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.

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.

Type Synthesis of Self-Alignment Parallel Ankle Rehabilitation Robot with Suitable Passive Degrees of Freedom

The current parallel ankle rehabilitation robot(ARR)suffers from the problem of difficult real-time alignment of the human-robot joint center of rotation,which may lead to secondary injuries to the patient.This study investigates type synthesis of a parallel self-alignment ankle rehabilitation robot(PSAARR)based on the kinematic characteristics of ankle joint rotation center drift from the perspective of introducing"suitable passive degrees of freedom(DOF)"with a suitable number and form.First,the self-alignment principle of parallel ARR was proposed by deriving conditions for transforming a human-robot closed chain(HRCC)formed by an ARR and human body into a kinematic suitable constrained system and introducing conditions of"decoupled"and"less limb".Second,the relationship between the self-alignment principle and actuation wrenches(twists)of PSAARR was analyzed with the velocity Jacobian matrix as a"bridge".Subsequently,the type synthesis conditions of PSAARR were proposed.Third,a PSAARR synthesis method was proposed based on the screw theory and type of PSAARR synthesis conducted.Finally,an HRCC kinematic model was established to verify the self-alignment capability of the PSAARR.In this study,93 types of PSAARR limb structures were synthesized and the self-alignment capability of a human-robot joint axis was verified through kinematic analysis,which provides a theoretical basis for the design of such an ARR.

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.

Cable-Driven Parallel Robot Workspace Identification and Optimal Design Based on the Upper Limb Functional Rehabilitation

An assessment of the human motion repeatability for three selected Activities of Daily Living(ADL)is performed in this paper.These exercises were prescribed by an occupational therapist for the upper limb rehabilitation.The movement patterns of five participants,recorded using a Qualisys motion capture system,are compared based on the Analysis of Variance(ANOVA)method.This survey is motivated by the need to find the appropriate task workspace of a 6-degrees of freedom cable-driven parallel robot for upper limb rehabilitation,which is able to reproduce the three selected exercises.This comparison is performed to justify,whether or not,there is enough similarity between the participants’gestures,and so a single reference trajectory can be adopted as the robot-prescribed workspace.Using the results of the comparative study,an optimization process of the sought robot design is carried out,where the structure size and the cable tensions simultaneously minimized.

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.

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.

Kinematics and Dynamics Analysis of a Quadruped Walking Robot with Parallel Leg Mechanism

It is desired to require a walking robot for the elderly and the disabled to have large capacity,high stiffness,stability,etc.However,the existing walking robots cannot achieve these requirements because of the weight-payload ratio and simple function.Therefore,Improvement of enhancing capacity and functions of the walking robot is an important research issue.According to walking requirements and combining modularization and reconfigurable ideas,a quadruped/biped reconfigurable walking robot with parallel leg mechanism is proposed.The proposed robot can be used for both a biped and a quadruped walking robot.The kinematics and performance analysis of a 3-UPU parallel mechanism which is the basic leg mechanism of a quadruped walking robot are conducted and the structural parameters are optimized.The results show that performance of the walking robot is optimal when the circumradius R,r of the upper and lower platform of leg mechanism are 161.7 mm,57.7 mm,respectively.Based on the optimal results,the kinematics and dynamics of the quadruped walking robot in the static walking mode are derived with the application of parallel mechanism and influence coefficient theory,and the optimal coordination distribution of the dynamic load for the quadruped walking robot with over-determinate inputs is analyzed,which solves dynamic load coupling caused by the branches’ constraint of the robot in the walk process.Besides laying a theoretical foundation for development of the prototype,the kinematics and dynamics studies on the quadruped walking robot also boost the theoretical research of the quadruped walking and the practical applications of parallel mechanism.

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.

Kinematic Sensitivity Analysis and Dimensional Synthesis of a Redundantly Actuated Parallel Robot for Friction Stir Welding

Friction stir welding(FSW)has been widely applied in many fields as an alternative to traditional fusion welding.Although serial robots can provide the orientation capability required to weld along curved surfaces,they cannot adequately support the huge axial downward forces that FSW generates.Available parallel mechanism architectures,particularly redundantly actuated architectures for FSW,are still very limited.In this paper,a redundantly actuated 2 UPR-2 RPU parallel robot for FSW is proposed,where U denotes a universal joint,R denotes a revolute joint and P denotes a prismatic pair.First,its semi-symmetric structure is described.Next,inverse kinematics analysis involving an analytical representation of rotational axes is implemented.Velocity analysis is also conducted,which leads to the formation of a Jacobian matrix.Sensitivity performance is evaluated utilizing level set and convex optimization methods,where the local sensitivity indices are unit consistent,coordinate free,and of definite physical significance.Furthermore,global and hierarchical sensitivity indices are proposed for the design process.Finally,dimension synthesis is conducted based on the sensitivity indices and the optimal link parameters of the parallel robot are obtained.In summary,this paper proposes a dimensional synthesis method for a redundantly actuated parallel robot for FSW based on sensitivity indices.

Biped Walking Robot Based on a 2-UPU+2-UU Parallel Mechanism

Existing biped robots mainly fall into two categories： robots with left and right feet and robots with upper and lower feet. The load carrying capability of a biped robot is quite limited since the two feet of a walking robot supports the robot alternatively during walking. To improve the load carrying capability, a novel biped walking robot is proposed based on a 2-UPU＋2-UU parallel mechanism. The biped walking robot is composed of two identical platforms（feet） and four limbs, including two UPU（universal-prismatic-universal serial chain） limbs and two UU limbs. To enhance its terrain adaptability like articulated vehicles, the two feet of the biped walking robot are designed as two vehicles in detail. The conditions that the geometric parameters of the feet must satisfy are discussed. The degrees-of-freedom of the mechanism is analyzed by using screw theory. Gait analysis, kinematic analysis and stability analysis of the mechanism are carried out to verify the structural design parameters. The simulation results validate the feasibility of walking on rugged terrain. Experiments with a physical prototype show that the novel biped walking robot can walk stably on smooth terrain. Due to its unique feet design and high stiffness, the biped walking robot may adapt to rugged terrain and is suitable for load-carrying.

Gait Analysis of a Radial Symmetrical Hexapod Robot Based on Parallel Mechanisms

Most gait studies of multi-legged robots in past neglected the dexterity of robot body and the relationship between stride length and body height.This paper investigates the performance of a radial symmetrical hexapod robot based on the dexterity of parallel mechanism.Assuming the constraints between the supporting feet and the ground with hinges,the supporting legs and the hexapod body are taken as a parallel mechanism,and each swing leg is regarded as a serial manipulator.The hexapod robot can be considered as a series of hybrid serial-parallel mechanisms while walking on the ground.Locomotion performance can be got by analyzing these equivalent mechanisms.The kinematics of the whole robotic system is established,and the influence of foothold position on the workspace of robot body is analyzed.A new method to calculate the stride length of multi-legged robots is proposed by analyzing the relationship between the workspaces of two adjacent equivalent parallel mechanisms in one gait cycle.Referring to service region and service sphere,weight service sphere and weight service region are put forward to evaluate the dexterity of robot body.The dexterity of single point in workspace and the dexterity distribution in vertical and horizontal projection plane are demonstrated.Simulation shows when the foothold offset goes up to 174 mm,the dexterity of robot body achieves its maximum value 0.164 4 in mixed gait.The proposed methods based on parallel mechanisms can be used to calculate the stride length and the dexterity of multi-legged robot,and provide new approach to determine the stride length,body height,footholds in gait planning of multi-legged robot.

STRUCTURE SYNTHESIS OF 4-DOF PARALLEL ROBOT MECHANISMS BASED ON SCREW THEORY

Structural synthesis for 4-DOF parallel manipulators using screw theory issystematically studied. Motion properties and constraint conditions of 4-DOF parallel manipulatorsaccording to the relationship between screw and reciprocal screw are analyzed. Mathematicalexpressions for constraint screws and twist screws of moving platform are constructed, and allpossible limbs, which provide one or more force constraints, are enumerated. Finally, a parallelmanipulator with 3-rotation-DOF and 1-translation-DOF is used as an example to describe thesynthesis procedure for symmetrical and non-symmetrical 4-DOF parallel manipulators.

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.

Robotic Intra-Operative Ultrasound:Virtual Environments and Parallel Systems

Robotic intra-operative ultrasound has the potential to improve the conventional practice of diagnosis and procedure guidance that are currently performed manually.Working towards automatic or semi-automatic ultrasound,being able to define ultrasound views and the corresponding probe poses via intelligent approaches become crucial.Based on the concept of parallel system which incorporates the ingredients of artificial systems,computational experiments,and parallel execution,this paper utilized a recent developed robotic trans-esophageal ultrasound system as the study object to explore the method for developing the corresponding virtual environments and present the potential applications of such systems.The proposed virtual system includes the use of 3 D slicer as the main workspace and graphic user interface(GUI),Matlab engine to provide robotic control algorithms and customized functions,and PLUS(Public software Library for Ultra Sound imaging research)toolkit to generate simulated ultrasound images.Detailed implementation methods were presented and the proposed features of the system were explained.Based on this virtual system,example uses and case studies were presented to demonstrate its capabilities when used together with the physical TEE robot.This includes standard view definition and customized view optimization for pre-planning and navigation,as well as robotic control algorithm evaluations to facilitate real-time automatic probe pose adjustments.To conclude,the proposed virtual system would be a powerful tool to facilitate the further developments and clinical uses of the robotic intra-operative ultrasound systems.

Kinematics of novel 6-HTRT parallel robot

A parallel robot featwes low inertia moment of end effector, high mechanical rigitity, high mobility, no accumulation of motion error at end effector and high capacity of load, and it has found a wide applications in various fields such as automobile assembly line, earth digging machine, conjuncture of aircraft and flight simulator. In this paper the kinematics of a novel style 6 HTRT Parallel Robot is studied. The algorithm for an inverse kinematic problem of the parallel robot considering the constraint condition is presented. By the use of vector cross product method, the comprehensive coefficient of the parallel mechanism is introduced and the Jacobian matrix of a 6 HTRT parallel robot is presented. The relationship between the velocity of end manipulator and the generalized velocity is also studied with the method of Jacobian matrix. Using the result of study in mechanical dimension synthesis, better performance is achieved with the parallel robot. In motion control, it will be helpful for us to simplify the control algorithm and make more efficient trajectory planning.

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.

Rapid Optimization of Tension Distribution for Cable-Driven Parallel Manipulators with Redundant Cables

The solution of tension distributions is infinite for cable-driven parallel manipulators（CDPMs） with redundant cables. A rapid optimization method for determining the optimal tension distribution is presented. The new optimization method is primarily based on the geometry properties of a polyhedron and convex analysis. The computational efficiency of the optimization method is improved by the designed projection algorithm, and a fast algorithm is proposed to determine which two of the lines are intersected at the optimal point. Moreover, a method for avoiding the operating point on the lower tension limit is developed. Simulation experiments are implemented on a six degree-of-freedom（6-DOF） CDPM with eight cables, and the results indicate that the new method is one order of magnitude faster than the standard simplex method. The optimal distribution of tension distribution is thus rapidly established on real-time by the proposed method.