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

Abstract

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.

Graphical abstract

Keywords

cable-driven parallel robots / parallel robots / redundant robots / evaluation index / force solution space

References

[1] Gosselin C, Schreiber L T. Redundancy in parallel mechanisms: a review. Applied Mechanics Reviews, 2018, 70(1): 010802

[2] Wang Y H, Hou S H, Zhang R Q, Tang X Q. Interaction force measurement of parallel robots based on structure-integrated force sensors using interpretable linear neural networks. Mechatronics, 2022, 87: 102895

[3] Li W, Lin C X, Gao F, Guo W Z. The kinematics and design for isotropy of six-DOF 3-CCC parallel mechanisms of general geometry and arbitrary actuation schemes. Mechanism and Machine Theory, 2022, 178: 105091

[4] Luces M, Mills J K, Benhabib B. A review of redundant parallel kinematic mechanisms. Journal of Intelligent & Robotic Systems, 2017, 86(2): 175–198

[5] Han G, Xie F G, Liu X J. Evaluation of the power consumption of a high-speed parallel robot. Frontiers of Mechanical Engineering, 2018, 13(2): 167–178

[6] Meng Q Z, Xie F G, Liu X J. Conceptual design and kinematic analysis of a novel parallel robot for high-speed pick-and-place operations. Frontiers of Mechanical Engineering, 2018, 13(2): 211–224

[7] Tang X Q. An overview of the development for cable-driven parallel manipulator. Advances in Mechanical Engineering, 2014, 6: 823028

[8] Zarebidoki M, Dhupia J S, Xu W L. A review of cable-driven parallel robots: typical configurations, analysis techniques, and control methods. IEEE Robotics & Automation Magazine, 2022, 29(3): 89–106

[9] Morinaga A, Ogawa T, Iwanaga K, Shimomoto Y, Yamamoto I. Development of motion reduction device for ship using underactuated parallel link mechanism. Sensors and Materials, 2021, 33(3): 897–906

[10] Silva D, Garrido J, Riveiro E. Stewart platform motion control automation with industrial resources to perform cycloidal and oceanic wave trajectories. Machines, 2022, 10(8): 711

[11] Idà E, Bruckmann T, Carricato M. Rest-to-rest trajectory planning for underactuated cable-driven parallel robots. IEEE Transactions on Robotics, 2019, 35(6): 1338–1351

[12] Qian L, Yao R, Sun J H, Xu J L, Pan Z C, Jiang P. Fast: its scientific achievements and prospects. The Innovation, 2020, 1(3): 100053

[13] Zhang Z K, Shao Z F, You Z, Tang X Q, Zi B, Yang G L, Gosselin C, Caro S. State-of-the-art on theories and applications of cable-driven parallel robots. Frontiers of Mechanical Engineering, 2022, 17(3): 37

[14] Gouttefarde M, Lamaury J, Reichert C, Bruckmann T. A versatile tension distribution algorithm for n-DOF parallel robots driven by n + 2 cables. IEEE Transactions on Robotics, 2015, 31(6): 1444–1457

[15] Jamshidifar H, Khajepour A, Fidan B, Rushton M. Kinematically-constrained redundant cable-driven parallel robots: modeling, redundancy analysis, and stiffness optimization. IEEE/ASME Transactions on Mechatronics, 2017, 22(2): 921–930

[16] Cui Z W, Tang X Q, Hou S H, Sun H N. Research on controllable stiffness of redundant cable-driven parallel robots. IEEE/ASME Transactions on Mechatronics, 2018, 23(5): 2390–2401

[17] Garg V, Nokleby S B, Carretero J A. Wrench capability analysis of redundantly actuated spatial parallel manipulators. Mechanism and Machine Theory, 2009, 44(5): 1070–1081

[18] Nokleby S B, Fisher R, Podhorodeski R P, Firmani F. Force capabilities of redundantly-actuated parallel manipulators. Mechanism and Machine Theory, 2005, 40(5): 578–599

[19] Pashkevich A, Wenger P, Chablat D. Design strategies for the geometric synthesis of Orthoglide-type mechanisms. Mechanism and Machine Theory, 2005, 40(8): 907–930

[20] Inner B, Kucuk S. A novel kinematic design, analysis and simulation tool for general Stewart platforms. Simulation, 2013, 89(7): 876–897

[21] XieZ HLi GLiuG FZhaoJ. Optimal design of a Stewart platform using the global transmission index under determinate constraint of workspace. Advances in Mechanical Engineering, 2017, 9(10): 1–14

[22] Liu X J, Wu C, Wang J S. A new approach for singularity analysis and closeness measurement to singularities of parallel manipulators. Journal of Mechanisms and Robotics, 2012, 4(4): 041001

[23] Xie F G, Liu X J, Wang J S. A 3-DOF parallel manufacturing module and its kinematic optimization. Robotics and Computer-Integrated Manufacturing, 2012, 28(3): 334–343

[24] WangY HTang X QXiangC YHouS H. Force sensitivity analysis and scale design of Stewart parallel manipulator. Advances in Mechanical Engineering, 2021, 13(7): 16878140211035996

[25] Isaksson M, Gosselin C, Marlow K. An introduction to utilising the redundancy of a kinematically redundant parallel manipulator to operate a gripper. Mechanism and Machine Theory, 2016, 101: 50–59

[26] Vieira H L, Fontes J V D C, Da Silva M M. Reliable redundancy resolution strategies for kinematically redundant parallel manipulators. Mechanism and Machine Theory, 2022, 167: 104531

[27] Yao J T, Gu W D, Feng Z Q, Chen L P, Xu Y D, Zhao Y S. Dynamic analysis and driving force optimization of a 5-DOF parallel manipulator with redundant actuation. Robotics and Computer-Integrated Manufacturing, 2017, 48: 51–58

[28] Müller A. On the terminology and geometric aspects of redundant parallel manipulators. Robotica, 2013, 31(1): 137–147

[29] Mousavi M R, Ghanbari M, Moosavian S A A, Zarafshan P. Explicit dynamics of redundant parallel cable robots. Nonlinear Dynamics, 2018, 94(3): 2077–2096

[30] Jamshidifar H, Khosravani S, Fidan B, Khajepour A. Vibration decoupled modeling and robust control of redundant cable-driven parallel robots. IEEE/ASME Transactions on Mechatronics, 2018, 23(2): 690–701

[31] SantosJ CChemori AGouttefardeM. Redundancy resolution integrated model predictive control of CDPRs: concept, implementation and experiments. In: Proceedings of IEEE International Conference on Robotics and Automation. Paris: IEEE, 2020, 3889–3895

[32] MerletJ P. On the redundancy of cable-driven parallel robots. In: Flores P, Viadero F, eds. New Trends in Mechanism and Machine Science. Cham: Springer, 2015, 31–39

[33] Sun G Y, Liu Z, Gao H B, Li N, Ding L, Deng Z Q. Direct method for tension feasible region calculation in multi-redundant cable-driven parallel robots using computational geometry. Mechanism and Machine Theory, 2021, 158: 104225

[34] Gao H B, Sun G Y, Liu Z, Sun C, Li N, Ding L, Yu H T, Deng Z Q. Tension distribution algorithm based on graphics with high computational efficiency and robust optimization for two-redundant cable-driven parallel robots. Mechanism and Machine Theory, 2022, 172: 104739

[35] Qi R H, Khajepour A, Melek W W. Redundancy resolution and disturbance rejection via torque optimization in hybrid cable-driven robots. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2022, 52(7): 4069–4079

[36] SchenkCBülthoff H HMasoneC. Robust adaptive sliding mode control of a redundant cable driven parallel robot. In: Proceedings of the 19th International Conference on System Theory, Control and Computing. Cheile Gradistei: IEEE, 2015, 427–434

[37] Peng J Q, Zhang C, Ge D M, Han Y. Two trajectory tracking control methods for space hyper-redundant cable-driven robots considering model uncertainty. Multibody System Dynamics, 2022, 56(2): 123–152

Nomenclature

Abbreviations
IFA	Internal force antagonism
PID	Proportion‒integral‒derivative
RCDPR	Redundant cable-driven parallel robot
RRPR	Redundant rigid parallel robot
Variables
Ai	ith connection point between the linkage and the base
ai	Position vector of Ai in O
Bi	ith connection point between the linkage and the moving platform
{}^{O^{\prime }}{\mathit{b}}_i	Position vector of B_i in O^{\prime }
Cλ	Initial value constants
E	Young’s modulus of the nylon material
f1, f2	Tensions of the first and second cables, respectively
fd	Dynamic antagonistic force
fs	Static antagonistic force
F	External force
G(s)	Transfer function
G	Gravity of the moving platform
i	Number of iterations
imax	Maximum number of iterations
J	Jacobian matrix of the parallel robots
J−	Inverse matrix of J
J+	Moore–Penrose pseudo-inverse matrix of J
k1, k2	Stiffnesses of the first and second cables, respectively
kD	Differential parameters in PID control
kI	Integral parameters in PID control
kmax	Maximum number of selections
kp	Proportional parameters in PID control
L	Length of the cable
\dot{\mathit{l}}	Velocity vector of the linkages
li	Linkage vector from Bi to Ai
m	Number the linkages
m1, m2	Masses of the first and second cables, respectively
M	Mass of the mass block
n	Degrees of freedom of the robot’s motion
Nba	Element in the bth row and ath column of N
N	Basis vector for the general solution of Eq. (8)
Nj	jth column of N
O	Base coordinate system
O^{\prime }	Moving coordinate system
Om, On	m- and n-dimensional zero vectors, respectively
p, \dot{\mathit{p}}	Position and velocity vectors of the moving platform, respectively
r	Degree of redundancy of parallel robots
R	Radius of the cable
R	Rotation matrix of O^{\prime } relative to O
s	Micro elements of the transfer function
S	Second matrix after singular value decomposition of J
t	Time
ti	Value of the ith joint force
ts1, ts2	First and second step time, respectively
Tsb	bth element of Ts
T	Value of the ith joint force
T(1)	Initial joint force
Tlast	Value of T for the last iteration
Ts	Special solution of the joint force
ui	Linkage unit vector
U, V	First and third matrices after singular value decomposition of J, respectively
x1, x2	Displacements of the first and second cables, respectively
xi	Initial position of the mass block
xm	Displacement of the mass block
xt	Target position of the mass block
xte1, xte2	First and second target positions with error, respectively
x	Pose of the moving platform
\dot{\mathit{x}}	Velocity vector of the moving platform
\varphi	Solution type
{\eta }_1	Index 1 (the maximum value of the Euclidean norm number of T)
{\eta }_2	Index 2 (the unit circle integral of {\Vert \mathit{T}\Vert }_{\text{max}} in the neighborhood of the coordinate \left[0,G\right])
\mathit{\lambda }	A random r-dimensional vector
{\lambda }_a^{(i)}	ath element of {\mathit{\lambda }}^{(i)}
\mathbf{\Theta }, \dot{\mathbf{\Theta }}	Angular displacement and velocity vectors of the moving platform, respectively
\tau	Update step
\mathrm{\Omega }	Output completion flag

Acknowledgements

The authors would like to acknowledge the financial support of the National Natural Science Foundation of China (Grant No. 51975307).

Conflict of Interest

The authors declare that they have no conflict of interest.

RIGHTS & PERMISSIONS

2023 Higher Education Press