Spatial Cable-driven Parallel Robots Research Articles

Design and performance investigation of a sliding-mode adaptive proportional–integral–derivative control for cable-breakage scenario

AbstractControlling a cable-driven parallel robot (CDPR) when a cable breaks is challenging. In this paper, a sliding mode adaptive PID control is designed to ensure a safe guidance of the load when a cable fails. Indeed, regardless when a cable breaks, this control makes it possible enchanting the guidance of the load inside the remaining wrench feasible workspace. In other words, it allows reducing the load oscillation and then increasing the safety of the recovery manoeuvre. Performances are evaluated through simulations by considering a spatial CDPR and comparing the results with a PID control.

Type Synthesis of a 3DOF Wrist Applying the Coupled-Input Cable-Driven Parallel Robot

Abstract The spatial cable-driven parallel robots (CDPRs) with low DOF (degree-of-freedom; n < 6) are like the physiological structure of bone and muscles, which are suitable for designing humanoid joints. Therefore, the type synthesis of the CDPR is of great interest for the design of new humanoid wrist joints. In this paper, we present a type synthesis of the coupled-input CDPRs to design a 3DOF wrist. Coupled input means that one actuator controls more than one cable. First, the Yamanouchi symbols of the coupled-input CDPRs are listed using the permutation group. In addition, two winding methods for the cable and the actuator are defined in the coupled-input CDPRs. Finally, a topology configuration of the coupled-input CDPR suitable for the 3DOF wrist model is determined based on a comparative analysis of the workspaces of a class of coupled-input CDPRs. It is shown that type synthesis of the coupled-input CDPRs is an effective way to innovate low DOF CDPRs.

Available wrench set robustness under hybrid joint-space control to uncertain wrench for a cable-driven parallel robot

For a overconstrained cable-driven parallel robot (CDPR), the number of cables is more than the number of the moving platform degrees of freedom. Therefore, a hybrid joint-space control method is used, where as many cables as the moving platform degrees of freedom are kinematically controlled, and the redundant ones are tension controlled. However, the selection of which cables to tension control is not straightforward. This work aims at evaluating the maximum value of the resistance to the wrench deviation, while tension-controlling a chosen cable set, by computing a performance index called available wrench set robustness (AWSR). In this case, the wrench deviation refers to the difference between the actual wrench and the nominal model wrench, which is related to the wrench uncertainties influenced by elements such as varying mass, shifted centre of mass and environmental disturbances. Firstly, owing to the inhomogeneous wrench deviation, a normalization method was proposed. Based on this, geometrically, the AWSR is defined as the minimum distance from the nominal wrench to the hyperplane boundary of available wrench set. As an application example of a planar CDPR with four cables and a spatial CDPR with eight cables, a comparison with previous methods illustrated that the proposed method significantly increased the range of wrench deviation, and this avoids situations where the configuration is not feasible using the traditional method. Therefore, the proposed method is more suitable for uncertain wrenches.

On Research of Cable Tension Distribution Algorithm for Four Cables - Three DOF Planar Cable-Driven Parallel Robot

One of the main concerns in controlling the cable-driven parallel robot (CDPR) mechanism is dealing with the distribution of tension on each cable, which is critical to the operation of the entire cable system. It can be said that adjusting the cable tension will determine the power consumption of the motors and the stiffness of the structure. Therefore, the problem that needs to be solved is how to handle the cable tension when the end-effector moves throughout the entire workspace. The tension of each cable needs to be adjusted properly to ensure it remains the same. Moment and force act in a static state, keeping the kinematic position of the end moving platform from being deflected and the main purpose is to ensure that the robot achieves a rigid state and eliminates vibration when moving. Because of that essential demand, this article will refer to the Quadratic programming algorithm to solve the problem of tension distribution for the Planar Cable-Driven Parallel Robot consisting of 4 cables with 3 degrees of freedom. This article will be the foundation for applying this algorithm to an 8-cable robot with 6 degrees of freedom (Spatial Cable-Driven Parallel Robot for example). At the same time, in this article, the simulation results for the algorithm will also be presented in this paper.

A Review of Cable-Driven Parallel Robots: Typical Configurations, Analysis Techniques, and Control Methods

Cable-driven parallel robots (CDPRs) have applications in large workspaces and at high operating speeds, which necessitates considering the mass and elasticity of cables for accurate analyses of kinematics, dynamics, workspace, trajectory planning, and control. In this article, first, the typical CDPR configurations along with their application areas are summarized. Then, various approaches, such as optimizing cable and motor configurations or integrating additional elements to the structure of CDPRs that can be used for workspace geometry optimization, are discussed. Afterward, different models for the cables with mass and elasticity, such as Irvine’s sagging or spring dampers studied in the literature for integrating into the kinematics and dynamics equations, are reported. Later, along with reviewing different approaches for trajectory planning of planar and spatial CDPRs, advances in configuration optimization for collision-free trajectory planning are addressed. Finally, kinematic and dynamic control algorithms to handle the effect of mass and elasticity of the cables and robust and adaptive control algorithms to tackle structured and unstructured uncertainties, such as in the mass and moment of the moving platform (MP) and external disturbances, are reported.

Workspace-Based Model Predictive Control for Cable-Driven Robots

The control of cable-driven robots is challenging due to the system’s nonlinearity, actuation redundancy, and the unilaterally bounded actuation constraints. To solve this problem, a workspace-based model predictive control (W-MPC) scheme is proposed, which combines the online model predictive control with offline workspace analysis. Using the workspace, a set of convex constraints can be generated for a given reference trajectory. This can then be used to formulate a convex optimization problem for the online W-MPC. Meanwhile, strict recursive feasibility and stability are obtained by taking advantage of the predictive feature of MPC. To demonstrate the effectiveness of the proposed W-MPC, simulation was performed on a 2-link planar cable-driven robot and a spatial cable-driven parallel robot for both nominal and non-nominal scenarios. Hardware experiment was also carried out using a 3 degree-of-freedom planar cable robot. The results show that the controller is efficient and effective to perform motion tracking with the cable force constraints satisfied despite the existence of various model uncertainties.

Optimal wrench-closure configuration of spatial reconfigurable cable-driven parallel robots

In this paper, a method for computing the optimal actuation of reconfigurable cable-driven parallel robots is presented. By using this method, the imperfect ability in exerting torque and limited orientation workspace of these robots may be improved. In a cable-driven parallel robot with reconfigurability, the attachment points of cables on the base are adjusted with regard to the movement of the end-effector on a trajectory. In such a design the redundant degree-of-freedom of the robot is increased accordingly. For an arbitrary pose of the end-effector, a spherical zone is defined in which the called wrench-closure condition is satisfied for a prescribed range of orientation. Taking the volume of such zone into consideration the optimal configuration of the robot may be determined. This configuration is found by appropriately changing the position of the moving attachment points on the base of the robot. By repeating this computation for a number of points on a specified trajectory, appropriate actuation plans are achieved. The computed optimal actuation guarantees balance of any external wrench by tension force of cables when the end-effector moves close to its trajectory. For a case of spatial reconfigurable cable-driven parallel robot, the optimal actuation is found based on Particle Swarm Optimization and performance of the robot is compared to the one with fixed cable attachment points on base. The result shows significant improvement of the performance of reconfigurable spatial cable-driven parallel robot.

A novel modified analytical method and finite element method for vibration analysis of cable-driven parallel robots

Cable-driven parallel robots (CDPRs) are vulnerable to vibration due to the inevitable flexible properties of the cables. Thus, vibration analysis is critical for CDPR’s operation in which highly accurate motion is required. However, most of the current methods related to vibration analysis of CDPRs rely on simple spring models which have limitations in their performance and complexity that are not general to analyze the vibration of various CDPRs. Hence, accurate, simple and general approaches for vibration analysis in CDPRs are need. To solve this problem, this paper presents the finite element method (FEM) and the modified analytical method to analyze the vibration of CDPRs. To validate these methods, free vibration analysis was conducted using the proposed methods for the planar and spatial cable-driven parallel robots. The natural frequencies of these two CDPRs were computed by the proposed two methods and compared with those of the commercial software, SAP2000. The solutions obtained by the FEM and the modified analytical models turned out to be close to SAP2000’s results, thereby verifying the validity of the proposed methods.

Efficient Wrench-Closure and Interference-Free Conditions Verification for Cable-Driven Parallel Robot Trajectories Using a Ray-Based Method

This letter introduces a novel approach to verify the feasibility of curved trajectories under both the interference-free (IFC) and wrench-closure (WCC) conditions for spatial cable-driven parallel robots (CDPRs). Existing ray-based methods can only be used either for translation or single degree-of-freedom (DoF) motion, limiting its use to verify the motion of practical trajectories. In this work, the trajectory representation proposed allows the IFC and WFC for the entire trajectory to be verified by simply solving a set of univariate polynomial equations. The translation motion is expressed as polynomial time parametric functions and the orientation motion is defined using a spherical linear interpolation (SLERP) in the quaternion representation for a desired start and end orientation. It is then shown that for the proposed trajectory representation, the IFC and WFC can be verified by solving a set of univariate polynomial equations. Moreover, the exact degree of the resulting polynomial equations are derived for a 6-DoF spatial CDPR. Simulation on a range of different trajectory forms, from linear, quadratic and cubic paths to higher degree functions, show the effectiveness of the method. Finally, comparison with the well-accepted point-wise method shows that the proposed method is more efficient, accurate and ensures the solution continuity.

Precise end-effector pose estimation in spatial cable-driven parallel robots with elastic cables using a data fusion method

In this paper a new method for estimating the end-effector pose in the cable-driven parallel robots (CDPRs) with elastic cables is introduced. In many applications, the end-effector pose is determined considering the direct kinematic and motor rotations obtained from encoders. Since the cable flexibility in the CDPRs leads to the end-effector vibration, the fast dynamic movement, caused by the cable flexibility, cannot be observed using only motor rotation. The issues concerned with the other common sensors, include expensiveness, inaccuracy for vibration measurement and requiring precise cable model. In this study, an inertial measurement unit (IMU), mounted on the end-effector and consisted of accelerometer and gyro sensors, is employed to detect the vibrational states. Therefore, motor encoders observe the slow dynamic movement whereas IMU detects the fast dynamic movement of the end-effector. Since the measurements, particularly using IMU, include noise and bias, the Kalman approach is employed for the data fusion of two measurement systems. Employing the contextual information, the estimations obtained by the encoders, IMU and Kalman estimator are fused based on the degree of trust to each data. The Kalman filter (KF) is typically applied to linear or linearized systems. Therefore, using the Feedback Linearization (FL) control law the slow error dynamic of the system is linearized. Considering the rigid model basis of the controller, the necessary condition ensuring the flexible system stability is presented employing the Lyapunov stability criterion. In the first simulation, it is shown that using KF on the feedback data, the system divergence in the presence of measurement noise is prevented. In the second simulation, the effectiveness of the proposed data fusion approach in precise estimation of the end-effector pose is demonstrated. It is shown that the mean estimation error using the encoder-based method with respect to the data fusion approach is 1.6 and 12.7 for the position and angular vibration, respectively. Finally, an experimental test is provided to demonstrate the effectiveness of the proposed method.

Kinematic Isotropic Configuration of Spatial Cable-Driven Parallel Robots

In this paper, the authors study the kinematic isotropic configuration of spatial cable-driven parallel robots by means of four different methods, namely, (i) symbolic method, (ii) geometric workspace, (iii) numerical workspace and global tension index (GTI), and (iv) numerical approach. The authors apply the mentioned techniques to two types of spatial cable-driven parallel manipulators to obtain their isotropic postures. These are a 6-6 cable-suspended parallel robot and a novel restricted three-degree-of-freedom cable-driven parallel robot. Eventually, the results of isotropic conditions of both cable robots are compared to show their applications.