Kinetostatic Analysis and Solution Classification of a Planar Tensegrity Mechanism

Tensegrity mechanisms have several interesting properties that make them suitable for a number of applications. Their analysis is generally challenging because the static equilibrium conditions often result in complex equations. A class of planar one-degree-of-freedom (dof) tensegrity mechanisms with three linear springs is analyzed in detail in this paper. The kinetostatic equations are derived and solved under several loading and geometric conditions. It is shown that these mechanisms exhibit up to six equilibrium configurations, of which one or two are stable. Discriminant varieties and cylindrical algebraic decomposition combined with Groebner base elimination are used to classify solutions as function of the input parameters.Comment: 7th IFToMM International Workshop on Computational Kinematics, May 2017, Poitiers, France. 201

Combining precision and power to maximize performance: a case study of the woodpecker's neck

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Prototype of a tensegrity manipulator to mimic bird necks

International audienceThis paper deals with the building of a 2D tensegrity mechanism. The considered mechanism is derived from the Snelson's X-shape mechanism and is used as an elementary part of the bird neck modelling. Indeed, an n-dof manipulator can be obtained by stacking in series n X-shape mechanisms. This paper explains the design and building process of a 1-dof prototype, both on hardware and software aspects, and will be used further to have experimental results on the dynamic modelling, control laws and ac-tuation strategy.Une structure de tenségrité est un assemblage d'éléments en compression (barres) et d'éléments en traction (câbles, ressorts) maintenus ensemble en équilibre [1],[2]. La tenségrité est connue en architecture et en art depuis plus d'un siècle [3] et est adaptée à la modélisation des organismes vivants [4]. Les mé-canismes de tenségrité ont été étudiés plus récemment pour leurs propriétés prometteuses en robotique telles que la faible inertie, la souplesse naturelle et la capacité de déploiement [5]. Un mécanisme de tenségrité est obtenu lorsqu'un ou plusieurs éléments sont actionnés. Ces travaux s'inscrivent dans le cadre du projet AVINECK, auquel participent des biologistes et des roboticiens dans le but principal de modéliser et de concevoir des cous d'oiseaux. En conséquence, une classe de manipulateurs de tenségrité planaire composée d'un assemblage en série de plusieurs mécanismes en X de Snelson [6], c'est-à-dire des mécanismes à quatre barres croisées avec des ressorts sur leurs côtés latéraux, a été choisie comme candidat approprié pour un modèle préliminaire plan d'un cou d'oiseau. Le prototype consiste en un mecanisme en X de Snelson. Les barres sont assemblées selon différents plans pour éviter les collisions internes. Le manipulateur est entraîné par des câbles parallèles aux res-sorts et traversant les axes grâce à des perçages. Chaque câble est attaché à un tambour. Le manipulateur est actionné par deux câbles, ce qui en fait un mécanisme antagoniste, dont on peut contrôler la raideur. Les pièces structurelles (barres, supports, tambours) sont imprimées en 3D en ABS. Chaque liaison pivot entre les barres et les axes est construite avec deux roulements qui assurent un centrage long, et toutes les pièces sont arrêtées axialement avec des colliers d'arbre. Nous avons décidé d'avoir une lon-gueur de barre transversale de 100 mm et une longueur de barre supérieure de 50 mm. Ces dimensions sont adaptées à plusieurs jeux de ressorts disponibles, c'est-à-dire que les ressorts considérés sont tou-jours en tension et ne sont pas trop étendus pour toutes les positions accessibles du manipulateur. Une fois la longueur et la raideur du ressort définies, le modèle statique est calculé afin d'obtenir la force d'entrée maximale pour les câbles. Cette force doit être suffisante pour actionner le mécanisme dans un grand espace de travail et pour résister aux chargements externes. La force appliquée par les câbles est directement liée au rayon du tambour et au couple du moteur. Le rayon du tambour influe également sur la vitesse de translation du câble. Un compromis est fait pour avoir des efforts et vitesses de câbles suffisants. Deux variateurs interagissent avec un microprocesseur sur lequel est programmé la loi de commande. Chaque moteur est équipé d'un codeur pour connaître la position réelle du mécanisme. Le bon compor-tement du mécanisme est assuré par une commande dynamique

Stacked Tensegrity Mechanism for Medical Application

In this article a multi-segmented planar tensegrity mechanism was presented. This mechanism has a three-segment structure with each segment residing on top of another. The size of the segments may decrease proportionally from base to top, resulting in a tapered shape from base to tip like an elephant trunk. The system was mechanically formulated as having linear springs and cables functioning as actuators. The singularities, as well as the stability of the parallel mechanism, were analyzed by using the principle of minimum energy. Optimization was also done to obtain the greatest angular deflection for a segment according to a ratio between the size of the base and the moving platform of the robotic system. The result of this work is a family of mechanisms that can generate the same workspace for different stability properties

Foreword to the Special Issue on the Computational Kinematics Conference, CK2017

Computational Kinematics is a wide field of science addressing applications ranging from robotics to mechanics, computer science, mathematics and computer graphics

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

Grasp plannind under task-specific contact constraints

Several aspects have to be addressed before realizing the dream of a robotic hand-arm system with human-like capabilities, ranging from the consolidation of a proper mechatronic design, to the development of precise, lightweight sensors and actuators, to the efficient planning and control of the articular forces and motions required for interaction with the environment. This thesis provides solution algorithms for a main problem within the latter aspect, known as the {\em grasp planning} problem: Given a robotic system formed by a multifinger hand attached to an arm, and an object to be grasped, both with a known geometry and location in 3-space, determine how the hand-arm system should be moved without colliding with itself or with the environment, in order to firmly grasp the object in a suitable way. Central to our algorithms is the explicit consideration of a given set of hand-object contact constraints to be satisfied in the final grasp configuration, imposed by the particular manipulation task to be performed with the object. This is a distinguishing feature from other grasp planning algorithms given in the literature, where a means of ensuring precise hand-object contact locations in the resulting grasp is usually not provided. These conventional algorithms are fast, and nicely suited for planning grasps for pick-an-place operations with the object, but not for planning grasps required for a specific manipulation of the object, like those necessary for holding a pen, a pair of scissors, or a jeweler's screwdriver, for instance, when writing, cutting a paper, or turning a screw, respectively. To be able to generate such highly-selective grasps, we assume that a number of surface regions on the hand are to be placed in contact with a number of corresponding regions on the object, and enforce the fulfilment of such constraints on the obtained solutions from the very beginning, in addition to the usual constraints of grasp restrainability, manipulability and collision avoidance. The proposed algorithms can be applied to robotic hands of arbitrary structure, possibly considering compliance in the joints and the contacts if desired, and they can accommodate general patch-patch contact constraints, instead of more restrictive contact types occasionally considered in the literature. It is worth noting, also, that while common force-closure or manipulability indices are used to asses the quality of grasps, no particular assumption is made on the mathematical properties of the quality index to be used, so that any quality criterion can be accommodated in principle. The algorithms have been tested and validated on numerous situations involving real mechanical hands and typical objects, and find applications in classical or emerging contexts like service robotics, telemedicine, space exploration, prosthetics, manipulation in hazardous environments, or human-robot interaction in general

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

Workspace, Joint space and Singularities of a family of Delta-Like Robot

International audienceThis paper presents the workspace, the joint space and the singularities of a family of delta-like parallel robots by using algebraic tools. The different functions of SIROPA library are introduced, which is used to induce an estimation about the complexity in representing the singularities in the workspace and the joint space. A Groebner based elimination is used to compute the singularities of the manipulator and a Cylindrical Algebraic Decomposition algorithm is used to study the workspace and the joint space. From these algebraic objects, we propose some certified three-dimensional plotting describing the shape of workspace and of the joint space which will help the engineers or researchers to decide the most suited configuration of the manipulator they should use for a given task. Also, the different parameters associated with the complexity of the serial and parallel singularities are tabulated, which further enhance the selection of the different configuration of the manipulator by comparing the complexity of the singularity equations