.4.2 Reachability Study 127 4.4.3 Simulation Results 128 4.5 Collaborative Speed Estimation Module – Module Development 135 4.5.1 General Approach 135 4.5.2 Case 1: Quasi-static Contact with Hand 135 4.5.3 Case 2: Transient Contact with Hand 143 4.5.4 Case 3: Transient Contact with Shoulder 145 4.6 Synthesis – Module Development 149 5. Practical Verification 155 5.1 Use Case Overview 155 5.2 Gripper Feasibility 155 5.3 Layout Discretization 156 5.4 Collaborative Speed Estimation 157 5.5 Cycle Time Estimation 158 5.6 Economic Evaluation 160 5.7 Synthesis – Practical Verification 161 6. Results and Conclusions 165 6.1 Scientific Findings and Results 165 6.2 Critical Appraisal and Outlook 17

Advanced Strategies for Robot Manipulators

Amongst the robotic systems, robot manipulators have proven themselves to be of increasing importance and are widely adopted to substitute for human in repetitive and/or hazardous tasks. Modern manipulators are designed complicatedly and need to do more precise, crucial and critical tasks. So, the simple traditional control methods cannot be efficient, and advanced control strategies with considering special constraints are needed to establish. In spite of the fact that groundbreaking researches have been carried out in this realm until now, there are still many novel aspects which have to be explored