Redundant Cable-driven Parallel Robot Research Articles

A Fast solution method for end-effector force extremum in redundant cable-driven parallel robots

A Fast solution method for end-effector force extremum in redundant cable-driven parallel robots

Comparison of internal force antagonism between redundant cable-driven parallel robots and redundant rigid parallel robots

Comparison of internal force antagonism between redundant cable-driven parallel robots and redundant rigid parallel robots

Research on workspace visual-based continuous switching sliding mode control for cable-driven parallel robots

AbstractAchieving the high-precision control of cable-driven parallel robots (CDPRs) is complex because of their structural properties. In this paper, a quintessential redundant CDPR is designed as the research subject, and a continuous switching sliding mode controller based on workspace vision is implemented to enhance the accuracy and stability of trajectory tracking. In addition, a virtual prototype of the CDPR with uncertainties is created in the simulation analysis software ADAMS, and co-simulation is performed with the control system designed in Simulink to validate the effectiveness of the proposed control strategy. Furthermore, a CDPR platform is established for trajectory tracking experiments using the visual-based position feedback method. The trajectory tracking performance with the three control schemes is then evaluated. The experimental results show that the continuous switching sliding mode control algorithm can significantly decrease trajectory tracking errors and exhibit superior trajectory tracking performance compared to the other control strategies.

Cable failure tolerant control and planning in a planar reconfigurable cable driven parallel robot.

The addition of geometric reconfigurability in a cable driven parallel robot (CDPR) introduces kinematic redundancies which can be exploited for manipulating structural and mechanical properties of the robot through redundancy resolution. In the event of a cable failure, a reconfigurable CDPR (rCDPR) can also realign its geometric arrangement to overcome the effects of cable failure and recover the original expected trajectory and complete the trajectory tracking task. In this paper we discuss a fault tolerant control (FTC) framework that relies on an Interactive Multiple Model (IMM) adaptive estimation filter for simultaneous fault detection and diagnosis (FDD) and task recovery. The redundancy resolution scheme for the kinematically redundant CDPR takes into account singularity avoidance, manipulability and wrench quality maximization during trajectory tracking. We further introduce a trajectory tracking methodology that enables the automatic task recovery algorithm to consistently return to the point of failure. This is particularly useful for applications where the planned trajectory is of greater importance than the goal positions, such as painting, welding or 3D printing applications. The proposed control framework is validated in simulation on a planar rCDPR with elastic cables and parameter uncertainties to introduce modeled and unmodeled dynamics in the system as it tracks a complete trajectory despite the occurrence of multiple cable failures. As cables fail one by one, the robot topology changes from an over-constrained to a fully constrained and then an under-constrained CDPR. The framework is applied with a constant-velocity kinematic feedforward controller which has the advantage of generating steady-state inputs despite dynamic oscillations during cable failures, as well as a Linear Quadratic Regulator (LQR) feedback controller to locally dampen these oscillations.

Initial-Pose Self-Calibration for Redundant Cable-Driven Parallel Robot Using Force Sensors Under Hybrid Joint-Space Control

This letter investigates initial-pose estimation (Cartesian position and orientation) for redundant cable-driven parallel robots (CDPRs). As the forward kinematics cannot be performed if the robot is equipped with incremental sensors, a calibration method using force sensors is proposed. The self-calibration problem is formulated as a non-linear least-squares optimization problem based on the hybrid joint-space control strategy. The redundant cables are tension-controlled; the other cables are maintained at a fixed length in the joint space. A position-determined cable adjustable force (P-CAF) performance index and the concept of calibratable space were proposed to maintain the quasi-static conditions. A simulated case study was used to validate the calibration process.

Rapid and safe wire tension distribution scheme for redundant cable-driven parallel manipulators

AbstractA non-iterative analytical approach is investigated to plan the safe wire tension distribution along with the cables in the redundant cable-driven parallel robots. The proposed algorithm considers not only tracking the desired trajectory but also protecting the system against possible failures. This method is used to optimize the non-negative wire tensions through the cables which are constrained based on the workspace conditions. It also maintains both actuators’ torque and cables’ tensile strength boundary limits. The pseudo-inverse problem solution leads to an n-dimensional convex problem, which is related to the robot degrees of redundancy. In this paper, a comprehensive solution is presented for a 1–3 degree(s) of redundancy in wire-actuated robots. To evaluate the effectiveness of this method, it is verified through an experimental study on the RoboCab cable robot in the infinity trajectory tracking task. As a matter of comparison, some standard methods like Active-set and sequential quadratic programming are also presented and the average elapsed time for each method is compared to the proposed algorithm.

Analysis of Reachable Workspace for Spatial Three-Cable Under-Constrained Suspended Cable-Driven Parallel Robots

Abstract The workspace is an important reference for designs of cable-driven parallel robots (CDPRs). Most current researches focus on calculating the workspace of redundant CDPRs. However, few literature study the workspaces of under-constrained CDPRs. In this paper, the static equilibrium reachable workspaces (SERWs) of spatial 3-cable under-constrained CDPRs are solved numerically since expressions describing workspace boundaries cannot be obtained in closed forms. The steps to solve the SERWs are as follows. First, expressions that describe the SERWs and their boundaries are proposed. Next, these expressions are instantiated through a novel anchor points model composed of linear equations, quadratic equations, and tension limits in cables. Then, based on the reformulated linearization technique (RLT), the constraints system is transformed into a system containing only linear equality constraints and linear inequality constraints. Finally, the framework of the branch-and-prune (BP) algorithm is adopted to solve this system. The effect of the algorithm is verified by two examples. One is searching the SERWs boundaries of a special three-cable-driven parallel robot (CDPR) whose anchor points layouts both on the moving platform (MP) and on the base are equilateral triangles, followed by a method to extract the SERW boundary where cables do not interfere with each other. The other is searching the SERWs boundaries of a general three-cable CDPR with randomly selected geometry arrangement. The presented method in this paper is universal for calculating the SERWs of spatial three-cable CDPRs with arbitrary geometry parameters.

Analysis of stiffness controllability of a redundant cable-driven parallel robot based on its configuration

To examine the influence of the configuration of a cable-driven parallel robot (CDPR) on its stiffness and stiffness controllability, a concept for a cable tension constraint workspace (CTCW) of CDPRs is introduced. Using a static force analysis, a static CDPR model was established and its stiffness model and a method for optimizing the cable tension were reviewed. To analyze and appraise the CDPR global and local stiffness controllability, a new concept of stiffness controllability degree is proposed and defined. In addition, a calculation method is proposed that uses the cable tension feasible region to effectively obtain the CTCW of the CDPRs according to the cable tension constraint condition. The driving cable layouts of the various CDPR configurations were optimized to maximize the CTCW volume as a performance index. In addition, the stiffness and stiffness controllability of each configuration CDPR were analyzed. The results of the theoretical and experimental analyses validated the efficacy of the presented method and serve as reference for the use of robots in practical applications or for design optimization.

Direct method for tension feasible region calculation in multi-redundant cable-driven parallel robots using computational geometry

With a low moving inertia, high payload-to-weight ratio, and large workspace, cable-driven parallel robots (CDPRs) are relevant in many applications, especially redundant CDPRs. As there exist an infinite number of tension distributions, this paper presents a novel computational geometry-based method to calculate a tension feasible region (TFR)—a preimage of tension distribution—for multi-redundant CDPRs. The proposed TFR algorithm overcomes some of the limitations of conventional iterative and vertices search methods. The TFR is first interpreted as a convex intersection of multiple boundary-parallel spaces, where its dimension is equal to redundancy r. To obtain the centroid of TFR, the vertices coordinates and order for r = 2 and 3 only need to be determined on surface. Static simulations with 6 degrees-of-freedom using 8-cable and 9-cable CDPRs are employed to demonstrate the algorithmic accuracy. Additionally, to illustrate that the optimal tension distribution has continuity, motion trajectories for the same CDPRs are calculated. Furthermore, the proposed algorithm minimizes computational time when compared to the performance of existing algorithms. Thus, the proposed method could rapidly establish the optimal tension distribution.

Effect of selection criterion on the kineto-static solution of a redundant cable-driven parallel robot considering cable mass and elasticity

Cable mass and elasticity play a prominent role in analyzing large-scale cable-driven parallel robots (CDPR). However, for catenary cables (i.e., cables with mass and elasticity), the inverse kinematics of CDPR becomes a non-linear kineto-static problem. Furthermore, for redundant CDPR, this leads to multiple kineto-static solutions. This paper focuses on investigating various selection criteria to determine a unique kineto-static solution for the redundant over-constrained CDPR. For this investigation, the effect of the proposed selection criteria on sagging, elastic elongations and cable tensions are analyzed. Appropriate selection criteria, according to the application requirements, are proposed. Additionally, a rigorous study is done to analyze the effect of considering conventional cable models (i.e., massless rigid and massless elastic cable model) instead of the catenary cable model for various payloads, cables, and selection criteria. This helps in determining when a massless rigid/elastic cable model can be used as an alternative to the catenary cable model, which in turn, can avoid the additional computational complexity. The proposed analysis is beneficial in appropriate selection of actuators, cables, selection criteria and model complexity for a given redundant CDPR.

Exact Kinematic Modeling and Identification of Reconfigurable Cable-Driven Robots With Dual-Pulley Cable Guiding Mechanisms

Cable guiding mechanisms (CGMs) directly influence the reconfigurability of cable-driven parallel robots (CDPRs). But due to the complicated kinematic model of pulley-based CGMs, the velocity and acceleration mappings from the moving platform (MP) to the cables were unknown, the continuity of cable velocity, acceleration, and tension was unguaranteed, and the calibration pose-search method was based on inaccurate CGM models. In this paper, we establish an analytic and compact model for CGM. Based on this model, the velocity and acceleration mappings from the MP to the cables are derived. The continuities of cable trajectory and tension are proved. The exact identification Jacobian and its derivative are also formulated, leading to the increased fidelity of pose-search methods. The proposed method and formulations are verified by simulations and experiments on a redundant CDPR.

Calculation and Analysis of Constant Stiffness Space for Redundant Cable-Driven Parallel Robots

In this paper, a new concept of the constant stiffness space (CSS) of cable-driven parallel robots (CDPRs) is presented to meet the requirement for the constant stiffness plane of CDPRs in ground simulation spacecraft landing addressing experiments. First, the previously studied stiffness model and cable tension feasible region are reviewed. Then, the concept of the stiffness relative contribution coefficient is proposed, which can directly reflect the influence of controllable stiffness on system stiffness and guide the selection of driving cables and the setting of cable tension limiting values. Further, a method to calculate the CSS is proposed. This method can effectively obtain the CSS of robots according to the target stiffness. Next, an evaluation index for the local and global stability of the CSS is presented to analyze and evaluate the stability of the CSS of CDPRs. The influences of the load and posture of the end-effector of a CDPR on the volume and stability of the CSS are analyzed. The analysis results can serve as guidelines for determining the CSS in practical applications. The correctness and efficacy of the proposed method are verified through the experimental and theoretical analyses. The results show that the proposed method is computationally efficient and can obtain the CSS of CDPRs within a given accuracy range.

Research on Controllable Stiffness of Redundant Cable-Driven Parallel Robots

In this paper, to solve the problem of variable stiffness of cable-driven parallel robots (CDPR), a new static stiffness analysis and cable tension distribution method are proposed for studying the CDPRs’ controllable stiffness. First, a three-dimensional Hessian matrix of the structure matrix to position differential is deduced by introducing a line vector and differential transform, and a static stiffness model is established for analyzing the relationship between cable tension and the stiffness of the robots. Furthermore, a calculation algorithm for cable tension polygons based on Graham's Scan is introduced that effectively obtains the cable tension feasible region (CTFR) of CDPRs. Next, a method involving “the relationship between the external force and the pose change value of the moving-platform” is proposed to measure the variation of system stiffness. The CDPR's controllable stiffness is also analyzed based on the CTFR by considering the variation of each driving-cable's tension and each component of the moving-platform's pose. The results of experimental and theoretical analyses verify the correctness and efficacy of the proposed method. In addition, they show that the proposed method is computationally efficient and easily establishes the relationship between cable tension and the CDPR's controllable stiffness.

Explicit dynamics of redundant parallel cable robots

Precise model-based control of parallel robots necessitates an analytically accurate and consolidated model of the robotic platform. Lack of accuracy in modeling causes lots of dynamic uncertainties. This fact can result in higher control gains and efforts. Furthermore, imposing modification for optimization purposes is implausible without the derivation of an exact model. Hence, in this paper an elaborative kinematical and dynamical model of redundant cable-driven parallel robots is studied. In fact, a general procedure for modeling of cable-actuated parallel robots is presented to tackle down the difficulties for model-based control. The presented dynamic modeling approach rigorously enumerates the kinematics of robot winches and pulleys. The intrinsic behavior of cables is represented with a linear spring and damper having variable mass and constant density in the workspace. To this end, sagging in cables is neglected as a computationally intractable effect with insignificant impact on robot’s dynamics. Next, model validation is carried out within an experimental study of a redundant cable-driven parallel robot, the RoboCab which is designed and manufactured in Advanced Robotics and Automated Systems (ARAS) Lab. Experimental results reveal the merits and capabilities of proposed model to capture the explicit dynamics of robot. Results also demonstrate the high rate of flexibility and applicability of model for dealing with diverse control applications.

Vibration Decoupled Modeling and Robust Control of Redundant Cable-Driven Parallel Robots

Trajectory tracking and vibration control of redundant cable-driven parallel robots (CDPR) attracted the attention of different researchers; however, the effects of the CDPRs end-effectors disturbing force/moment on the undesired vibrations and minimization of such effects has received few attention. A new general dynamic modeling and robust control structure for redundant CDPR is proposed in this paper, which evaluates such factors and tries to minimize their effects on the performance of CDPRs. Considering the effects of redundant cables on the CDPRs’ stiffness improvement, we neglect the second and higher order terms of motion errors that helps to separate the moving platform's undesired vibration equation from its desired (nominal) equation of motion. The obtained vibration model forms a linear parametric variable (LPV) dynamic system that lets us investigate the effects of external disturbances on the undesired vibration in different directions, and use a wide class of well-established robust and optimal vibration control techniques. Consequently, in order to minimize the effect of disturbances on the moving platform trajectory tracking performance, a robust and optimal vibration compensator is designed using the $LPV-H_\infty$ control design techniques. Based on the platform's desired trajectory, the proposed control scheme calculates the cables’ nominal tension required for trajectory tracking and further generates the auxiliary signals to augment these tensions to counteract the undesirable vibrations. Based on the obtained dynamic model, the developed approach is simplified for kinematically-constrained redundant CDPRs as a new actuation method with restricted rotational degrees of freedom. Via numerical analysis and experimental tests of a planar kinematically-constrained CDPR, the proposed modeling and robust control design approach are examined and compared with other common control design methodologies. Moreover, the effectiveness of kinematically-constrained actuation method in vibration elimination and control design simplification of CDPRs is demonstrated.

Finding Measurement Configurations for Accurate Robot Calibration: Validation With a Cable-Driven Robot

It is well known that, by properly selecting the measurement configurations in robot calibrations, the observability index of unknown parameters can be maximized, leading to high calibration accuracy. For this purpose, many configuration-search methods were proposed. However, the established methods were mainly based on derivative-free or metaheuristic techniques, whose computational costs were high. Moreover, the robustness of observability index and convergences of configuration searches were not investigated. In this paper, by extending a recent result in matrix perturbation theory to robot kinematics, we establish the closed-form mapping from configuration perturbations to singular-value variations. Based on this mapping, an efficient configuration-search method is proposed, the robustness of the observability index under bounded configuration perturbations is analyzed, and the convergence of configuration searches is studied. The proposed methods were validated by simulations on serial and parallel robots. With roughly estimated initial parameters, self-calibration experiments on a redundant cable-driven parallel robot were performed. The effectiveness of the proposed methods is demonstrated by the experiment results.

Kinematically-Constrained Redundant Cable-Driven Parallel Robots: Modeling, Redundancy Analysis, and Stiffness Optimization

This paper develops a general model for kinematically-constrained redundant cable-driven parallel robots (CDPRs), and studies stiffness improving effects and redundancy resolution of such robots aiming stiffness optimization to minimize their undesired perturbations under external disturbances in a desired direction. In the developed model, assuming an axially flexible model for the cables, motion equation is derived. Considering the role of constrained cables in restriction of CDPR's rotational degrees of freedom, the vibration equation of the moving platform is separated from the equation of motion. The resulted vibration equation is a linear dynamic system with a stiffness matrix formed by the cables’ tension and the constrained cables’ axial stiffness. Based on that, the substantial effects of constrained cables and the potential effects of cables’ tension on the stiffness improvement of CDPRs are shown. Accordingly, the cables’ tension redundancy problem is formulated. Redundancy resolution is studied considering the directional stiffness of the moving platform as the objective function to maximize. This objective function is derived as a linear function of cables’ redundant tensions and the corresponding redundancy problem solved by using a time-efficient method of linear programming. The developed model and the proposed redundancy resolution approach are experimentally tested on an actual warehousing robot to maximize its translational stiffness. Comparison of theoretical and experimental results demonstrates the validity of the proposed optimization approach and the effectiveness of kinematically-constrained actuation method.

Adaptive Vibration Control of a Flexible Cable Driven Parallel Robot

A cable-driven parallel robot (CDPR) possesses significant advantages over common rigid-link mechanisms including: large workspace, low inertia, small size actuators, and high speed motion. However, CDPRs have considerable restrictions consist of: holding tension in all cables, cables axial flexibility, and mechanism low rigidity resulting in mechanism undesired vibrations. In majority of previous studies related to redundant CDPRs control, the cables’ flexibility is assumed negligible and redundancy problem is solved regardless of mechanism stiffness. Vibration control of a new flexible redundant kinematically-constrained CDPR with warehousing applications is studied in this research. In proposed methods, for minimization of undesired vibrations, the CDPR redundancy problem is solved based on maximizing its stiffness. Proposed controllers are designed based on linear methods of pole placement and also linear quadratic regulation (LQR) technique. Transforming the designed controllers to adaptive ones has shown performance improvements in case of moving platform mass and inertia uncertainty. Simulations results show robustness and high performance of designed controllers beside practicality of the inputs.