A Hybrid Strategy of Differential Evolution and Modified Particle Swarm Optimization for Numerical Solution of a Parallel Manipulator

This paper presents a hybrid strategy combined with a differential evolution (DE) algorithm and a modified particle swarm optimization (PSO), denominated as DEMPSO, to solve the nonlinear model of the forward kinematics. The proposed DEMPSO takes the best advantage of the convergence rate of MPSO and the global optimization of DE. A comparison study between the DEMPSO and the other optimization algorithms such as the DE algorithm, PSO algorithm, and MPSO algorithm is performed to obtain the numerical solution of the forward kinematics of a 3-RPS parallel manipulator. The forward kinematic model of the 3-RPS parallel manipulator has been developed and it is essentially a nonlinear algebraic equation which is dependent on the structure of the mechanism. A constraint equation based on the assembly relationship is utilized to express the position and orientation of the manipulator. Five configurations with different positions and orientations are used as an example to illustrate the effectiveness of the proposed DEMPSO for solving the kinematic problem of parallel manipulators. And the comparison study results of DEMPSO and the other optimization algorithms also show that DEMPSO can provide a better performance regarding the convergence rate and global searching properties

Modeling parallel robot kinematics for 3T2R and 3T3R tasks using reciprocal sets of Euler angles

Industrial manipulators and parallel robots are often used for tasks, such as drilling or milling, that require three translational, but only two rotational degrees of freedom ("3T2R"). While kinematic models for specific mechanisms for these tasks exist, a general kinematic model for parallel robots is still missing. This paper presents the definition of the rotational component of kinematic constraints equations for parallel robots based on two reciprocal sets of Euler angles for the end-effector orientation and the orientation residual. The method allows completely removing the redundant coordinate in 3T2R tasks and to solve the inverse kinematics for general serial and parallel robots with the gradient descent algorithm. The functional redundancy of robots with full mobility is exploited using nullspace projection

Novel Design and Analysis of Parallel Robotic Mechanisms

A parallel manipulator has several limbs that connect and actuate an end effector from the base. The design of parallel manipulators usually follows the process of prescribed task, design evaluation, and optimization. This dissertation focuses on interference-free designs of dynamically balanced manipulators and deployable manipulators of various degrees of freedom (DOFs). 1) Dynamic balancing is an approach to reduce shaking loads in motion by including balancing components. The shaking loads could cause noise and vibration. The balancing components may cause link interference and take more actuation energy. The 2-DOF (2-RR)R or 3-DOF (2-RR)R planar manipulator, and 3-DOF 3-RRS spatial manipulator are designed interference-free and with structural adaptive features. The structural adaptions and motion planning are discussed for energy minimization. A balanced 3-DOF (2-RR)R and a balanced 3-DOF 3-RRS could be combined for balanced 6-DOF motion. 2) Deployable feature in design allows a structure to be folded. The research in deployable parallel structures of non-configurable platform is rare. This feature is demanded, for example the outdoor solar tracking stand has non-configurable platform and may need to lie-flat on floor at stormy weathers to protect the structure. The 3-DOF 3-PRS and 3-DOF 3-RPS are re-designed to have deployable feature. The 6-DOF 3-[(2-RR)UU] and 5-DOF PRPU/2-[(2-RR)UU] are designed for deployable feature in higher DOFs. Several novel methods are developed for rapid workspace evaluation, link interference detection and stiffness evaluation. The above robotic manipulators could be grouped as a robotic system that operates in a green way and works harmoniously with nature

Kinematics and Robot Design II (KaRD2019) and III (KaRD2020)

This volume collects papers published in two Special Issues “Kinematics and Robot Design II, KaRD2019” (https://www.mdpi.com/journal/robotics/special_issues/KRD2019) and “Kinematics and Robot Design III, KaRD2020” (https://www.mdpi.com/journal/robotics/special_issues/KaRD2020), which are the second and third issues of the KaRD Special Issue series hosted by the open access journal robotics.The KaRD series is an open environment where researchers present their works and discuss all topics focused on the many aspects that involve kinematics in the design of robotic/automatic systems. It aims at being an established reference for researchers in the field as other serial international conferences/publications are. Even though the KaRD series publishes one Special Issue per year, all the received papers are peer-reviewed as soon as they are submitted and, if accepted, they are immediately published in MDPI Robotics. Kinematics is so intimately related to the design of robotic/automatic systems that the admitted topics of the KaRD series practically cover all the subjects normally present in well-established international conferences on “mechanisms and robotics”.KaRD2019 together with KaRD2020 received 22 papers and, after the peer-review process, accepted only 17 papers. The accepted papers cover problems related to theoretical/computational kinematics, to biomedical engineering and to other design/applicative aspects

Multi-objective particle swarm optimization for the structural design of concentric tube continuum robots for medical applications

Concentric tube robots belong to the class of continuum robotic systems whose morphology is described by continuous tangent curvature vectors. They are composed of multiple, interacting tubes nested inside one another and are characterized by their inherent flexibility. Concentric tube continuum robots equipped with tools at their distal end have high potential in minimally invasive surgery. Their morphology enables them to reach sites within the body that are inaccessible with commercial tools or that require large incisions. Further, they can be deployed through a tight lumen or follow a nonlinear path. Fundamental research has been the focus during the last years bringing them closer to the operating room. However, there remain challenges that require attention. The structural synthesis of concentric tube continuum robots is one of these challenges, as these types of robots are characterized by their large parameter space. On the one hand, this is advantageous, as they can be deployed in different patients, anatomies, or medical applications. On the other hand, the composition of the tubes and their design is not a straightforward task but one that requires intensive knowledge of anatomy and structural behavior. Prior to the utilization of such robots, the composition of tubes (i.e. the selection of design parameters and application-specific constraints) must be solved to determine a robotic design that is specifically targeted towards an application or patient. Kinematic models that describe the change in morphology and complex motion increase the complexity of this synthesis, as their mathematical description is highly nonlinear. Thus, the state of the art is concerned with the structural design of these types of robots and proposes optimization algorithms to solve for a composition of tubes for a specific patient case or application. However, existing approaches do not consider the overall parameter space, cannot handle the nonlinearity of the model, or multiple objectives that describe most medical applications and tasks. This work aims to solve these fundamental challenges by solving the parameter optimization problem by utilizing a multi-objective optimization algorithm. The main concern of this thesis is the general methodology to solve for patient- and application-specific design of concentric tube continuum robots and presents key parameters, objectives, and constraints. The proposed optimization method is based on evolutionary concepts that can handle multiple objectives, where the set of parameters is represented by a decision vector that can be of variable dimension in multidimensional space. Global optimization algorithms specifically target the constrained search space of concentric tube continuum robots and nonlinear optimization enables to handle the highly nonlinear elasticity modeling. The proposed methodology is then evaluated based on three examples that include cooperative task deployment of two robotic arms, structural stiffness optimization under the consideration of workspace constraints and external forces, and laser-induced thermal therapy in the brain using a concentric tube continuum robot. In summary, the main contributions are 1) the development of an optimization methodology that describes the key parameters, objectives, and constraints of the parameter optimization problem of concentric tube continuum robots, 2) the selection of an appropriate optimization algorithm that can handle the multidimensional search space and diversity of the optimization problem with multiple objectives, and 3) the evaluation of the proposed optimization methodology and structural synthesis based on three real applications

Contribuições para a enumeração e para a análise de mecanismos e manipuladores paralelos

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia Mecânica, Florianópolis, 2010A fase de projeto conceitual demecanismos emanipuladores paralelos, i.e. estruturas cinematicas, destina-se ao desenvolvimento da concepçao da cadeia cinematica. As etapas fundamentais para o desenvolvimento da concepao da cadeia cinematica sao sintese e analise. A sintese corresponde à enumeraçao de concepcoes e a analise corresponde `a seleçao das concepçoes mais promissoras considerando os requisitos de projeto. O objetivo deste trabalho é aplicar ferramentas da teoria de grupos e teoria de grafos para a enumeraçao e para a analise de estruturas cinematicas. A enumeraçao sera desenvolvida de forma sistematica em tres niveis: enumeraçao de cadeias cinematicas, enumeraçao de mecanismos e enumeraçao de manipuladores paralelos. A aplicaçao de ferramentas da teoria de grafos e grupos permite desenvolver novos metodos para enumeraçao e, consequentemente, obter novos resultados. A analise sera simplificada considerando um novo metodo que avalia as simetrias das cadeias cinematicas. Uma cadeia cinematica é representada de forma univoca atraves de um grafo. A representaçao atraves do grafo permite a manipulaçao computacional do problema de enumeraçao de cadeias cinematicas. A aplicaçao de ferramentas integradas da teoria de grafos e teoria de grupos permite identificar as simetrias das cadeias cinematicas atraves do grupo de automorfismos do grafo e, assim, é possivel identificar quais são as possiveis escolhas de base para novos mecanismos e avaliar quais sao as possiveis escolhas de base e efetuador final para manipuladores paralelos. O primeiro nivel da sintese corresponde à enumeraçao de cadeias cinematicas com determinada mobilidade, numero de elos, numero de juntas que operam num determinado sistema de helicoides. O segundo nivel da sintese corresponde a enumeraçao de mecanismos. Um mecanismo é uma cadeia cinematica com um elo escolhido para ser a base. Assim, a enumeraçao de mecanismos consiste em determinar todas as possiveis escolhas de bases para uma determinada cadeia cinematica. O principal conceito empregado neste nivel é o de simetria de grafos não coloridos e orbitas do grupo de automorfismos. O terceiro nivel da sintese corresponde `a enumeraçao de manipuladores paralelos. Um manipulador paralelo é uma cadeia cinematica com um elo escolhido para ser a base e outro para ser o efetuador final. Em outras palavras, um manipulador paralelo é um mecanismo com um elo escolhido para ser o efetuador final. Assim, a enumeraçao de manipuladores paralelos consiste em determinar todas as possiveis escolhas de efetuador final para um determinado mecanismo. O principal conceito empregado neste nivel é a simetria de grafos coloridos e orbitas do grupo de automorfismos de grafos coloridos. Na etapa de analise das concepcoes enumeradas serao abordadas propriedades bem estabelecidas na literatura: mobilidade, variedade, conectividade, grau de controle, redundancia e simetria. Mobilidade e variedade sao propriedades globais das estruturas cinematicas. Conectividade, grau de controle e redundancia sao propriedades locais, i.e. entre dois elos da estrutura cinematica e sao dadas por matrizes n×n, onde n é o número de elos da cadeia. A simetria pode ser considerada uma propriedade global e/ou local da estrutura cinem´atica. A aplicaçao de ferramentas integradas da teoria de grafos e teoria de grupos permite demonstrar que as propriedades locais sao invariantes pela acao do grupo de automorfismos do grafo, i.e. elas sao propriedades simetricas. Desta forma, a representaçao matricial é reduzida de n×n para o×n, onde o é o numero de orbitas do grupo de automorfismos do grafo aassociado à estrutura cinematica. Essa abordagem permite simplificar a analise de estruturas cinematicas apenas considerando as simetrias das cadeia associadas

Haptische Mensch-Maschine-Schnittstelle für ein laparoskopisches Chirurgie-System

Für eine Vielzahl von Operationen im Bauchraum ist heute die Laparoskopie Stand der Technik, so z.B. die Cholezytektomie zur Entfernung der Gallenblase. Hierbei handelt es sich um ein minimalinvasives Verfahren bei dem der Zugang zum Operationsgebiet durch kleinste Schnitte in der Bauchdecke des Patienten erfolgt. Bei der Operation kommen lange starre Instrumente zu Einsatz. Im Gegensatz zu einer offenen Operation haben die Hände des Chirurgen keinen direkten Zugang zum operierten Gewebe. Ein Abtasten des Gewebes ist nicht möglich, der haptische Sinn zur Diagnose und Navigation im Operationsgebiet steht dem Operateur folglich nicht zur Verfügung. Diese Einschränkung erhöht die Komplexität laparoskopischer Eingriffe erheblich. Auch die Beweglichkeit im Operationsfeld ist stark eingeschränkt. Eine technische Antwort auf diese Einschränkungen sind haptische Telemanipulationssysteme. Sie bestehen aus einer angetriebenen Instrumentenspitze sowie einem haptischen Bedienelement, das die Kontaktkräfte zwischen Instrumentenspitze und Gewebe an den Bediener meldet. Hierzu erfasst ein Kraftsensor an der Instrumentenspitze die auftretenden Kontaktkräfte. Antriebe im Bedienelement erzeugen daraus eine Kraftinformation und leiten sie über einen Mechanismus an den Bediener weiter. Die vorliegende Arbeit befasst sich mit der Erweiterung der Entwurfsmethodik für haptische Bedienelemente und der Realisierung eines neuartigen Bedienelements. Basis ist eine Analyse des chirurgischen Szenarios in der minimalinvasiven Leberchirurgie. Daraus leitet sich das Entwurfsziel eines haptischen Bedienelementes mit drei kartesischen Freiheitsgraden ab. Auf Grund ihrer guten dynamischen Eigenschaften sind besonders parallelkinematische Mechanismen zur Übertragung haptischer Informationen geeignet. Sie zeichnen sich durch eine große Struktursteifigkeit und geringe bewegte Massen aus. Ihr kinematisches Übertragungsverhalten ist hingegen meist komplex. Aus der Analyse der kinematischen Bedingungen für ein rein kartesisches Ausgangsverhalten ergibt sich ein möglicher Lösungsraum geeigneter Topologien. Alle bestehen aus drei Beinen mit je 5 Gelenkfreiheitsgraden, einer Basis-Plattform und einer Tool-Centre-Point-Plattform zur Ausgabe der haptischen Information. Für den vorliegenden Fall ist eine RUU- bzw. DELTA-Struktur geeignet. Diese Struktur übersetzt drei Antriebsmomente in eine rein kartesische Ausgabe. Basierend auf der Analyse der kinematischen Entwurfsziele für haptische Mechanismen erfolgte eine Auslegung des Mechanismus im Hinblick auf isotropes, d.h. richtungsunabhängiges Übertragungsverhalten. Charakteristisches Maß ist die globale Konditionszahl. Entscheidend für die Qualität der haptischen Rückmeldung ist das dynamische Übertragungsverhalten haptischer Bedienelemente. Für eindimensionale Systeme ist in der Literatur zur Modellierung der Zwei-Tor Ansatz basierend auf der elektromechanischen Netzwerktheorie eingeführt. Im Rahmen dieser Arbeit erfolgt erstmalig die Erweiterung auch für den mehrdimensionalen Fall. Damit ist es möglich, auch die dynamischen Eigenschaften mehrdimensionaler Mechanismen mit dem Zwei-Tor Ansatz abzubilden. Dies erlaubt Anwendung des Entwurfsverfahrens der "Transparenz" für mehrdimensionale Systeme. Zur Analyse der mechanischen Eigenschaften des operierten Gewebes entstehen zwei Messplätze für die Frequenzbereiche f = 10...10^4 Hz (taktile Wahrnehmung) und f=DC...50 Hz (kinästhetische Wahrnehmung). Sie ermöglichen die messtechnische Charakterisierung der mechanischen Impedanz und die Ableitung mechanischer Schaltungen. Damit lässt sich die Impedanz des Gewebes rechnerisch im Gütekriterium der Transparenz zur Bewertung eines haptischen Telemanipulationssystems einsetzen. Die Realisierung eines haptischen Bedienelements erfolgt für ein neuartiges, tragbares Teleoperationssystem. Das Bedienkonzept ist an Hand eines ergonomischen Funktionsmusters im Tierversuch evaluiert. Kernkomponente ist ein haptisches Joystick mit drei kartesischen Freiheitsgraden durch einen RUU-Mechanismus. Der Arbeitsraum beträgt 743,5 cm³. Das Bedienelement ist mit einer Impedanz-gesteuerten Systemstruktur entworfen und feinwerktechnisch umgesetzt. Als Antriebe kommen drei EC-Motoren zum Einsatz. Mit einem maximalen Moment von 0,2 Nm erzeugen sie eine haptische Rückmeldung von 5N in 82% des Volumens im Arbeitsraum. Die zum Betrieb erforderlichen kinematischen Berechnungen sind auf einem Steuerrechner implementiert. Zusammen mit der Leistungselektronik ist dieser in einem mobilen Rack integriert. Der Nachweis der Funktionsfähigkeit erfolgt an einem experimentellen Telemanipulationssystem im Laborbetrieb

Flexible robotic device for spinal surgery

Surgical robots have proliferated in recent years, with well-established benefits including: reduced patient trauma, shortened hospitalisation, and improved diagnostic accuracy and therapeutic outcome. Despite these benefits, many challenges in their development remain, including improved instrument control and ergonomics caused by rigid instrumentation and its associated fulcrum effect. Consequently, it is still extremely challenging to utilise such devices in cases that involve complex anatomical pathways such as the spinal column. The focus of this thesis is the development of a flexible robotic surgical cutting device capable of manoeuvring around the spinal column. The target application of the flexible surgical tool is the removal of cancerous tumours surrounding the spinal column, which cannot be excised completely using the straight surgical tools in use today; anterior and posterior sections of the spine must be accessible for complete tissue removal. A parallel robot platform with six degrees of freedom (6 DoFs) has been designed and fabricated to direct a flexible cutting tool to produce the necessary range of movements to reach anterior and posterior sections of the spinal column. A flexible water jet cutting system and a flexible mechanical drill, which may be assembled interchangeably with the flexible probe, have been developed and successfully tested experimentally. A model predicting the depth of cut by the water jet was developed and experimentally validated. A flexion probe that is able to guide the surgical cutting device around the spinal column has been fabricated and tested with human lumber model. Modelling and simulations show the capacity for the flexible surgical system to enable entering the posterior side of the human lumber model and bend around the vertebral body to reach the anterior side of the spinal column. A computer simulation with a full Graphical User Interface (GUI) was created and used to validate the system of inverse kinematic equations for the robot platform. The constraint controller and the inverse kinematics relations are both incorporated into the overall positional control structure of the robot, and have successfully established a haptic feedback controller for the 6 DoFs surgical probe, and effectively tested in vitro on spinal mock surgery. The flexible surgical system approached the surgery from the posterior side of the human lumber model and bend around the vertebral body to reach the anterior side of the spinal column. The flexible surgical robot removed 82% of mock cancerous tissue compared to 16% of tissue removed by the rigid tool.Open Acces