Dynamically Feasible Trajectories of Fully-Constrained Cable-Suspended Parallel Robots

Cable-Driven Parallel Robots employ multiple cables, whose lengths are controlled by winches, to move an end-effector (EE). In addition to the advantages of other parallel robots, such as low moving inertias and the potential for high dynamics, they also provide specific advantages, such as large workspaces and lower costs. Thus, over the last 30 years, they have been the object of academic research; also, they are being employed in industrial applications. The main issue with cable actuation is its unilaterality, as cables must remain in tension: if they become slack, there is a risk of losing control of the EE's pose. This complicates the control of cable-driven robots and is among the most studied topics in this field. Most previous works resort to extra cables or rigid elements pushing on the EE to guarantee that cables remain taut, but this complicates robot design. An alternative is to use the gravitational and inertial forces acting on the EE to keep cables in tension. This thesis shows that the robot's workspace can be greatly increased, by considering two model architectures. Moreover, practical limits to the feasibility of a motion, such as singularities of the kinematic chain and interference between cables, are considered. Even if a motion is feasible, there is no guarantee that it can be performed with an acceptable precision in the end-effector's pose, due to the inevitable errors in the positioning of the actuators and the elastic deflections of the structure. Therefore, a set of indexes are evaluated to measure the sensitivity of the end-effector's pose to actuation errors. Finally, the stiffness of one of the two architectures is modeled and indexes to measure the global compliance of the robot due to the elasticity of the cables are presented.I robot paralleli a cavi impiegano cavi, la cui lunghezza è controllata da argani, per muovere un elemento terminale o end-effector (EE). Oltre ai vantaggi degli altri robot paralleli, come basse inerzie in movimento e la possibilità di raggiungere velocità e accelerazioni elevate, possono anche fornire vantaggi specifici, come ampi spazi di lavoro e costi inferiori. Pertanto, negli ultimi 30 anni, questi robot sono stati oggetto di ricerche accademiche e stanno trovando applicazione anche in campo industriale. Il problema principale dell'azionamento mediante cavi è che è unilaterale, poiché i cavi possono essere tesi ma non compressi: quando diventano laschi, si rischia di perdere il controllo della posa dell'EE. Questo complica il controllo dei robot ed è uno dei temi più studiati nel settore. Gli studi compiuti sinora ricorrono prevalentemente a cavi addizionali o a elementi rigidi che spingono sull'EE per garantire che i cavi rimangano tesi, ma questo complica la progettazione dei robot. Un'alternativa è sfruttare le forze gravitazionali e inerziali che agiscono sull'EE per mantenere i cavi in tensione. Questa tesi dimostra che, in questo caso, lo spazio di lavoro del robot può essere notevolmente aumentato, applicando questo concetto a due architetture modello. Inoltre, vengono considerati i limiti imposti all'effettiva realizzabilità di un movimento, come le singolarità della catena cinematica e l'interferenza tra i cavi. Anche se un movimento è fattibile, non è garantito che si possa eseguire con precisione accettabile, a causa degli inevitabili errori di posizionamento degli attuatori e delle deformazioni elastiche della struttura. Si valutano quindi alcuni indici per misurare la sensibilità della posizione dell'elemento terminale agli errori di azionamento. Infine, è modellata la rigidezza di una delle due architetture proposte e sono presentati indici per misurare la cedevolezza globale del robot dovuta all'elasticità dei cavi

Modeling, Control and Estimation of Reconfigurable Cable Driven Parallel Robots

The motivation for this thesis was to develop a cable-driven parallel robot (CDPR) as part of a two-part robotic device for concrete 3D printing. This research addresses specific research questions in this domain, chiefly, to present advantages offered by the addition of kinematic redundancies to CDPRs. Due to the natural actuation redundancy present in a fully constrained CDPR, the addition of internal mobility offers complex challenges in modeling and control that are not often encountered in literature. This work presents a systematic analysis of modeling such kinematic redundancies through the application of reciprocal screw theory (RST) and Lie algebra while further introducing specific challenges and drawbacks presented by cable driven actuators. It further re-contextualizes well-known performance indices such as manipulability, wrench closure quality, and the available wrench set for application with reconfigurable CDPRs. The existence of both internal redundancy and static redundancy in the joint space offers a large subspace of valid solutions that can be condensed through the selection of appropriate objective priorities, constraints or cost functions. Traditional approaches to such redundancy resolution necessitate computationally expensive numerical optimization. The control of both kinematic and actuation redundancies requires cascaded control frameworks that cannot easily be applied towards real-time control. The selected cost functions for numerical optimization of rCDPRs can be globally (and sometimes locally) non-convex. In this work we present two applied examples of redundancy resolution control that are unique to rCDPRs. In the first example, we maximize the directional wrench ability at the end-effector while minimizing the joint torque requirement by utilizing the fitness of the available wrench set as a constraint over wrench feasibility. The second example focuses on directional stiffness maximization at the end-effector through a variable stiffness module (VSM) that partially decouples the tension and stiffness. The VSM introduces an additional degrees of freedom to the system in order to manipulate both reconfigurability and cable stiffness independently. The controllers in the above examples were designed with kinematic models, but most CDPRs are highly dynamic systems which can require challenging feedback control frameworks. An approach to real-time dynamic control was implemented in this thesis by incorporating a learning-based frameworks through deep reinforcement learning. Three approaches to rCDPR training were attempted utilizing model-free TD3 networks. Robustness and safety are critical features for robot development. One of the main causes of robot failure in CDPRs is due to cable breakage. This not only causes dangerous dynamic oscillations in the workspace, but also leads to total robot failure if the controllability (due to lack of cables) is lost. Fortunately, rCDPRs can be utilized towards failure tolerant control for task recovery. The kinematically redundant joints can be utilized to help recover the lost degrees of freedom due to cable failure. This work applies a Multi-Model Adaptive Estimation (MMAE) framework to enable online and automatic objective reprioritization and actuator retasking. The likelihood of cable failure(s) from the estimator informs the mixing of the control inputs from a bank of feedforward controllers. In traditional rigid body robots, safety procedures generally involve a standard emergency stop procedure such as actuator locking. Due to the flexibility of cable links, the dynamic oscillations of the end-effector due to cable failure must be actively dampened. This work incorporates a Linear Quadratic Regulator (LQR) based feedback stabilizer into the failure tolerant control framework that works to stabilize the non-linear system and dampen out these oscillations. This research contributes to a growing, but hitherto niche body of work in reconfigurable cable driven parallel manipulators. Some outcomes of the multiple engineering design, control and estimation challenges addressed in this research warrant further exploration and study that are beyond the scope of this thesis. This thesis concludes with a thorough discussion of the advantages and limitations of the presented work and avenues for further research that may be of interest to continuing scholars in the community

How to Expand the Workspace of Parallel Robots

In this chapter, methods for expanding the workspace of parallel robots are introduced. Firstly, methods for expanding the translational workspace of the parallel robot are discussed. The parallel robot has multiple solutions of the inverse and forward displacement analysis. By changing its configurations from one solution to another, the parallel robot can expand its translational workspace. However, conventional nonredundant parallel robot encounters singularity during the mode change. Singularity-free mode changes of the parallel robot by redundant actuation are introduced. Next, methods for expanding the rotational workspace of the parallel robot are shown. In order to achieve the large rotation, some mechanical gimmicks by gears, pulleys, and helical joints have been embedded in the moving part. A novel differential screw-nut mechanism for expanding the rotational workspace of the parallel robot is introduced

Redundant Unilaterally Actuated Kinematic Chains: Modeling and Analysis

Unilaterally Actuated Robots (UAR)s are a class of robots defined by an actuation that is constrained to a single sign. Cable robots, grasping, fixturing and tensegrity systems are certain applications of UARs. In recent years, there has been increasing interest in robotic and other mechanical systems actuated or constrained by cables. In such systems, an individual constraint is applied to a body of the mechanism in the form of a pure force which can change its magnitude but cannot reverse its direction. This uni-directional actuation complicates the design of cable-driven robots and can result in limited performance. Cable Driven Parallel Robot (CDPR)s are a class of parallel mechanisms where the actuating legs are replaced by cables. CDPRs benefit from the higher payload to weight ratio and increased rigidity. There is growing interest in the cable actuation of multibody systems. There are potential applications for such mechanisms where low moving inertia is required. Cable-driven serial kinematic chain (CDSKC) are mechanisms where the rigid links form a serial kinematic chain and the cables are arranged in a parallel configuration. CDSKC benefits from the dexterity of the serial mechanisms and the actuation advantages of cable-driven manipulators. Firstly, the kinematic modeling of CDSKC is presented, with a focus on different types of cable routings. A geometric approach based on convex cones is utilized to develop novel cable actuation schemes. The cable routing scheme and architecture have a significant effect on the performance of the robot resulting in a limited workspace and high cable forces required to perform a desired task. A novel cable routing scheme is proposed to reduce the number of actuating cables. The internal routing scheme is where, in addition to being externally routed, the cable can be re-routed internally within the link. This type of routing can be considered as the most generalized form of the multi-segment pass-through routing scheme where a cable segment can be attached within the same link. Secondly, the analysis for CDSKCs require extensions from single link CDPRs to consider different routings. The conditions to satisfy wrench-closure and the workspace analysis of different multi-link unilateral manipulators are investigated. Due to redundant and constrained actuation, it is possible for a motion to be either infeasible or the desired motion can be produced by an infinite number of different actuation profiles. The motion generation of the CDSKCs with a minimal number of actuating cables is studied. The static stiffness evaluation of CDSKCs with different routing topologies and isotropic stiffness conditions were investigated. The dexterity and wrench-based metrics were evaluated throughout the mechanism's workspace. Through this thesis, the fundamental tools required in studying cable-driven serial kinematic chains have been presented. The results of this work highlight the potential of using CDSKCs in bio-inspired systems and tensegrity robots

Optimum-synthesis methods for cable-driven parallel mechanisms

Les mécanismes parallèles entraînés par câbles sont une classe spéciale de mécanismes parallèles pours lesquels les liaisons rigides sont remplacées par des câbles. Ces mécanismes comprennent une plateforme mobile et une base fixe, qui sont reliées par plusieurs câbles. Le contrôle des longueurs des câbles produit le mouvement désiré de la plateforme mobile. Ces mécanismes ont le potentiel de fournir des espaces de travail à grande échelle comparativement aux mécanismes parallèles conventionnels car les câbles peuvent être enroulés sur des bobines sur de grandes longueurs. Cependant, cette caractéristique est limitée par la nature des câbles, qui doivent demeurer en tension afin de produire un mouvement désiré de la plateforme principale. L'objectif principal de cette thèse est de concevoir des méthodes efficaces pour la synthèse dimensionelle optimale des mécanismes parallèles entraînés par câbles surcontraints, c'est-à-dire, des mécanismes pour lesquels le nombre de câbles excède le nombre de degrés de liberté. Plus précisément, nous souhaitons obtenir la géométrie des mécanismes parallèles entraînés par câbles dont l'espace des poses polyvalente (EPP) comprend des espaces de travail prescrits. L'espace des poses polyvalentes d'un mécanisme parallèle entraîné par câbles est l'ensemble des poses (les positions et les orientations) de l'organe terminal pour lesquelles tous les torseurs appliqués sont réalisables. Un torseur appliqué est dit réalisable, s'il peut être produit par un ensemble de câbles dont les tensions sont non-négatives. Une fois le problème de la synthèse dimensionnelle résolu, nous pouvons appliquer la solution à plusieurs reprises pour différents nombres de câbles afin d'effectuer la synthèse de la structure. Cette thèse est divisée en trois parties principales. Tout d'abord, l'espace des poses polyvalentes des mécanismes parallèles plans entraînés par câbles et les caractéristiques de leurs frontières sont étudiés. Cette étude révèle les relations jusqu'ici inconnues entre l'EPP à orientation constante (EPPOC) et les aires orientées. Un algorithme graphique est proposé afin de déterminer les types de sections coniques formant les frontières de l'EPPOC . Puis, sur la base des expressions mathématiques obtenues, une méthodologie est proposée pour résoudre le problème de la synthèse dimensionnelle des mécanismes parallèles plans entraînés par câbles pour les orientations discrètes c'est-àdire, les translations. L'algorithme est basé sur des techniques de relaxation convexe qui nous amènent à formuler la synthèse dimensionnelle comme un programme non linéaire. L'idée est de maximiser la taille de plusieurs boîtes qui représentent une approximation d'un espace de travail prescrit, tout en essayant de les garder à l'intérieur de l'EPP du mécanisme parallèle plan entraîné par câbles pendant la procédure d' optimisation. Une telle approximation de l'espace de travail prescrit est obtenue via la méthode d'analyse par intervalles. L'algorithme obtenu est étendu au cas de l'orientation en continu pour un intervalle donné d'angles d'orientation. En fait, nous introduisons un programme non linéaire permettant de varier la géométrie du mécanisme parallèle plan entraîné par câbles et maximiser le facteur d'échelle de l'ensemble prescrit de boîtes. Lorsque le facteur d'échelle optimal est supérieur ou égal à un, l'EPP du mécanismes parallèle plan entraîné par câbles résultant contient l'ensemble des boîtes prescrit. Sinon, l'EPP obtenu offre généralement une bonne couverture des boîtes prescrites. Enfin, sur la base des résultats obtenus pour des mécanismes parallèles plans entraînés par câbles, un algorithme est proposé pour résoudre la synthèse dimensionelle de mécanismes parallèles spatiaux entraînés par câbles. Comme pour le cas plan, nous proposons un programme non linéaire à grande échelle dont les solutions optimales peuvent fournir des geometries de mécanismes parallèles spatiaux entraînés par câbles pour un espace de travail prescrit dans une plage donnée des angles d'orientation. L'efficacité de ces méthodes est émontrée par plusieurs exemples en utilisant un logiciel développé. En outre, cette thèse fournit un outil efficace pour les concepteurs de robots parallèles entraînés par câble

Position and singularity analysis of a class of planar parallel manipulators with a reconfigurable end-effector

Parallel robots with configurable platforms are a class of robots in which the end-effector has an inner mobility, so that its overall shape can be reconfigured: in most cases, the end-effector is thus a closed-loop kinematic chain composed of rigid links. These robots have a greater flexibility in their motion and control with respect to rigid-platform parallel architectures, but their kinematics is more challenging to analyze. In our work, we consider n-RRR planar configurable robots, in which the end-effector is a chain composed of n links and revolute joints, and is controlled by n rotary actuators located on the base of the mechanism. In particular, we study the geometrical design of such robots and their direct and inverse kinematics for n = 4, n = 5 and n = 6; we employ the bilateration method, which can simplify the kinematic analysis and allows us to generalize the approach and the results obtained for the 3-RRR mechanism to n-RRR robots (with n > 3). Then, we study the singularity configurations of these robot architectures. Finally, we present the results from experimental tests that have been performed on a 5–RRR robot prototype

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