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

Planning wrench-feasible motions for cable-driven hexapods

Motion paths of cable-driven hexapods must carefully be planned to ensure that the lengths and tensions of all cables remain within acceptable limits, for a given wrench applied to the platform. The cables cannot go slack-to keep the control of the robot-nor excessively tightto prevent cable breakage-even in the presence of bounded perturbations of the wrench. This paper proposes a path-planning method that accommodates such constraints simultaneously. Given two configurations of the robot, the method attempts to connect them through a path that, at any point, allows the cables to counteract any wrench lying in a predefined uncertainty region. The configuration space, or C-space for short, is placed in correspondence with a smooth manifold, which facilitates the definition of a continuation strategy to search this space systematically from one configuration, until the second configuration is found, or path nonexistence is proved by exhaustion of the search. The force Jacobian is full rank everywhere on the C-space, which implies that the computed paths will naturally avoid crossing the forward singularity locus of the robot. The adjustment of tension limits, moreover, allows to maintain a meaningful clearance relative to such locus. The approach is applicable to compute paths subject to geometric constraints on the platform pose or to synthesize free-flying motions in the full 6-D C-space. Experiments illustrate the performance of the method in a real prototype.Postprint (author's final draft

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

Workspace Analysis of a 4 Cable-Driven Spatial Parallel Robot

International audienceThis paper presents 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 using MATLAB. The maximum force on the cables and tilting angle of the platform are used to define the feasible static equilibrium workspace and the results obtained are used 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

Design, analysis, and control of a cable-driven parallel platform with a pneumatic muscle active support

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.The neck is an important part of the body that connects the head to the torso, supporting the weight and generating the movement of the head. In this paper, a cable-driven parallel platform with a pneumatic muscle active support (CPPPMS) is presented for imitating human necks, where cable actuators imitate neck muscles and a pneumatic muscle actuator imitates spinal muscles, respectively. Analyzing the stiffness of the mechanism is carried out based on screw theory, and this mechanism is optimized according to the stiffness characteristics. While taking the dynamics of the pneumatic muscle active support into consideration as well as the cable dynamics and the dynamics of the Up-platform, a dynamic modeling approach to the CPPPMS is established. In order to overcome the flexibility and uncertainties amid the dynamic model, a sliding mode controller is investigated for trajectory tracking, and the stability of the control system is verified by a Lyapunov function. Moreover, a PD controller is proposed for a comparative study. The results of the simulation indicate that the sliding mode controller is more effective than the PD controller for the CPPPMS, and the CPPPMS provides feasible performances for operations under the sliding mode control

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

Computing wrench-feasible paths for cable-driven hexapods

Motion paths of cable-driven hexapods must carefully be planned to ensure that the lengths and tensions of all cables remain within acceptable limits, for a given wrench applied to the platform. The cables cannot go slack -to keep the control of the robot- nor excessively tight -to prevent cable breakage- even in the presence of bounded perturbations of the wrench. This paper proposes a path planning method that accommodates such constraints simultaneously. Given two configurations of the robot, the method attempts to connect them through a path that, at any point, allows the cables to counteract any wrench lying in a predefined uncertainty region. The feasible C-space is placed in correspondence with a smooth manifold, which facilitates the definition of a continuation strategy to search this space systematically from one configuration, until the second configuration is found, or path non-existence is proved at the resolution of the search. The force Jacobian is full rank everywhere on the C-space, which implies that the computed paths will naturally avoid crossing the forward singularity locus of the robot. The adjustment of tension limits, moreover, allows to maintain a meaningful clearance relative to such locus. The approach is applicable to compute paths subject to geometric constraints on the platform pose, or to synthesize free-flying motions in the full six-dimensional C-space. Experiments are included that illustrate the performance of the method in a real prototype.Postprint (published version

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