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

Robot Assisted Shoulder Rehabilitation: Biomechanical Modelling, Design and Performance Evaluation

The upper limb rehabilitation robots have made it possible to improve the motor recovery in stroke survivors while reducing the burden on physical therapists. Compared to manual arm training, robot-supported training can be more intensive, of longer duration, repetitive and task-oriented. To be aligned with the most biomechanically complex joint of human body, the shoulder, specific considerations have to be made in the design of robotic shoulder exoskeletons. It is important to assist all shoulder degrees-of-freedom (DOFs) when implementing robotic exoskeletons for rehabilitation purposes to increase the range of motion (ROM) and avoid any joint axes misalignments between the robot and human’s shoulder that cause undesirable interaction forces and discomfort to the user. The main objective of this work is to design a safe and a robotic exoskeleton for shoulder rehabilitation with physiologically correct movements, lightweight modules, self-alignment characteristics and large workspace. To achieve this goal a comprehensive review of the existing shoulder rehabilitation exoskeletons is conducted first to outline their main advantages and disadvantages, drawbacks and limitations. The research has then focused on biomechanics of the human shoulder which is studied in detail using robotic analysis techniques, i.e. the human shoulder is modelled as a mechanism. The coupled constrained structure of the robotic exoskeleton connected to a human shoulder is considered as a hybrid human-robot mechanism to solve the problem of joint axes misalignments. Finally, a real-scale prototype of the robotic shoulder rehabilitation exoskeleton was built to test its operation and its ability for shoulder rehabilitation

Adaptive Passivity-Based Pose Tracking Control of Cable-Driven Parallel Robots for Multiple Attitude Parameterizations

The proposed control method uses an adaptive feedforward-based controller to establish a passive input-output mapping for the CDPR that is used alongside a linear time-invariant strictly positive real feedback controller to guarantee robust closed-loop input-output stability and asymptotic pose trajectory tracking via the passivity theorem. A novelty of the proposed controller is its formulation for use with a range of payload attitude parameterizations, including any unconstrained attitude parameterization, the quaternion, or the direction cosine matrix (DCM). The performance and robustness of the proposed controller is demonstrated through numerical simulations of a CDPR with rigid and flexible cables. The results demonstrate the importance of carefully defining the CDPR's pose error, which is performed in multiplicative fashion when using the quaternion and DCM, and in a specific additive fashion when using unconstrained attitude parameters (e.g., an Euler-angle sequence)

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

A comparative study of 4-cable planar manipulators based on cylindrical algebraic decomposition

International audienceThe aim of this paper is to present a systematic method for verifying the force-closure condition for general 3-DOF fully-constrained cable manipulators with four cables as based on the CAD (Cylindrical Algebraic Decomposition). A fundamental requirement for a cable manipulator to be fully controllable is that all its cables must be in tension at any working configurations. In other words, all the cable forces must be positive (assuming a positive cable force representing a tension and a negative cable force being a compression). Such a force feasibility problem is indeed referred to a force-closure problem (also called vector-closure problem assuming that the vectors of interest are the row vectors of the Jacobian matrix of the manipulator). The boundaries of the workspace can be obtained by the study of the Jacobian matrix of the manipulator. Therefore, this is equivalent to study the singularity conditions of four 3-RPR parallel robots. By using algebraic tools, it is possible to determine the singularity surfaces and their intersections yielding the workspace. Thus, it will be shown that the use of the CAD allows to get an implicit representation of the workspace as a set of cells. A comparative workspace analysis of three designs of mobile platforms, a line, a square and a triangle will be presented and discussed in this paper for a planar 4-cable fully-constrained robot

Low Mobility Cable Robot with Application to Robotic Warehousing

Cable-based robots consist of a rigid mobile platform connected via flexible links (cables, wires, tendons) to a surrounding static platform. The use of cables simplifies the mechanical structure and reduces the inertia, allowing the mobile platform to reach high motion acceleration in large workspaces. These attributes give, in principle, an advantage over conventional robots used for industrial applications, such as the pick and place of objects inside factories or similar exterior large workspaces. However, unique cable properties involve new theoretical and technical challenges: all cables must be in tension to avoid collapse of the mobile platform. In addition, positive tensions applied to cables may affect the overall stiffness, that is, cable stretch might result in unacceptable oscillations of the mobile platform. Fully constrained cable-based robots can be distinguished from other types of cable-based robots because the motion and force generation of the mobile platform is accomplished by controlling both the cable lengths and the positive cable tensions. Fully constrained cable-based robots depend on actuator redundancy, that is, the addition of one or more actuated cables than end-effector degrees of freedom. Redundancy has proved to be beneficial to expand the workspace, remove some types of singularities, increase the overall stiffness, and support high payloads in several proposed cable-based robot designs. Nevertheless, this strategy demands the development of efficient controller designs for real-time applications. This research deals with the design and control of a fully constrained cable-based parallel manipulator for large-scale high-speed warehousing applications. To accomplish the design of the robot, a well-ordered procedure to analyze the cable tensions, stiffness and workspace will be presented to obtain an optimum structure. Then, the control problem will be investigated to deal with the redundancy solution and all-positive cable tension condition. The proposed control method will be evaluated through simulation and experimentation in a prototype manufactured for testing

Kinematics and Robot Design I, KaRD2018

This volume collects the papers published on the Special Issue “Kinematics and Robot Design I, KaRD2018” (https://www.mdpi.com/journal/robotics/special_issues/KARD), which is the first issue of the KaRD Special Issue series, hosted by the open access journal “MDPI Robotics”. The KaRD series aims at creating an open environment where researchers can present their works and discuss all the topics focused on the many aspects that involve kinematics in the design of robotic/automatic systems. 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”. KaRD2018 received 22 papers and, after the peer-review process, accepted only 14 papers. The accepted papers cover some theoretical and many design/applicative aspects

System Identification and Adaptive Control of Planar Cable Robots

Cable-based robots generally perform better than other parallel robots with rigid links in terms of wider workspace and higher acceleration of end-effector because of light weight of robot links. Cable robots allow easy installation for outside applications at the expense of the requirement of a precise assembly of its components at the cable anchor points. In this study, system identification and adaptive control of cable planar robots are considered. Firstly, a parametric model is developed for estimation of position errors of anchor points for fully-constrained and redundant planar cable robots. A novel method based on inclusion of virtual cables facilitates the linear separation of the uncertain parameters from the input-output signals for redundant planar robots. A least-squares and gradient based parameter estimation algorithm provide the estimates of the system parameters. Further, this work deals with the design and comparison of three adaptive position control schemes combined with a classical PID controller for fully constrained and redundant planar robots. Then, three Lyapunov based adaptive controllers based on the (i) sliding mode, (ii) PD and (iii) backstepping schemes are designed to compensate for the matrix uncertainties appear in the system dynamics resulting from errors in the anchor point locations. Next, the adaptive controllers are evaluated and compared with a classical PID controller through simulations for a desired 2D singularity-free pose of the mobile platform. Supremacy of the PD control scheme over the aforementioned control schemes is observed through simulations. The least-squares algorithm is compared with the gradient-based method in terms of the speed of convergence of the estimated parameters as well. Finally, we establish linear parametric forms for common friction models, recursive least-squares on-line friction estimator is presented and adaptive friction compensation scheme is designed. The efficiency of this design is discussed via simulation results

Design and Optimization of a Robot for Abrasive Waterjet Polishing of Hydraulic Turbine Blades

RÉSUMÉ Dans l’industrie de fabrication de turbine hydraulique, toutes les surfaces de turbines qui sont en contact avec de l’eau devraient être polies afin d’obtenir la qualité et l’efficacité maximales. Pour cela, il est nécessaire d’utiliser une méthode de polissage qui peut avoir accès à toutes les surfaces des turbines incluant leurs bords, leurs zones restreintes et leurs courbures serrées. En raison des propriétés particulières qu’offre la technique de polissage par jet d’eau abrasif, celle-ci peut être utilisée pour accomplir cette tâche. Par conséquent, dans cette recherche, les propriétés de cette méthode non-conventionnelle sont examinées dans un premier temps et les principaux paramètres affectant ses performances sont alors déterminés. Ensuite, les conditions nécessaires de manipulations de la buse de pulvérisation vis-à-vis des surfaces courbes sont étudiées et les propriétés d’un bras robotisé pour manipuler celle-ci sont obtenues afin de réaliser cette tâche d’une manière appropriée. Par après, plusieurs mécanismes robotiques tels que des mécanismes sériels, parallèles à membrures, parallèles à câbles, et des robots hybrides sont considérés et leurs capacités à être utilisé dans ce processus sont analysées. Il est alors démontré qu’une l’architecture hybride est le meilleur candidat à retenir pour le design d’un robot de polissage par jet d’eau abrasif. Ensuite, l’architecture conceptuelle d’un robot hybride à 5 DDL est proposée. La structure du robot est constituée d’un mécanisme parallèle à câbles à 3 DDL et d’un poignet sériel à 2 DDL. Afin d’améliorer les propriétés cinématiques du mécanisme à câbles tout en minimisant le nombre d’actionneurs nécessaires, il est proposé d’utiliser des différentiels pour guider ce robot manipulateur. Aussi, la rigidité et la compacité du mécanisme sont améliorées en utilisant une liaison prismatique. Par la suite, les systèmes à câbles différentiels sont examinés et les différences entre leurs propriétés cinématiques et celles de systèmes actionnés indépendamment pour chaque câble sont décrites. Il est démontré que la force résultante de tous les câbles d’un différentiel à câbles doit être prise en compte dans son analyse cinématique. En effet, dans un système différentiel planaire, la direction de la force résultante n’est pas fixée vers un point particulier. Mais plutôt, elle se déplace dans le plan de ce système différentiel. Cette propriété peut être bénéfique pour les propriétés cinématiques des robots à câbles. En comparant deux types d’espace de travail de plusieurs robots planaires actionnés par des mécanismes différentiels par rapport à leurs équivalents pleinement actionnés, il est alors montré qu’en utilisant ces mécanismes, les espaces de travail des robots planaires à câbles peuvent être améliorés. Cependant, cette même propriété qui augmente la plage de variation de la direction de la force résultante dans un câble différentiel, diminue aussi son amplitude. Ainsi, le design optimal d’un différentiel à câble résulte d’un compromis entre ces deux propriétés.----------ABSTRACT In hydraulic turbine manufacturing, all surfaces of the turbines which are in contact with the water flow should be polished to obtain the desired quality and maximal efficiency. For this, it is needed to use an effective polishing method which can have access to all surfaces of the turbines including edges, narrow areas and tight bends. Because of the particular properties of the abrasive waterjet polishing technique, it can be used to accomplish this task. Therefore, in this research, the properties of this non-conventional method are first investigated and the main parameters affecting its performance are then determined. Next, the manipulation requirements of the jet nozzle over free-form surfaces are studied and the properties of a robotic arm to appropriately perform this task are obtained. Afterwards, several robotic mechanisms, e.g., serial, linkage-driven parallel, cabledriven parallel, and hybrid robots are considered and their abilities to be used in this process are investigated. It is then shown that a hybrid architecture is the best candidate for the design of an abrasive waterjet polishing robot. Next, the conceptual design of a 5-DOF hybrid robot is proposed. The structure of this robot is made of a 3-DOF cable-driven parallel mechanism and a 2-DOF serial wrist. To improve the kinematic properties of the cable-driven mechanism while the number of required actuators is kept at a minimum, it is proposed to use cable differentials to drive this manipulator. Also, the rigidity and compactness of the mechanism is improved through the use of a prismatic joint in its structure. Afterwards, differentially driven cable systems are investigated and the differences between their kinematic properties and these of independently actuated cables are described. It is shown that the resultant force of all cables of a cable differential should be taken into account in its kinematic analysis. Indeed, in a planar differential, the direction of the resultant force is not fixed toward a particular point. Instead, it moves within the plane of that differential. This property can be beneficial in the kinematic properties of differentially driven cable robots. By comparing two types of workspaces of several planar robots actuated by differentials with their fully actuated counterparts, it is then shown that using these mechanisms, these workspaces of planar cable robots can be improved. However, the same property that increases the range of variation of the resultant force direction in a cable differential, decreases its magnitude. Thus, the optimal design of a cable differential is a trade-off between these two properties. Next, a synthesis method is presented to find all possible arrangements of the cable differentials to generalize the idea of using such mechanisms in the design of planar cable robots. Additionally, the application of differentials in spatial robots is also investigated and it is shown that they have properties similar to the planar types

Design and Analysis of a Cable-Driven Test Apparatus for Flapping-Flight Research

The biology, physiology, kinematics, and aerodynamics of insect flight have been a longstanding fascination for biologists and engineers. The former three are easily obtained through the observation of the organic species. The latter though, is very difficult to study in this fashion. In many cases, aerodynamic forces and fluid-body interactions can be simulated with computational fluid dynamics; another option is to use dynamically-scaled, experimental set-ups to measure physically these values. An archetypal, experimental set-up may include one or two scaled wings, where each wing is actuated to achieve upwards of three degrees of freedom. The three degrees of freedom correspond biologically to the stroke, deviation, and rotation motions of real insects. The wing modules may be fixed to rotate about a central, fourth axis, mimicking the insect body rotation. Alternatively, the wing modules can be fixed to translate in one direction, copying the forward flight pattern of an insect. These experiments usually are performed in a tank of mineral oil, seeded to highlight the fluid\u27s movement. Unfortunately, the current state of experimental apparatuses limit the number and complexity of studiable flight patterns. The goal is to use a subset of robotics called cable-driven parallel manipulators to improve upon and expand the capabilities of these apparatuses. For these robots, rigid links are replaced with tensioned cables and actuated via electric motors. Each cable attaches to the central manipulator platform, similar to other parallel manipulators. Some advantages of a cable-driven design are large position workspaces, low inertia, high manipulator dynamics, large strength-to-weight ratio, and no actuator-error stack-up. Cable manipulators have been researched in the lab and have been deployed commercially, such as at professional sports stadiums. The manipulator uses a standard cuboid frame, with eight winches actuating eight cables. The manipulator platform is a scaled insect body, with each wing capable of three degrees of freedom, and an optimized attachment frame for the cables. The manipulator\u27s workspace for six degrees of freedom was derived from previous works and simulated in MathWorks\u27 MATLAB for a variety of parameterizations. The lead design incorporates a novel, new cable configuration for realizing greater rotational capability over standard cable-driven manipulators. While a standard, Straight cable configuration allows for large translation but almost no rotation, the new Twist cable configuration provides a smaller yet spread out workspace that is sustainable through singular rotations up to at least 45°, as well as simultaneous rotations about multiple axes. Optimal trends for the attachment frame are discerned from comparing a multitude of size permutations for singular rotations. No one attachment frame holds equal rotational potential about all three axes; however, the strengths and weaknesses of an attachment frame easily are adaptable based on the proposed insect maneuver. To showcase the versatility of the apparatus with a 6 in × 2 in × 4 in attachment frame, four different flight maneuvers are analyzed. The first two case studies prove the cable-driven apparatus can combine the individual functions of existing experimental apparatuses: MATLAB simulations show the device can perform a stationary 116° yaw rotation and separately can translate the end effector 32 in along one axis. A third case study investigates a previously published work on an evasive pitching maneuver from a hawkmoth. In the original study, the normally six-degree-of-freedom movement was distilled down to only one-dimensional translation and pitch rotation, such that it could be replicated in the lab. Using the cable-driven apparatus though, it is possible instead to reproduce the generalized, six-degree-of-freedom maneuver. Finally, a conceptual flight pattern is created to demonstrate the unique advantages of the cable-driven apparatus. The flight path models a pitched dive into a banked quarter turn, with a pitched climb upon exiting the turn. The equal necessity and coupling of all degrees of freedom for this maneuver means it cannot be performed on current experimental apparatuses, except for the cable-driven apparatus. This new cable-driven test apparatus, with its unique design and modifications, would improve the capabilities for experimental studies and provide the most realistic set-up for flapping-flight research