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

Abstract

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.

Graphical abstract

Keywords

cable-driven parallel robot / kinematics / optimization / dynamics / control

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Nomenclature

Abbreviations
3D	Three dimensional
AFI	Average force index
CDPR	Cable-driven parallel robot
CSPR	Cable-suspended parallel robot
CSS	Constant stiffness space
DFW	Dynamic feasible workspace
DOF	Degree-of-freedom
FAST	Five-hundred-meter Aperture Spherical radio Telescope
FCW	Force closure workspace
FEM	Finite element method
FFW	Force feasible workspace
LPV	Linear parameter-varying
MFI	Maximum force index
P, R, T	Prismatic, rotation, translation joints, respectively
PID	Proportional-integral-derivative
VSD	Variable stiffness device
WCW	Wrench closure workspace
WFW	Wrench feasible workspace
Variables
Ai	Cross-sectional area of the ith cable
{\mathit{a}}_i	Position of cable outlet point Ai on the base
{\mathit{b}}_i	Position of the cable connection point Bi in the local coordinate system
Ei	Elastic modulus of the ith cable
{\mathit{f}}_{ik}\left(\mathit{p},\mathit{a}\right)	Inverse kinematics of the CDPR
F	External force acting on the end effector
G(T)	Target function for cable force optimization
H	Hessian matrix
I	Unit matrix
J	Structure matrix of the CDPR
{\mathit{J}}^{+}	Moore‒Penrose inverse of matrix J
K	Stiffness matrix of the CDPR
K1	Geometric stiffness matrix or the active stiffness
K2	Cable stiffness matrix or the passive stiffness
li	Length of the ith cable
L	Vector of cable lengths
m	Numbers of driving cables
M	External torque acting on the end effector
n	Number of terminal DOFs
p	Order of the norm
\mathit{p}	Position of the end effector
{}^{}O{\mathit{R}}_p	Rotation matrix of the end effector frame {P‒xyz} with respect to the base frame {O‒XYZ}
ti	Amplitude of the tension on the ith cable
tmin, tmax	Minimum and maximum limits of the cable-force range, respectively
tref,i	Target cable force of the ith cable
T	Cable-force vector of the CDPR
{\mathit{u}}_i	Unit directional vector of the ith cable
W	External wrench acting on the end effector
X	Motion of the end effector
\lambda	Arbitrary vector of n-dimension

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 52105025 and U19A20101). The authors would like to thank the National Institute of Standards and Technology, JASO Industrial Cranes, Max Planck Institute for Biological Cybernetics, Institute for Fluid Dynamics and Ship Theory at the Hamburg University of Technology, and ONERA for providing and giving the permission to use some of the figures in the paper. The authors would also like to thank the editors and reviewers for their pertinent comments and suggestions.

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