Cable Robot Performance Evaluation by Wrench Exertion Capability

Although cable driven robots are a type of parallel manipulators, the evaluation of their performances cannot be carried out using the performance indices already developed for parallel robots with rigid links. This is an obvious consequence of the peculiar features of flexible cables-a cable can only exert a tensile and limited force in the direction of the cable itself. A comprehensive performance evaluation can certainly be attained by computing the maximum force (or torque) that can be exerted by the cables on the moving platform along a specific (or any) direction within the whole workspace. This is the idea behind the index-called the Wrench Exertion Capability (WEC)-which can be employed to evaluate the performance of any cable robot topology and is characterized by an efficient and simple formulation based on linear programming. By significantly improving a preliminary computation method for the WEC, this paper proposes an ultimate formulation suitable for any cable robot topology. Several numerical investigations on planar and spatial cable robots are presented to give evidence of the WEC usefulness, comparisons with popular performance indices are also provided

Inverse geometrico-static problem of underconstrained . . .

This paper studies underconstrained cable-driven parallel robots (CDPRs) with three cables. A major challenge in the study of these robots is the intrinsic coupling between kinematics and statics, which must be tackled simultaneously. Effective elimination procedures are presented which provide the complete solution sets of the inverse geometrico-static problems (IGPs) with assigned orientation or position. In the former case, the platform orientation is given, whereas the platform position and the cable lengths and tensions must be computed. In the latter case, the platform position is known, whereas the platform orientation and the cable lengths and tensions are to be calculated. The described problems are proven to admit at the most 1 and 24 real solutions, respectively

Natural oscillations of underactuated cable-driven parallel robots

Underactuated Cable-Driven Parallel Robots (CDPR) employ a number of cables smaller than the degrees of freedom (DoFs) of the end-effector (EE) that they control. As a consequence, the EE is underconstrained and preserves some freedoms even when all actuators are locked, which may lead to undesirable oscillations. This paper proposes a methodology for the computation of the EE natural oscillation frequencies, whose knowledge has proven to be convenient for control purposes. This procedure, based on the linearization of the system internal dynamics about equilibrium con_gurations, can be applied to a generic robot suspended by any number of cables comprised between 2 and 5. The kinematics, dynamics, stability and stiffness of the robot free motion are investigated in detail. The validity of the proposed method is demonstrated by experiments on 6-DoF prototypes actuated by 2, 3, and 4 cables. Additionally, in order to highlight the interest in a robotic context, this modelling strategy is applied to the trajectory planning of a 6-DoF 4-cable CDPR by means of a frequency-based method (multi-mode input shaping), and the latter is experimentally compared with traditional non-frequency-based motion planners

Kinematics and statics of cable-driven parallel robots by interval-analysis-based methods

In the past two decades the work of a growing portion of researchers in robotics focused on a particular group of machines, belonging to the family of parallel manipulators: the cable robots. Although these robots share several theoretical elements with the better known parallel robots, they still present completely (or partly) unsolved issues. In particular, the study of their kinematic, already a difficult subject for conventional parallel manipulators, is further complicated by the non-linear nature of cables, which can exert only efforts of pure traction. The work presented in this thesis therefore focuses on the study of the kinematics of these robots and on the development of numerical techniques able to address some of the problems related to it. Most of the work is focused on the development of an interval-analysis based procedure for the solution of the direct geometric problem of a generic cable manipulator. This technique, as well as allowing for a rapid solution of the problem, also guarantees the results obtained against rounding and elimination errors and can take into account any uncertainties in the model of the problem. The developed code has been tested with the help of a small manipulator whose realization is described in this dissertation together with the auxiliary work done during its design and simulation phases.Negli ultimi decenni il lavoro di una parte sempre maggiore di ricercatori che si occupano di robotica si è concentrato su un particolare gruppo di robot appartenenti alla famiglia dei manipolatori paralleli: i robot a cavi. Nonostante i numerosi studi al riguardo, questi robot presentano ancora oggi numerose problematiche del tutto (o in parte) irrisolte. Lo studio della loro cinematica nello specifico, già complesso per i manipolatori paralleli tradizionali, è ulteriormente complicato dalla natura non lineare dei cavi, i quali possono esercitare sforzi di sola trazione. Il lavoro presentato in questa tesi si concentra dunque sullo studio della cinematica dei robot a cavi e sulla messa a punto di tecniche numeriche in grado di affrontare parte delle problematiche ad essa legate. La maggior parte del lavoro è incentrata sullo sviluppo di una procedura per la soluzione del problema geometrico diretto di un generico manipolatore a cavi basata sull'analisi per intervalli. Questa tecnica di analisi numeirica, oltre a consentire una rapida soluzione del problema, permette di garantire i risultati ottenuti in caso di errori di cancellazione e arrotondamento e consente di considerare eventuali incertezze presenti nel modello del problema. Il codice sviluppato è stato testato attraverso un piccolo prototipo di manipolatore a cavi la cui realizzazione, avvenuta durante il percorso di dottrato, è descritta all'interno dell'elaborato unitamente al lavoro collaterale svolto durante la fase di progettazione e simulazione.Pendant les dernières décennies, le travail d'une partie toujours croissante de chercheurs qui s'occupent de robotique s'est focalisé sur un groupe spécifique de robots qui fait partie de la famille des manipulateurs parallèles: les robots à câbles. Malgré les nombreux études que l'on a consacré à ce sujet, ces robots présentent encore aujourd'hui plusieurs problématiques complètement ou partiellement irrésolues. En particulier l'étude de leur cinématique, qui se révèle déjà complexe pour les manipulateurs parallèles traditionnels, est rendu encore plus compliqué par la nature non linéaire des câbles qui peuvent seulement exercer des efforts de traction. Le travail présenté dans ma thèse concentre donc son attention sur l'étude de la cinématique des robots à câbles et sur la mise au point de techniques numériques capables d'aborder une partie des problématiques liées à cela. La plupart du travail se concentre sur l'élaboration d'un algorithme pour la résolution du problème géométrique direct d'un manipulateur à câbles général qui se fonde sur l'analyse par intervalles. Cette technique d'analyse permet non seulement de résoudre rapidement le problème mais également de garantir les résultats obtenus en cas d'erreur de cancellation et d'arrondi et de prendre en considération les incertitudes éventuellement presentes dans le modèle du problème. Le code développé a été testé grâce à un petit prototype de manipulateur à câbles dont la réalisation, qui a eu lieu pendant le parcours de doctorat, est décrite à l'intérieur du devoir en accord avec la phase de conception du projet et de simulation

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

Influence of payload and platform dimensions on the static workspace of a 4-cable driven parallel robot

International audienceThis paper presents the influence of payload and platform dimensions on the static equilibrium workspace of an under-constrained cable-driven robot with four cables taking into account the forces and the moments due to the forces acting on the moving platform. The problem is formulated as a non-linear optimization problem with maintaining static equilibrium as the objective function. The simulations are done in MATLAB. The maximum force on the cables, the payload acting on the platform and the dimensions of the moving platform are varied and their corresponding effects on the static equilibrium is studied. The obtained results are analyzed to finalize the design of the collaborative cable-driven robot to be installed in existing production lines for the agile handling of parts in a manufacturing industry

Direct kinematics of CDPR with extra cable orientation sensors: the 2 and 3 cables case with perfect measurement and ideal or elastic cables

International audienceDirect kinematics (DK) of cable-driven parallel robots (CDPR) based only on cable lengths measurements is a complex issue even with ideal cables and consequently even harder for more realistic cable models. A natural way to simplify the DK solving is to add sensors. We consider here sensors that give a partial or complete measurement of the cable direction at the anchor points and spatial CDPR with 2/3 cables and we assume that these measurements are exact. We provide a solving procedure and maximal number of DK solutions for an extensive combination of sensors while considering two different cables models: ideal and linearly elastic without deformation

Rest-to-Rest Trajectory Planning for Underactuated Cable-Driven Parallel Robots

This article studies the trajectory planning for underactuated cable-driven parallel robots (CDPRs) in the case of rest-to-rest motions, when both the motion time and the path geometry are prescribed. For underactuated manipulators, it is possible to prescribe a control law only for a subset of the generalized coordinates of the system. However, if an arbitrary trajectory is prescribed for a suitable subset of these coordinates, the constraint deficiency on the end-effector leads to the impossibility of bringing the system at rest in a prescribed time. In addition, the behavior of the system may not be stable, that is, unbounded oscillatory motions of the end-effector may arise. In this article, we propose a novel trajectory-planning technique that allows the end effector to track a constrained geometric path in a specified time, and allows it to transition between stable static poses. The design of such a motion is based on the solution of a boundary value problem, aimed at a finding solution to the differential equations of motion with constraints on position and velocity at start and end times. To prove the effectiveness of such a method, the trajectory planning of a six-degrees-of-freedom spatial CDPR suspended by three cables is investigated. Trajectories of a reference point on the moving platform are designed so as to ensure that the assigned path is tracked accurately, and the system is brought to a static condition in a prescribed time. Experimental validation is presented and discussed

Direct kinematics of CDPR with extra cable orientation sensors: the 2 and 3 cables case with perfect measurement and sagging cables

International audienceDirect kinematics (DK) of cable-driven parallel robots (CDPR) based only on cable lengths measurements is a complex issue even with ideal cables and consequently even harder for more realistic cable models such as sagging cable. A natural way to simplify the DK solving is to add sensors. We consider here sensors that give a partial or complete measurement of the cable direction at the anchor points and/or measure the orientation of the platform of CDPR with 2 or 3 cables and we assume that the measurements are exact. We provide a solving procedure and maximal number of DK solutions for an extensive combination of sensors for CDPR with sagging cables. We show that at least two measurements are necessary for the planar 2 cables case while six are necessary for the spatial 3 cables case. For spatial CDPR with n cables we prove that at least 2n additional sensors will be required to get a closed-form solution of the DK

On the robustness of cable configurations of suspended cable-driven parallel robots

International audienceCable-driven parallel robot (CDPR) are parallel robots that use coilable cables as legs. We are interested here in suspended CDPR for which there is no cable that exert a downward force on the platform. If we assume that the cables are mass-less and not elastic it has been shown that at a given pose whatever is the number m > 6 of cables there will always be at most 6 cables under tension simultaneously. A cable configuration (CC) at a given pose is the set of cables number that are under tension and usually there are several possible CC for the same pose. These CC are not equivalent in terms of cable tensions, sensitivity to measurement errors and therefore it make sense from a control viewpoint to enforce the " best " CC to obtain the optimal robot configuration, which can be done by controlling the length of the cables that are not members of the CC so that we are sure that they are slack. Hence we are interested in ranking the different CC in term of ro-bustness. We propose several ranking indices for a CC and algorithms to calculate these indices at a pose, on a tra-jectory or when the robot moves on a surface and we show examples for a CDPR with 8 cables