Error Modelling and Experimental Validation of a Planar 3-PPR Parallel Manipulator with Joint Clearances

International audienceThis paper deals with the error modelling and analysis of a 3-\underline{P}PR planar parallel manipulator with joint clearances. The kinematics and the Cartesian workspace of the manipulator are analyzed. An error model is established with considerations of both configuration errors and joint clearances. Using this model, the upper bounds and distributions of the pose errors for this manipulator are established. The results are compared with experimental measurements and show the effectiveness of the error prediction model

A New Index for Detecting and Avoiding Type II Singularities for the Control of Non-Redundant Parallel Robots

[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/10251/19427

Minimal Representation for the Control of Gough-Stewart Platforms via Leg Observation Considering a Hidden Robot Model

International audienceThis paper presents new insights about the sensor-based control of Gough-Stewart (GS) platforms. Previous works have shown that it was possible to control the GS platform by observing its legs directions instead of using the encoders values or the measurement of the platform pose. It was demonstrated that observing only three legs directions was enough for the control but no physical explanations were given. Moreover, sometimes, the GS platform was not converging to the desired pose and the reasons of these divergences were not disclosed. This paper aims at answering to this two opened problems. It is shown that observing three leg directions involves controlling the displacement of a hidden robot whose models differs from those of the usual GS platform. This robot has assembly modes and singular configurations different from those of the GS platform. This involves that the legs to observe should be chosen carefully in order to avoid inaccuracy problems. In this sense, the accuracy analysis of the new robot is performed to show the importance of the leg selection. All these results are validated on a GS platform simulator created using ADAMS/Controls and interfaced with Matlab/Simulink

A comprehensive survey of the analytical, numerical and experimental methodologies for dynamics of multibody mechanical systems with clearance or imperfect joints

"Available online 19 December 2017"A comprehensive survey of the literature of the most relevant analytical, numerical, and experimental approaches for the kinematic and dynamic analyses of multibody mechanical systems with clearance joints is presented in this review. Both dry and lubricated clearance joints are addressed here, and an effort is made to include a large number of research works in this particular field, which have been published since the 1960′s. First, the most frequently utilized methods for modeling planar and spatial multibody mechanical systems with clearance joints are analyzed, and compared. Other important phenomena commonly associated with clearance joint models, such as wear, non-smooth behavior, optimization and control, chaos, and uncertainty and links’ flexibility, are then discussed. The main assumptions procedures and conclusions for the different methodologies are also examined and compared. Finally, future developments and new applications of clearance joint modeling and analysis are highlighted.This research was supported in part by the China 111 Project (B16003) and the National Natural Science Foundation of China under Grants 11290151, 11472042 and 11221202. The work was also supported by the Portuguese Foundation for Science and Technology with the reference project UID/EEA/04436/2013, by FEDER funds through the COMPETE 2020 – Programa Operacional Competitividade e Internacionalização (POCI) with the reference project POCI-01-0145-FEDER-006941.info:eu-repo/semantics/publishedVersio

Tolerance analysis by static analogy on 2D assemblies with fits and fasteners

In tolerance analysis, the effect of clearance fits is especially difficult to estimate because the mating parts are not necessarily in actual contact and can take an infinite number of relative positions. The treatment of these situations is allowed in most of the available methods, possibly introducing additional elements in the dimension chains with appropriate statistical assumptions. The paper provides a similar extension for the static analogy, a previously proposed method that converts the tolerance analysis problem into an equivalent problem of force analysis. The procedure represents each fit, possibly between patterns of features (e.g., fasteners and holes), with a proper constraint in the equivalent static model. The ability of the constraint to transmit forces and torques is determined according to the types and directions of misalignments allowed by the joint clearance. With simple rules, this avoids complications in the static model, which must include only the constraint between parts rather than the geometric details of the mating features. The extended method, currently limited to 2D dimension chains, is demonstrated on examples involving both dimensional and geometric tolerances. The comparison with existing methods shows the correctness of the proposed procedure. The simplicity of the workflow confirms the possibility, already demonstrated for the static analogy, of avoiding numerical simulations or even the use of computer-based tools

Modelling, Control and Performance Evaluation of a Single-Axis Compliant Nano-Positioning System

This thesis presents the results from a preliminary activity devoted to the implementation of high-performance controller for a single axis compliant nano-positioning system. Preliminarily, this work discusses the mechanical design of the system, its peculiar features, and presents a system transfer function. After a detailed description of the design, the thesis discusses both theoretical and practical aspects of three control techniques used and the experimental results obtaine

Incorporation of the influences of kinematics parameters and joints tilting for the calibration of serial robotic manipulators

Serial robotic manipulators are calibrated to improve and restore their accuracy and repeatability. Kinematics parameters calibration of a robot reduces difference between the model of a robot in the controller and its actual mechanism to improve accuracy. Kinematics parameter’s error identification in the standard kinematics calibration has been configuration independent which does not consider the influence of kinematics parameter on robot tool pose accuracy for a given configuration. This research analyses the configuration dependent influences of kinematics parameters error on pose accuracy of a robot. Based on the effect of kinematics parameters, errors in the kinematics parameters are identified. Another issue is that current kinematics calibration models do not incorporate the joints tilting as a result of joint clearance, backlash, and flexibility, which is critical to the accuracy of serial robotic manipulators, and therefore compromises a pose accuracy. To address this issue which has not been carefully considered in the literature, this research suggested an approach to model configuration dependent joint tilting and presents a novel approach to encapsulate them in the calibration of serial robotic manipulators. The joint tilting along with the kinematics errors are identified and compensated in the kinematics model of the robot. Both conventional and proposed calibration approach are tested experimentally, and the calibration results are investigated to demonstrate the effectiveness of this research. Finally, the improvement in the trajectory tracking accuracy of the robot has been validated with the help of proposed low-cost measurement set-up.Thesis (M.Phil.) (Research by Publication) -- University of Adelaide, School of Mechanical Engineering , 201

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

Design of novel generation of rigid revolute, cardan and ball joints

The thesis is focused on the design and fabrication of different joints as part of a team member of three master’s students to design a parallel robot in the fishery. The general approach of how to design a parallel robot is presented. Then, the design and fabrication of a fully articulated snow crab as a model is given in order to use as a test model for the parallel robot. A new design of the revolute joint with a novel concept is presented in this work. The revolute joint with a conical shape uses two sleeves between the joint parts which are coated with Molybdenum Disulfide (MoS₂). The role of MoS₂ is to lubricate the inner parts of the revolute joint. A method for choosing the taper angle is presented based on the application. The authors fabricated the proposed new design at the machine shop of Memorial University and the joint proved to have successful functionality. Afterwards, the design and fabrication of the fork revolute joint, cardan joint (universal joint) and ball joint based on the design of the revolute joint is represented. Overall, the design of different joint types in this thesis is usable not only in the parallel robot but also in many mechanisms and applications