A Review on Cable-driven Parallel Robots

Cable-driven parallel robots(CDPRs) are categorized as a type of parallel manipulators. In CDPRs, flexible cables are used to take the place of rigid links. The particular property of cables provides CDPRs several advantages, including larger workspaces, higher payload-to-weight ratio and lower manufacturing costs rather than rigid-link robots. In this paper, the history of the development of CDPRs is introduced and several successful latest application cases of CDPRs are presented. The theory development of CDPRs is introduced focusing on design, performance analysis and control theory. Research on CDPRs gains wide attention and is highly motivated by the modern engineering demand for large load capacity and workspace. A number of exciting advances in CDPRs are summarized in this paper since it is proposed in the 1980 s, which points to a fruitful future both in theory and application. In order to meet the increasing requirements of robot in different areas, future steps foresee more in-depth research and extension applications of CDPRs including intelligent control, composite materials, integrated and reconfigurable design.

Analytical/Numerical Modelling of Two Parallel Robots as Laser Calibration Instruments Controlled by Classical/Intelligent Schemes

Industrial metrology deals with measurements in production environment. It concerns calibration procedures as well as control of measurement processes. Measuring devices have been evolving from manual theodolites, electronic theodolites, robotic total stations, to a relatively new kind of laser-based systems known as laser trackers. Laser trackers are 3D coordinate measuring devices that accurately measure large （and relatively distant） objects by computing spatial coordinates of optical targets held against those objects. In addition, laser trackers are used to align truthfully large mechanical parts. However, such aligning can be done in moving parts, for instance during robot calibration in a welding line. In this case, serial robots are controlled in order to keep a prescribed trajectory to accomplish its task properly. Nevertheless, in spite of a good control algorithm design, as time goes by, deviations appear and a calibration process is necessary. It is well known that laser tracker systems are produced by very well established enterprises but their laser products may result expensive for some （small） industries. We offer two parallel robot-based laser tracker systems models whose implementation would result cheaper than sophisticated laser devices and takes advantage of the parallel robot bondages as accuracy and high payload. The types of parallel robots evaluated were 3-SPS-1-S and 6-PUS. Modelling of the parallel robots was done by analytical and numerical techniques. The latter includes classical and artificial intelligence-based algorithms. The control performance was evaluated between classical and intelligent controllers.

Velocity Constraints Based Approach for Online Trajectory Planning of High‑Speed Parallel Robots

High-speed parallel robots have been extensively utilized in the light industry.However,the influence of the nonlinear dynamic characteristics of high-speed parallel robots on system’s dynamic response and stable operation cannot be ignored during the high-speed reciprocating motion.Thus,trajectory planning is essential for efficiency and stability from pick-and-place(PAP)actions.This paper presents a method for planning the equal-height pick-and-place trajectory considering velocity constraints to improve the PAP efficiency and stability of high-speed parallel robots.The velocity constraints in the start-and-end points can reduce vibration from picking and placing,making the trajectory more suitable to complex beltline situations.Based on velocity constraints,trajectory optimization includes trajectory smoothness and joint torque to optimize cycle time is carried out.This paper proposes an online trajectory optimization solution.By using back propagation(BP)neural networks,the solution is simplified and can be solved in real-time.Simulation and experiments were carried out on the SR4 parallel robot.The results show that the proposed method improves the efficiency,smoothness,and stability of the robot.This paper proposes an online trajectory planning method which is velocity constraints based and can improve the efficiency and stability of high-speed parallel robots.The work of this research is conducive to finely applying high-speed parallel robots.

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

The internal force antagonism(IFA)problem is one of the most important issues limiting the applications and popularization of redundant parallel robots in industry.Redundant cable-driven parallel robots(RCDPRs)and redundant rigid parallel robots(RRPRs)behave very differently in this problem.To clarify the essence of IFA,this study first analyzes the causes and influencing factors of IFA.Next,an evaluation index for IFA is proposed,and its calculating algorithm is developed.Then,three graphical analysis methods based on this index are proposed.Finally,the performance of RCDPRs and RRPRs in IFA under three configurations are analyzed.Results show that RRPRs produce IFA in nearly all the areas of the workspace,whereas RCDPRs produce IFA in only some areas of the workspace,and the IFA in RCDPRs is milder than that RRPRs.Thus,RCDPRs more fault-tolerant and easier to control and thus more conducive for industrial application and popularization than RRPRs.Furthermore,the proposed analysis methods can be used for the configuration optimization design of RCDPRs.

State-of-the-art on theories and applications of cable-driven parallel robots

Cable-driven parallel robot(CDPR)is a type of high-performance robot that integrates cable-driven kinematic chains and parallel mechanism theory.It inherits the high dynamics and heavy load capacities of the parallel mechanism and significantly improves the workspace,cost and energy efficiency simultaneously.As a result,CDPRs have had irreplaceable roles in industrial and technological fields,such as astronomy,aerospace,logistics,simulators,and rehabilitation.CDPRs follow the cutting-edge trend of rigid-flexible fusion,reflect advanced lightweight design concepts,and have become a frontier topic in robotics research.This paper summarizes the kernel theories and developments of CDPRs,covering configuration design,cable-force distribution,workspace and stiffness,performance evaluation,optimization,and motion control.Kinematic modeling,workspace analysis,and cable-force solution are illustrated.Stiffness and dynamic modeling methods are discussed.To further promote the development,researchers should strengthen the investigation in configuration innovation,rapid calculation of workspace,performance evaluation,stiffness control,and rigid-flexible coupling dynamics.In addition,engineering problems such as cable materials,reliability design,and a unified control framework require attention.

Linear quadratic optimal controller for cable-driven parallel robots

In recent years, various cable-driven parallel robots have been investigated for their advantages, such as low structural weight, high acceleration, and large work- space, over serial and conventional parallel systems. However, the use of cables lowers the stiffness of these robots, which in turn may decrease motion accuracy. A linear quadratic （LQ） optimal controller can provide all the states of a system for the feedback, such as position and velocity. Thus, the application of such an optimal controller in cable-driven parallel robots can result in more efficient and accurate motion compared to the performance of classical controllers such as the proportional-integral-derivative controller. This paper presents an approach to apply the LQ optimal controller on cabledriven parallel robots. To employ the optimal control theory, the static and dynamic modeling of a 3-DOF planar cable-driven parallel robot （Feriba-3） is developed. The synthesis of the LQ optimal control is described, and the significant experimental results are presented and discussed.

A Closed-Loop Dynamic Controller for Active Vibration Isolation Working on A Parallel Wheel-Legged Robot

Serving the Stewart mechanism as a wheel-legged structure,the most outstanding superiority of the proposed wheel-legged hybrid robot(WLHR)is the active vibration isolation function during rolling on rugged terrain.However,it is difficult to obtain its precise dynamic model,because of the nonlinearity and uncertainty of the heavy robot.This paper presents a dynamic control framework with a decentralized structure for single wheel-leg,position tracking based on model predictive control(MPC)and adaptive impedance module from inside to outside.Through the Newton-Euler dynamic model of the Stewart mechanism,the controller first creates a predictive model by combining Newton-Raphson iteration of forward kinematic and inverse kinematic calculation of Stewart.The actuating force naturally enables each strut to stretch and retract,thereby realizing six degrees-of-freedom(6-DOFs)position-tracking for Stewart wheel-leg.The adaptive impedance control in the outermost loop adjusts environmental impedance parameters by current position and force feedback of wheel-leg along Z-axis.This adjustment allows the robot to adequately control the desired support force tracking,isolating the robot body from vibration that is generated from unknown terrain.The availability of the proposed control methodology on a physical prototype is demonstrated by tracking a Bezier curve and active vibration isolation while the robot is rolling on decelerate strips.By comparing the proportional and integral(PI)and constant impedance controllers,better performance of the proposed algorithm was operated and evaluated through displacement and force sensors internally-installed in each cylinder,as well as an inertial measurement unit(IMU)mounted on the robot body.The proposed algorithm structure significantly enhances the control accuracy and vibration isolation capacity of parallel wheel-legged robot.

Error modeling of 3-RSR parallel robot based on D-H transformation matrix

By selecting any one limb of 3-RSR parallel robot as a research object, the paper establishes a position and orienta- tion relationship matrix between the moving platform and the base by means of Denavit-Hartenberg （D-H） transformation matrix. The error mapping model is derived from original error to the error of the platform by using matrix differential method. This model contains all geometric original errors of the robot. The nonlinear implicit function relation between po- sition and orientation error of the platform and the original geometric errors is simplified as a linear explicit function rela- tion. The results provide a basis for further studying error analysis and error compensation.

Optimal Design and Force Control of a Nine-Cable-Driven Parallel Mechanism for Lunar Takeoff Simulation

Traditional simulation methods are unable to meet the requirements of lunar takeo simulations, such as high force output precision, low cost, and repeated use. Considering that cable-driven parallel mechanisms have the advantages of high payload to weight ratio, potentially large workspace, and high-speed motion, these mechanisms have the potential to be used for lunar takeo simulations. Thus, this paper presents a parallel mechanism driven by nine cables. The purpose of this study is to optimize the dimensions of the cable-driven parallel mechanism to meet dynamic workspace requirements under cable tension constraints. The dynamic workspace requirements are derived from the kinematical function requests of the lunar takeo simulation equipment. Experimental design and response surface methods are adopted for building the surrogate mathematical model linking the optimal variables and the optimization indices. A set of dimensional parameters are determined by analyzing the surrogate mathematical model. The volume of the dynamic workspace increased by 46% after optimization. Besides, a force control method is proposed for calculating output vector and sinusoidal forces. A force control loop is introduced into the traditional position control loop to adjust the cable force precisely, while controlling the cable length. The e ectiveness of the proposed control method is verified through experiments. A 5% vector output accuracy and 12 Hz undulation force output can be realized. This paper proposes a cable-driven parallel mechanism which can be used for lunar takeo simulation.

Design, modeling, and evaluation of parallel continuum robots: A survey

Parallel continuum robots(PCRs) have attracted increasing attention in the robotics community due to their simplicity in structure,inherence with compliance, and easiness of realization. Over the past decade, a variety of novel designs have been reported to enrich their diversity. However, there is a lack of systematic review of these emerging robots. To this end, this paper conducts a comprehensive survey on the mechanism design, kinetostatic modeling and analysis, and performance evaluation. For these robots, kinetostatic modeling plays a fundamental role throughout the design, analysis, and control stages. A systematic review of the existing approaches for kinetostatic modeling and analysis is provided, and a comparison is made to distinguish their differences. As well, a classification is made according to the characteristics of structure and actuation. In addition, performance evaluation on the workspace, stability, and singularity is also overviewed. Finally, the scenarios of potential applications are elaborated, and future research prospects are discussed. We believe that the information provided in this paper will be particularly useful for those who are interested in PCRs.

Error Modeling and Sensitivity Analysis of a Parallel Robot with SCARA(Selective Compliance Assembly Robot Arm) Motions

Parallel robots with SCARA（selective compliance assembly robot arm） motions are utilized widely in the field of high speed pick-and-place manipulation. Error modeling for these robots generally simplifies the parallelogram structures included by the robots as a link. As the established error model fails to reflect the error feature of the parallelogram structures, the effect of accuracy design and kinematic calibration based on the error model come to be undermined. An error modeling methodology is proposed to establish an error model of parallel robots with parallelogram structures. The error model can embody the geometric errors of all joints, including the joints of parallelogram structures. Thus it can contain more exhaustively the factors that reduce the accuracy of the robot. Based on the error model and some sensitivity indices defined in the sense of statistics, sensitivity analysis is carried out. Accordingly, some atlases are depicted to express each geometric error’s influence on the moving platform’s pose errors. From these atlases, the geometric errors that have greater impact on the accuracy of the moving platform are identified, and some sensitive areas where the pose errors of the moving platform are extremely sensitive to the geometric errors are also figured out. By taking into account the error factors which are generally neglected in all existing modeling methods, the proposed modeling method can thoroughly disclose the process of error transmission and enhance the efficacy of accuracy design and calibration.

Multi-objective Optimization of a Parallel Ankle Rehabilitation Robot Using Modified Differential Evolution Algorithm

Dimensional synthesis is one of the most difficult issues in the field of parallel robots with actuation redundancy. To deal with the optimal design of a redundantly actuated parallel robot used for ankle rehabilitation, a methodology of dimensional synthesis based on multi-objective optimization is presented. First, the dimensional synthesis of the redundant parallel robot is formulated as a nonlinear constrained multi-objective optimization problem. Then four objective functions, separately reflecting occupied space, input/output transmission and torque performances, and multi-criteria constraints, such as dimension, interference and kinematics, are defined. In consideration of the passive exercise of plantar/dorsiflexion requiring large output moment, a torque index is proposed. To cope with the actuation redundancy of the parallel robot, a new output transmission index is defined as well. The multi-objective optimization problem is solved by using a modified Differential Evolution（DE） algorithm, which is characterized by new selection and mutation strategies. Meanwhile, a special penalty method is presented to tackle the multi-criteria constraints. Finally, numerical experiments for different optimization algorithms are implemented. The computation results show that the proposed indices of output transmission and torque, and constraint handling are effective for the redundant parallel robot; the modified DE algorithm is superior to the other tested algorithms, in terms of the ability of global search and the number of non-dominated solutions. The proposed methodology of multi-objective optimization can be also applied to the dimensional synthesis of other redundantly actuated parallel robots only with rotational movements.

Algebraic Method‑Based Point‑to‑Point Trajectory Planning of an Under‑Constrained Cable‑Suspended Parallel Robot with Variable Angle and Height Cable Mast

To avoid impacts and vibrations during the processes of acceleration and deceleration while possessing flexible working ways for cable-suspended parallel robots(CSPRs),point-to-point trajectory planning demands an under-constrained cable-suspended parallel robot(UCPR)with variable angle and height cable mast as described in this paper.The end-effector of the UCPR with three cables can achieve three translational degrees of freedom(DOFs).The inverse kinematic and dynamic modeling of the UCPR considering the angle and height of cable mast are completed.The motion trajectory of the end-effector comprising six segments is given.The connection points of the trajectory segments(except for point P3 in the X direction)are devised to have zero instantaneous velocities,which ensure that the acceleration has continuity and the planned acceleration curve achieves smooth transition.The trajectory is respectively planned using three algebraic methods,including fifth degree polynomial,cycloid trajectory,and double-S velocity curve.The results indicate that the trajectory planned by fifth degree polynomial method is much closer to the given trajectory of the end-effector.Numerical simulation and experiments are accomplished for the given trajectory based on fifth degree polynomial planning.At the points where the velocity suddenly changes,the length and tension variation curves of the planned and unplanned three cables are compared and analyzed.The OptiTrack motion capture system is adopted to track the end-effector of the UCPR during the experiment.The effectiveness and feasibility of fifth degree polynomial planning are validated.

Optimal Design of a 3-Leg 6-DOF Parallel Manipulator for a Specific Workspace

Researchers seldom study optimum design of a six-degree-of-freedom（DOF） parallel manipulator with three legs based upon the given workspace.An optimal design method of a novel three-leg six-DOF parallel manipulator（TLPM） is presented.The mechanical structure of this robot is introduced,with this structure the kinematic constrain equations is decoupled.Analytical solutions of the forward kinematics are worked out,one configuration of this robot,including position and orientation of the end-effector are graphically displayed.Then,on the basis of several extreme positions of the kinematic performances,the task workspace is given.An algorithm of optimal designing is introduced to find the smallest dimensional parameters of the proposed robot.Examples illustrate the design results,and a design stability index is introduced,which ensures that the robot remains a safe distance from the boundary of sits actual workspace.Finally,one prototype of the robot is developed based on this method.This method can easily find appropriate kinematic parameters that can size a robot having the smallest workspace enclosing a predefined task workspace.It improves the design efficiency,ensures that the robot has a small mechanical size possesses a large given workspace volume,and meets the lightweight design requirements.

Residual Vibration Reduction of High-Speed Pick-and-Place Parallel Robot Using Input Shaping

Because of their elastic links and joints,high-speed parallel robots for pick-and-place operations inevitably suffer from residual vibrations that significantly degrade their positioning accuracy.An effective approach based on the input shaping technique is presented in this paper for suppressing the residual vibration in these parallel robots.After addressing the design principle of an input shaper for a parallel robot with flexible actuated joints,a robust optimal input shaper is developed by considering the configuration-dependent flexible modes and minimizing the maximum percentage of residual vibration at the end-effector.The input shaper allows a good overall performance to be achieved throughout the entire workspace.Experimental results on a 4-DOF SCARA-type parallel robot show that the residual vibration of the end-effector is dramatically reduced and the dynamic positioning accuracy of the robot significantly improved.

Design considerations of high precision 6-HTRT parallel manipulator

Describes a new architecture of a parallel robot with six degrees of freedom and focuses on improving orientation accuracy of movable platform in mechanism, error correction and control methods. A set of formulations about inverse kinematics, Jacobin matrix, and forward kinematics for the high precision 6-HTRT parallel robots is presented. The analysis of errors existing in the manipulator is discussed and a novel approach for error correction is advanced. By DSP technique, inverse kinematics is solved in real time conditions with high precision and the hardware control system is given. The experimental results demonstrate the effectiveness of the proposed technique.

CONTINUATION METHOD APPLIED IN KINEMATICS OF PARALLEL ROBOT

Continuation method solving forward kinematics problem of parallel robot was discussed. And through a coefficient-parameter continuation method the efficiency and feasibility of continuation method were improved. Using this method all forward solutions of a new parallel robot model which was put forward lately by Robot Open Laboratory of Science Institute of China were obtained. Therefore it provided the basis of mechanism analysis and real-time control for new model.

Mechanics Unloading Analysis and Experimentation of a New Type of Parallel Biomimetic Shoulder Complex

The structure design for high ratio of carrying capacity to deadweight is one of the challenges for the bionic mechanism,while the problem concerning high carrying capacity has not yet be solved for the existing shoulder complex.A new type biomimetic shoulder complex,which adopts 3-PSS/S（P for prismatic pair,S for spherical pair） spherical parallel mechanism（SPM）,is proposed.The static equilibrium equations of each component are established by using the vector method and the equations for constrain forces with certain load are solved.Then the constrain force on the middle limb and that on the side limbs are compared in order to verify the unloading performance of the mechanism.In addition,the prototype mechanism of the shoulder complex is developed,and the force feedback experiment is conducted to verify the static analysis,which indicates that the middle limb suffers most of the external force and the effect of mechanics unloading is achieved.The 3-PSS/S spherical parallel mechanism is presented for the shoulder complex,and the realization of mechanics unloading is benefit for the improvement of the carrying capacity of the shoulder complex.

Study on singularity analysis with differential transform method for 3-RRUR parallel robot based on Jacobian matrix

Parallel robot is used in many different fields nowadays, but the singularity of 3-RRUR parallel robot is more complicated, so a method to analyze the singularity of the 3-RRUR parallel robot is very necessary. First, the Jacobian matrix was built based on the differential transform method through the transfer matrixes between the poles. The connection between the position parameters and singularity condition was built through the analysis of the Jacobian matrix. Second, the effect on the singularity from the position parameters was analyzed, and then the singularity condition was confirmed. The effect on the singularity condition from position parameters was displayed by the curved surface charts to provide a basic method for the designing of the parallel robot. With this method, the singularity condition could be got when the length of each link is firmed, so it can be judged that if a group of parameters are appropriate or not, and the method also provides warrant for workspace and path planning of the parallel robot.

Exact Computation of Parallel Robot's Generalized Inertia Matrix

According to the definition of the new hypothetical states which have obvious physical significance and are termed as no-gravity static and accelerated states, a method for exact computation of the parallel robot＇s generalized inertia matrix is presented. Based on the matrix theory, the generalized inertia matrix of the parallel robot can be computed on the assumption that the robot is in these new hypothetical states respectively. The approach is demonstrated by the Delta robot as an example. Based on the principle of the virtual work, the inverse dynamics model of the robot is formulized after the kinematics analysis. Finally, a numerical example is given and the element distribution of the Delta robot＇s inertia matrix in the workspace is studied. The method has computationa＇, advantage of numerical accuracy for the Delta robot and can be parallelized easily.