Cable-Driven Parallel Robots

This paper addresses the dynamic trajectory planning of three-DOF spatial cable-suspended parallel robots. Based on a dynamic model of the suspended robot, a set of algebraic inequalities is obtained that represents the constraints on the cable tensions. Dynamic feasibility is then established using interval arithmetics on the latter inequalities in order to obtain global conditions on the trajectory parameters that can guarantee that the cable tensions remain positive throughout the trajectory. Such conditions are obtained for a variety of parametric trajectories. When periodic functions are used in the design of the trajectories, it is shown that special frequencies arise that are akin to natural frequencies of pendulum-type systems. These special frequencies can be used in practice to greatly simplify the trajectory planning. An experimental implementation on a three-dof cable-suspended prototype is presented. As demonstrated, the proposed trajectory planning approach can be used to plan dynamic trajectories that go beyond the static workspace of the mechanism, thereby opening novel applications and possibilities for cable-suspended robots.

The objective of this paper is providing the first experimental evidence of the effectiveness of an off-line trajectory planning approach developed to ensure positive and bounded cable tensions in under constrained planar two-degree-of-freedom translational cable robots. The hybrid (serial/parallel) topology of the investigated robot is general enough to ensure wide applicability of the proposed trajectory planning method, which translates the usual bilateral tensile cable force constraints into kinematic constraints on the velocity and acceleration of the robot tool center point along the desired path. Kinematic constraints are computed making use of the robot dynamic model and can then be incorporated in any trajectory planning algorithm. In this work a smooth trajectory planning algorithm based on quintic polynomials is adopted. The experimental setup is presented and the results obtained by applying the method to two sample paths are discussed.

This paper addresses the problem of time-energy optimal control of cable robot with the trajectory planning as the overall mission. The final dynamic equations were organized in a closed form similar to serial manipulator equations. Thus, employing the Pontryagin maximum principle, it was verified that the optimal motions are all bang–bang controls with bounded control torque on the winches. This consists of minimizing a cost function, considering dynamic equations of motion as well as bounds on joint torques. Here, the cost function was chosen as a weighted balance of traveling time and mechanical energy of the actuators. The approaches of solving concrete optimal control laws based on Two-Point Boundary Value Problems were provided in this paper and the algorithm was tested in simulation yielding acceptable results.

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 platform—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 platform, the method attempts to connect them through a path that, at any point, allows the cables to counteract any wrench lying inside a predefined uncertainty region. The resulting C-space is placed in correspondence with a smooth manifold, which allows defining a continuation strategy to search this space systematically from one configuration, until the second configuration is found, or path non-existence is proved by exhaustion of the search. The approach is illustrated on the NIST Robocrane hexapod, but it remains applicable to general cable-driven hexapods, either to navigate their full six-dimensional C-space, or any of its slices.

This paper introduces a real-time capable tension distribution algorithm for n degree-of-freedom cable-driven parallel robots (CDPR) actuated by \(n+2\) cables. It is based on geometric considerations applied to the two-dimensional convex polytope of feasible cable tension distribution. This polytope is defined as the intersection between the set of inequality constraints on the cable tension values and the affine space of tension solutions to the mobile platform static or dynamic equilibrium. The algorithm proposed in this paper is dedicated to \(n\) degree-of-freedom CDPR actuated by \(n+2\) cables. Indeed, it takes advantage of the two-dimensional nature of the corresponding feasible tension distribution convex polytope to improve the computational efficiency of a tension distribution strategy proposed elsewhere. The fast computation of the polytope vertices and of its barycenter made us successfully validate the real-time compatibility of the presented algorithm.

This paper addressed the determination of the tension distribution in the slack steel wires of the incompletely constrained cable-driven parallel mechanism of FAST telescope. Slack rope hung with piecewise uniform mass is specially investigated. First, the general formulation based on the wrench matrix was derived. Then the analytical model of slack rope was built to give the quantized relation between direction and amplitude of tension vector. The wrench matrix is not only platform pose dependent but influenced by rope geometry. Finally, a performance index based on minimal tension variance is selected to optimize the tension distribution among steel wires. Levenberg-Marquardt method is applied to solve the quadratic program and a discrete-mesh plan is proposed for the whole focal surface. An example of computation is given to verify the effect of the resolution.

Cable-driven parallel robots rely on cables instead of rigid links to manipulate the endeffector in the workspace. The cable force distribution is the result of cable elongation and the force coupling at the endeffector. In this paper, the experimental investigation of the force coupling is presented. In the experiment, the cable length in each individual cable was varied, and the resulting progression of the force distribution and the deflection were measured. With this approach, the steady state gain matrix for the transfer function between a delta in cable length and the resulting changes in the cables forces can be determined. Furthermore, the impact of the observed force coupling on cable force control is discussed.

Nowadays there are very little robot systems in operation in the field of medium to large-scale handling and assembly mostly due to lack of repetitive processes or shortcomings in programming and configuring such robots. In this paper we introduce a family of cable-driven parallel robot called IPAnema that are designed for industrial processes. We address the system architecture, key components such as winches and controller, as well as design tools. Furthermore, some experimental data from the evaluation are presented to illustrate the performance of cable robots.

Picturing the interest of research institutions and industrial actors, the list of research and demonstration parallel cable-driven robot prototypes is growing by the day. LIRMM and Tecnalia have decided to put knowledge in common in order to develop novel concepts for cable-driven parallel robotics and demonstrate its capabilities in industrial tasks. We have developed together a reconfigurable cable robot for this purpose. The robot main characteristics, e.g. footprint, mobile platform geometry and drawing point layout can be modified at will, making it particularly suitable for studying in good conditions new configurations or novel control laws, as well as any scenario suggested by our partners. The present paper first provides an overview of the robot. Afterwards, a more specific view on the different components and the capabilities of reconfiguration are presented, as well as examples of layouts meant for various research and industrial projects.

In order to use a cable-driven parallel robot to inspect an existing surface, a straightforward solution consists in fixing the robot components on this surface. In most cases, however, there are conditions that limit these fixations, for example structural reasons since the frame of the surface has probably not been specifically calculated to withstand the forces generated by the parallel cable-driven robot. In the particular case of inspection of the façade of a building, civil engineering specifications apply, which may drastically reduce the engineering possibilities from the point of view of the parallel cable-driven robot designers. This paper introduces a detailed example of implementation of a parallel cable-driven robot on the Media-TIC building located in Barcelona in Spain. In this highly technological building, the main façade parallel cable-driven robot in intended to work as a sensor for monitoring the environment, but also as an interface between the building and its occupiers. The various constraints—due to normative, structural and aesthetic reasons—that were tackled are described in the paper, along with the elected detailed design of the robot that complies with these constraints.

Since few years, wire robots are making their way into industrial application. Besides the continuation of research in the fields of kinematics and dynamics modeling, control, workspace analysis, and design, new challenges like robustness, energy efficiency and maturity arise due to practical requirements. This holds especially true for the actuation and deflection components of the system. In the past, a wide range of actuation and deflection concepts were presented. Within this contribution, at first known ideas of deflection concepts are reviewed and compared. In the following, a new deflection concept using passively guided skids is presented which homogenizes the load capabilities of a wire robot over its workspace. Subsequently, new approaches optimizing the energy consumption based on the installation of counterweights and pre-stressed springs are discussed. Using those passive elements, not only static pre-tension can be generated but, in the case of using springs, also dynamic motions can be boosted by using the eigenmotions of the oscillator consisting of the end effector and the attached springs. The paper describes both the theoretical background as well as simulation results for eigenmotion utilization showing that the concept is capable of drastically reducing wire forces generated by the active components, i.e. the motors, for a given task.

High strength fibre ropes are facing a strongly increasing interest for rope driven applications. Basic characteristics such as strength are already competitive or even outperforming wire ropes; however other limitations still prevent their full reliable industrial use. One particular application where the advantages of high strength fibre ropes do have an extraordinary important effect on the usability of the application is the use in robot systems with multi-rope kinematics. Basic requirements of these systems are (among others) high accuracy paired with a high efficiency, which means high process velocities as well as high accelerations and decelerations. Many tests have already been conducted to simulate a wide range of load settings—however up to date testing of fibre ropes in high speed usage is still mostly missing. This article describes the state of the art of high strength fibre rope usage in material handling, discusses advantages and disadvantages of these ropes and points out the most important challenges for research and improvement of rope driven robot systems.

The idea of multi-body cable-driven mechanisms is an extension of the original cable robots where the moving platform is replaced by a multi-body. Cables with variable lengths are attached between the fixed base and the links of the multi-body to provide the motion. There are possible applications for such mechanisms where complex motions as well as low moving inertia are required. One of the main challenges with such mechanisms is the high chance of interference between the cables or between the cables and the links of the multi-body mechanism. This can further reduce the usable workspace. In this article, the idea of adding passive cables in series with springs (spring cable) to improve the workspace is investigated. The spring cables can be added between the multi-body and ground or between the links. The idea is applied to a two-link planar multi-body cable-driven mechanism. The wrench feasible workspace (WFW) is found using the interval analysis. The WFW is shown to improve both in shape and volume.

The wrench-closure workspace (WCW) of cable-driven parallel mechanisms is the set of poses for which any wrench can be produced at the end-effector by a set of positive cable tensions. In this paper, we tackle the dimensional synthesis problem of finding a geometry for a planar cable-driven parallel mechanism (PCDPM) whose constant orientation wrench closure workspace (COWCW) contains a prescribed workspace. To this end, we first introduce a linear program to verify whether a given pose is inside or outside the WCW of a given PCDPM. The relaxation of this linear program over a box leads to a nonlinear feasibility problem that can only be satisfied when this box is completely inside the COWCW. We extend this feasibility problem to find a PCDPM geometry whose COWCWs include a given set of boxes. These multiple boxes may represent an estimate of the prescribed workspace, which may be obtained through interval analysis. Finally, we introduce a nonlinear program through which the PCDPM geometry is changed while maximizing the scaling factor of the prescribed set of boxes. When the optimum scaling factor is greater or equal to one, the COWCW of the resulting PCDPM contains the set of boxes. Otherwise, the COWCW generally offers a good coverage of the set of boxes.

The kinematic sensitivity has been recently proposed as a unit-consistent performance index to circumvent several shortcomings of some notorious indices such as dexterity. This paper presents a systematic interval approach for computing an index by which two important kinematic properties, namely feasible workspace and kinematic sensitivity, are blended into each other. The proposed index may be used to efficiently design different parallel mechanisms, and cable driven robots. By this measure, and for parallel manipulators, it is possible to visualize constant orientation workspace of the mechanism where the kinematic sensitivity is less than a desired value considered by the designer. For cable driven redundant robots, the controllable workspace is combined with the desired kinematic sensitivity property, to determine the so-called feasible kinematic sensitivity workspace of the robot. Three case studies are considered for the development of the idea and verification of the results, through which a conventional planar parallel manipulator, a redundant one and a cable driven robot is examined in detail. Finally, the paper provides some hints for the optimum design of the mechanisms under study by introducing the concept of minimum feasible kinematic sensitivity covering the whole workspace.

This paper studies the direct geometrico-static analysis of under- constrained cable-driven parallel robots with 3 cables. The task consists in finding all equilibrium configurations of the end-effector when the cable lengths are assigned. An interval-analysis-based procedure is proposed to numerically find the real solutions of the problem for a robot of generic geometry. Three equation sets obtained by different approaches are implemented in the problem-solving algorithm and a comparison between the main merits and drawbacks of each one of them is reported.

This paper studies the direct geometrico-static problem of under- constrained parallel robots suspended by \(4\) cables. The task consists in determining the end-effector pose and the cable tensions when the cable lengths are assigned. The problem is challenging, because kinematics and statics are coupled and they must be solved simultaneously. An effective elimination procedure is presented that provides the complete solution set, thus proving that, when all cables are in tension, 216 potential solutions exists in the complex field. A least-degree univariate polynomial free of spurious factors is obtained in the ideal governing the problem and solutions are numerically computed via both an eigenvalue formulation and homotopy continuation. Equilibrium configurations with slack cables are also considered.

This paper describes the implementation of extended pulley kinematics for parallel cable robots. An algorithm for the extended kinematics taking into account cable pulleys is discussed and implemented in real-time. This solution uses an iterative solver which can be computationally costly, depending on convergence. The convergence was tested for a specific geometry and successfully implemented on the cable robot IPAnema. Accuracy of both the standard and extended kinematics were tested according to the ISO 9283 standard. The Absolute accuracy was measured to be 22.32 mm for the standard and 17.50 mm for the extended kinematics which shows some improvement. A method for testing accuracy of orientations is also introduced.

This paper proposes a methodology for the identification of the combined kinematic and dynamic parameters of a 6-Degrees of Freedom (6-DoF) Cable-Driven Parallel Robots (CDPRs) model. This methodology aims to ensure that the errors on the kinematic parameters do not affect the performances of the dynamic parameters estimation step. The proposed methodology has been implemented on a 6-DoF INCA robot. The identified model fits the system behaviour with good accuracy, and should then be used for the synthesis and analysis of kinematic and dynamic position / vision control strategies.

In this paper the differential kinematics for cable-driven robots is derived and the use for calibration, system investigation and a force based forward kinematics is shown. The Jacobians for each part of the kinematic chain are derived with respect to the platform pose and the most important system parameters. Beside the consideration of geometrical quantities, the differential relations between non-geometrical quantities such as cable stiffness and cable forces are determined. The decomposition in the most fundamental Jacobians allows to analyse and compute more complex relations by reassembling the Jacobians as needed. This approach allows more insight in the system behavior and enables the reuse of the individual modules. The purpose of this paper is to provide the framework and the key equations and to show the use for calibration, force based forward kinematics and system analysis as well as for control purposes.

In this paper dynamic analysis and experimental performance of robust PID control for fully-constrained cable driven robots are studied in detail. Since in this class of manipulators cables should remain in tension for all maneuvers through their whole workspace, feedback control of such robots becomes more challenging than conventional parallel robots. To ensure that all the cables remain in tension, a corrective term is used in the proposed PID control scheme. In design of PID control it is assumed that there exist bounded norm uncertainties in Jacobian matrix and in all dynamics matrices. Then a robust PID controller is proposed to overcome partial knowledge of robot, and to guarantee boundedness of tracking errors. Finally, the effectiveness of the proposed PID algorithm is examined through experiments and it is shown that the proposed control structure is able to provide suitable performance in practice.

This paper reports preliminary investigations for H\(_\infty \) control of cable-driven parallel robot. This methodology specially suits for multi-input multi-output systems including flexible modes, which is the case of cable robots with flexible cables. A nonlinear model is first developed accounting for flexible cables for the case where actuators are speed controlled. A first method based on a rigid model is proposed as an adaptation for speed-controlled actuators of the well-known Jacobian-based method. A low-pass filter is tuned in order to increase the reachable bandwidth. The H\(_\infty \) controller is derived from a linear dynamic model. One interest is that one single controller manages both the position of the end-effector and the cable tension. The simulation results show that improvements are possible in the bandwidth thanks to the H\(_\infty \) control.

The kinematically indeterminate cable suspension manipulator Cablev moves a payload platform in space by three spatially arranged cables with independently controllable winches. As the position of the platform is not fully determined by the lengths of the cables, undesired sway motions of the payload platform may occur. To make the payload platform track prescribed translational and rotational reference trajectories in space, a two-stage control concept is presented. A nonlinear feedforward control that exploits the flatness property of the system generates control inputs for the undisturbed motion along reference trajectories. Sway motions caused by disturbances are actively damped by a linear feedback of measured state variables enabling an asymptotically stable tracking behaviour. Experimental results from the prototype system Cablev are shown.

The mass of the cables is not considered in most existing research on cable-driven mechanisms (CDM). Moreover, of those papers where cable mass is considered, few have examined its effects on mechanism stiffness. The research presented herein seeks to better understand these effects with regards to a planar two-degree-of-freedom suspended CDM. The mechanism’s stiffness matrix is first developed and then used to generate mappings of intuitive stiffness indices over the workspace. The sagging of the cables under their own weight is found to heavily influence mechanism stiffness. The importance of maintaining a minimum level of cable tension to minimize the effect of cable sagging on the mechanism’s stiffness and workspace is also demonstrated.

A Five Hundred meter Aperture Spherical radio Telescope (FAST) is being built in China, and a similarity model was set up in Beijing for further study of FAST. In FAST, A six-cable driven parallel manipulator is adopted as the first level adjustable feed support system. This paper addresses the complete modeling method of the six-cable driven parallel manipulator of FAST with cable mass and elastic deformation. Comparing with the precise catenary modeling equation, modeling and solution of line equation is easier and quicker, but has modeling error for cable driven parallel manipulator. Hence, analysis and compensation method of the modeling error is studied in detail, which encourages the line equation to model and solve the six-cable driven parallel manipulator accurately. Finally, simulation and experiment have been done for supporting the modeling and error compensation methods in this paper.

Cable-driven parallel manipulator is one of the best solutions for large workspace applications. But when long-span cables are involved the effect of cable vibration on the positioning precision of the end-effector should be carefully evaluated since these cables are prone to vibration, degrading the performance of manipulators. In this paper a dynamic model of cable-driven parallel manipulators is presented where each cable is divided into several elements to account for cable vibration. A simple linear cable element is presented where nodal force is related to both nodal position and element length to involve the effect of cable length variation. Numerical examples are presented to demonstrate the effect of cable vibration. The results show that it is necessary to take into consideration cable dynamics for manipulators operating at high speed and vibration of cables can shorten their corresponding chord length.