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The objective of this thesis is to analyze the kinematics of a mobile parallel robot with contribution that pertain to the singularity analysis, the optimization of geometric parameters and the optimal control to avoid singularities when navigating across singular geometric configurations. The analysis of the workspace and singularities is performed in a prescribed reference workspace regions using discretization method. Serial and parallel singularities are analytically analyzed and all possible singular configurations are presented. Kinematic conditioning index is used to determine the robot’s proximity to a singular configuration. A method for the determination of a continuous and singularity-free workspace is detailed. The geometric parameters of the system are optimized in various types of pipe-like structures with respect to a suitable singularity index, in order to avoid singularities during the navigation across elbows. The optimization problem is formulated with an objective to maximize the reachable workspace and minimize the singularities. The objective function is also subjected to constraints such as collision avoidance, singularity avoidance, workspace continuity and contact constraints imposed between the boundaries and the wheels of the robot. A parametric variation method is used as a technique to optimize the design parameters. The optimal design parameters found are normalized with respect to the width of the pipe-like structures and therefore the results are generalized to be used in the development phase of the robot. An optimal control to generate singularity-free trajectories when the robotic device has to cross a geometric singularity in a sharp 90◦ elbow is proposed. Such geometric singularity inherently leads to singularities in the Jacobian of the system, and therefore a modified device with augmented number of degrees of freedom is introduced to be able to generate non-singular trajectories.

Design of linear actuator for parallel kinematic structure is described in this master´s thesis. The parallel kinematic structure is described in the first part. Open kinematics structure and close kinematics structure are compared. Their benefits and disadvantages are also mentioned. Construction of some parallel robots is illustrated. Linear actuators of different company are described. Mechanical parameters and construction of linear actuator are compared. Design of linear actuator is described in practical part of master´s thesis. A few variation of linear actuator are introduced. Individual variants are evaluated by Multicriteria Decisional Analysis and a final conception is selected. Final conception of linear actuator is elaborated. Reasons for selection of every part of linear actuator are given and basic mechanical calculation design part is made. FEA analysis of the structural part of linear actuator is made. Design of linear actuator is evaluated in the final part.

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[ES] Los robots paralelos (PR por sus siglas en inglés) son mecanismos donde el efector final está unido a la base, mediante al menos dos cadenas cinemáticas abiertas. Los PRs ofrecen una gran capacidad de carga y alta precisión, lo que los hace adecuados para diversas aplicaciones, entre ellas la interacción persona-robot. Sin embargo, en las proximidades de una singularidad Tipo II (singularidad dentro del espacio de trabajo), un PR pierde el control sobre los movimientos del efector final. La pérdida de control representa un riesgo importante para los usuarios, especialmente en rehabilitación robótica. En las últimas décadas, los PR se han popularizado en la rehabilitación de miembros inferiores debido al aumento del número de personas que viven con limitaciones físicas. Así, esta tesis trata sobre la detección y evitación de singularidades de Tipo II para asegurar total control de un PR no redundante para la rehabilitación y diagnóstico de rodilla, denominado 3UPS+RPU. En la literatura, existen varios índices para detectar y medir la cercanía a una singularidad basados en métodos analíticos y geométricos. Sin embargo, algunos de estos índices carecen de significado físico y son incapaces de identificar los actuadores responsables de la pérdida de control. Esta tesis aporta dos novedosos índices para detectar y medir la proximidad a una singularidad de Tipo II, capaces de identificar el par de actuadores responsables de la singularidad. Los dos índices son los ángulos entre los componentes lineal (T_i,j) y angular (O_i,j) de dos Twist Screw de Salida (OTS por sus siglas en inglés) normalizados i,j. Una singularidad Tipo II es detectada cuando T_i,j = O_i,j = 0 y su proximidad se mide mediante los mínimos ángulos T_i,j (minT) y O_i,j (minO) para los casos plano y espacial, respectivamente. La eficacia de los índices T_i,j y O_i,j se evalúa de forma teórica y experimental en un robot 3UPS+RPU y un mecanismo de cinco barras. Además, se propone un procedimiento experimental para el adecuado establecimiento del límite de cercanía a una singularidad de Tipo II mediante la aproximación progresiva del PR a una singularidad y la medición de la última posición controlable. Posteriormente, se desarrollan dos nuevos algoritmos deterministas para liberar y evitar una singularidad de Tipo II basados en minT y minO para PR no redundantes. minT y minO se utilizan para identificar los dos actuadores a mover para liberar o evitar el PR de una singularidad. Ambos algoritmos requieren una medición precisa de la pose alcanzada por el efector final. El algoritmo para liberar un PR de una configuración singular se aplica con éxito en un controlador híbrido basado en visión artificial para el PR 3UPS+RPU. El controlador utiliza un sistema de fotogrametría para medir la pose del robot debido a la degeneración del modelo cinemático en las proximidades de una singularidad. El algoritmo de evasión de singularidades Tipo II se aplica a la planificación offline y online de trayectorias no singulares para un mecanismo de cinco barras y el PR 3UPS+RPU. Estas aplicaciones verifican el bajo coste computacional y la mínima desviación introducida en la trayectoria original por los nuevos algoritmos. La implementación directa de un controlador de fuerza/posición en el PR 3UPS+RPU es insegura porque el paciente podría llevar involuntariamente al PR a una singularidad. Por lo tanto, esta tesis concluye presentando un novedoso controlador de fuerza/posición complementado con el algoritmo de evasión de singularidades de Tipo II. El nuevo controlador se evalúa durante rehabilitación activa de una pierna de maniquí y una pierna humana no lesionada. Los resultados muestran que el nuevo controlador combinado mantiene el PR 3UPS+RPU lejos de configuraciones singulares con una desviación mínima de la trayectoria original. Por lo tanto, esta tesis habilita el 3UPS+RPU PR para la rehabilitación segura de miembros inferiores lesionados. / [CAT] Els robots paral·lels (PR per les seues sigles en anglés) són mecanismes on l'efector final està unit a la base, mitjançant almenys dues cadenes cinemàtiques obertes. Els PRs ofereixen una gran capacitat de càrrega i alta precisió, la qual cosa els fa adequats per a diverses aplicacions, entre elles la interacció persona-robot. No obstant això, en les proximitats d'una singularitat Tipus II (singularitat dins de l'espai de treball), un PR perd el control sobre els moviments de l'efector final. La pèrdua de control representa un risc important per als usuaris, especialment en rehabilitació robòtica. En les últimes dècades, els PR s'han popularitzat en la rehabilitació de membres inferiors a causa de l'augment del nombre de persones que viuen amb limitacions físiques. Així, aquesta tesi tracta sobre la detecció i evació de singularitats de Tipus II per a assegurar total control d'un PR no redundant per a la rehabilitació i diagnòstic de genoll, denominat 3UPS+RPU. En la literatura, existeixen diversos índexs per a detectar i mesurar la proximitat a una singularitat basats en mètodes analítics i geomètrics. No obstant això, alguns d'aquests índexs manquen de significat físic i són incapaços d'identificar els actuadors responsables de la pèrdua de control. Aquesta tesi aporta dos nous índexs per a detectar i mesurar la proximitat a una singularitat de Tipus II, capaços d'identificar el parell d'actuadors responsables de la singularitat. Els dos índexs són els angles entre els components lineal (T_i,j) i angular (O_i,j) de dues Twist Screw d'Eixida (OTS per les seues sigles en engonals) normalitzats i,j. Una singularitat Tipus II és detectada quan T_i,j = O_i,j = 0 i la seua proximitat es mesura mitjançant els minimos angles T_i,j (minT) i O_i,j (minO) per als casos pla i espacial, respectivament. L'eficàcia dels índexs T_i,j i O_i,j es evalua de manera teòrica i experimental en un robot 3UPS+RPU i un mecanisme de cinc barres. A més, es proposa un procediment experimental per a l'adequat establiment del límit de proximitat a una singularitat de Tipus II mitjançant l'aproximació progressiva del PR a una singularitat i el mesurament de l'última posició controlable. Posteriorment, es desenvolupen dos nous algorismes deterministes per a alliberar i evadir una singularitat de Tipus II basats en minT i minO per a PR no redundants. minT i minO s'utilitzen per a identificar els dos actuadors a moure per a alliberar o evadir el PR d'una singularitat. Aquests algorismes requereixen un mesurament precís de la posa aconseguida per l'efector final. L'algorisme per a alliberar un PR d'una configuració singular s'aplica amb èxit en un controlador híbrid basat en visió artificial per al PR 3UPS+RPU. El controlador utilitza un sistema de fotogrametria per a mesurar la posa del robot a causa de la degeneració del model cinemàtic en les proximitats d'una singularitat. L'algorisme d'evació de singularitats Tipus II s'aplica a la planificació offline i en línia de trajectòries no singulars per a un mecanisme de cinc barres i el PR 3UPS+RPU. Aquestes aplicacions verifiquen el baix cost computacional i la mínima desviació introduïda en la trajectòria original pels nous algorismes. La implementació directa d'un controlador de força/posició en el PR 3UPS+RPU és insegura perquè el pacient podria portar involuntàriament al PR a una singularitat. Per tant, aquesta tesi conclou presentant un nou controlador de força/posició complementat amb l'algorisme d'evació de singularitats de Tipus II. El nou controlador s'avalua durant la rehabilitació activa d'una cama de maniquí i una cama humana no lesionada. Els resultats mostren que el nou controlador combinat manté el PR 3UPS+RPU lluny de configuracions singulars amb una desviació mínima de la trajectòria original. Per tant, aquesta tesi habilita el 3UPS+RPU PR per a la rehabilitació segura dels membres inferiors lesionats. / [EN] Parallel Robots (PR)s are mechanisms where the end-effector is linked to the base by at least two open kinematics chains. The PRs offer a high payload and high accuracy, making them suitable for various applications, including human robot interaction. However, in proximity to a Type II singularity (singularity within the workspace), a PR loses control over the movements of the end-effector. The loss of control represents a major risk for users, especially in robotic rehabilitation. In the last decades, PRs have become popular in lower limb rehabilitation because of the increment in the number of people living with physical limitations. Thus, this thesis is about the detection and avoidance of Type II singularities to ensure complete control of a non-redundant PR for knee rehabilitation and diagnosis named 3UPS+RPU. In the literature, several indices exist to detect and measure the closeness to a singular configuration based on analytical and geometrical methods. However, some of these indices have no physical meaning, and they are unable to identify the actuators responsible for the loss of control. This thesis contributes two novel indices to detect and measure the proximity to a Type II singularity capable of identifying the pair of actuators responsible for the singularity. The two indices are the angles between the linear (T_i,j) and the angular (O_i,j) components of two i,j normalised Output Twist Screws (OTSs). A Type II singularity is detected when the angles T_i,j = O_i,j = 0 and its closeness is measured by the minimum T_i,j (minT) and minimum O_i,j (minO) for planar and spatial cases, respectively. The effectiveness of the indices T_i,j and O_i,j is evaluated from a theoretical and experimental perspective in a 3UPS+RPU and a five bars mechanism. Moreover, an experimental procedure is proposed for setting a proper limit of closeness to a Type II singularity by the progressive approach of the PR to singular configuration and measuring the last controllable pose. Subsequently, two novel deterministic algorithms for releasing and avoiding Type II singularities based on minT and minO are developed for non-redundant PRs. The minT and minO are used to identify the two actuators to move for release or prevent the PR from the singularity. Both algorithms require an accurate measuring of the pose reached by the end-effector. The algorithm to release a PR from a singular configuration is successfully applied in a vision-based hybrid controller for the 3UPS+RPU PR. The controller uses a photogrammetry system to measure the pose of the robot due to the degeneration of the kinematic model in the vicinity of a singularity. The Type II singularity avoidance algorithm is applied to offline and online free-singularity trajectory planning for a five-bar mechanism and the 3UPS+RPU PR. These applications verify the low computation cost and the minimum deviation introduced in the original trajectory for both novel algorithms. The direct implementation of a force/position controller in the 3UPS+RPU PR is unsafe because the patient could unintentionally drive the PR to a Type II singularity. Therefore, this thesis concludes by presenting a novel force/position controller complemented with the Type II singularity avoidance algorithm. The complemented controller is evaluated during patient-active exercises in a mannequin leg and an uninjured human limb. The results show that the novel combined controller keeps the 3UPS+RPU PR far from singular configurations with a minimum deviation on the original trajectory. Hence, this thesis enables the 3UPS+RPU PR for the safe rehabilitation of injured lower limbs. / Pulloquinga Zapata, JL. (2023). A New Index for Detecting and Avoiding Type II Singularities for the Control of Non-Redundant Parallel Robots [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/194271

Cable-actuated manipulators (or 'cable robots') constitute a relatively new classification of robots which use motors, located at fixed remote locations, to manipulate an end-effector by extending or retracting cables. These manipulators possess a number of unique properties which make them proficient with tasks involving high payloads, large workspaces, and dangerous or contaminated environments. However, a number of challenges exist which have limited the mainstream emergence of cable robots. This thesis addresses two of the most important of these issues-- workspace analysis and disturbance compensation. Workspace issues are particularly important, as many large-scale applications require the end-effector to operate in regions of a particular shape, and to exert certain minimum forces throughout those regions. The 'Force-Feasible Workspace' represents the set of end-effector positions, for a given robot design, for which the robot can exert a set of required forces on its environment. This can be considered as the robot's 'usable' workspace, and an analysis of this workspace shape for point-mass cable robots is therefore presented to facilitate optimal cable robot design. Numerical simulation results are also presented to validate the analytical results, and to aid visualization of certain complex workspace shapes. Some cable robot applications may require mounting motors to moving bases (i.e. mobile robots) or other surfaces which are subject to disturbances (i.e. helicopters or crane arms). Such disturbances can propagate to the end-effector and cause undesired motion, so the rejection of motor mount disturbances is also of interest. This thesis presents a strategy for measuring these disturbances and compensating for them. General approaches and implementation issues are explored qualitatively with a simple one-degree-of-freedom prototype (including a strategy for mitigating accelerometer drift), and quantitative simulation results are presented as a proof of concept.

At the beginning of this master’s thesis the definition of types of robots using parallel kinematics are presented, its possibilities of usage and current prototypes are described. The second chapter focuses on the proposal of robot construction and sizing electric and non-electric components of robot hardware. Derivation of direct and inverse transform mechanisms with creating flowcharts of their algorithms are stated in the two following chapters. The state machine controlled from user interface is then programmed based on these flowcharts. At the end of the work, cable-driven robot positioning accuracy is evaluated and platform workspace, together with motion and electric parameters, are measured.