Abstract
This paper focuses on the singularity of actuation coordination of redundantly actuated parallel manipulators and proposes a series of novel indices to evaluate the actuation coordination. The singularity is analyzed based on the coordinated dynamics model and divided into two categories: input singularity and output singularity. Influences of the singularity on the control performance of redundantly actuated parallel manipulators are studied with mechanisms 2RPU + 2UPR + RPR and 3RPR. Local and global performance indices of redundantly actuated parallel manipulators with actuation coordination are put forward, and the dimension optimization method considering the proposed indices is studied based on mechanism 6RPS. The research of this article possesses good reference significance for the performance analysis and control application of redundantly actuated parallel manipulators.
Graphical Abstract Figure
References
1.
Zhao
, Y.
, and Gao
, F.
, 2009
, “Dynamic Performance Comparison of the 8PSS Redundant Parallel Manipulator and Its Non-Redundant Counterpart—the 6PSS Parallel Manipulator
,” Mech. Mach. Theory
, 44
(5
), pp. 991
–1008
. 2.
Lee
, G.
, Park
, S.
, Lee
, D.
, Park
, F. C.
, Jeong
, J. i.
, and Kim
, J.
, 2015
, “Minimizing Energy Consumption of Parallel Mechanisms via Redundant Actuation
,” IEEE/ASME Trans. Mechatron.
, 20
(6
), pp. 2805
–2812
. 3.
Cheng
, H.
, Yiu
, Y.-K.
, and Li
, Z.
, 2003
, “Dynamics and Control of Redundantly Actuated Parallel Manipulators
,” IEEE/ASME Trans. Mechatron.
, 8
(4
), pp. 483
–491
. 4.
Garg
, V.
, Nokleby
, S. B.
, and Carretero
, J. A.
, 2009
, “Wrench Capability Analysis of Redundantly Actuated Spatial Parallel Manipulators
,” Mech. Mach. Theory
, 44
(5
), pp. 1070
–1081
. 5.
Müller
, A.
, and Maisser
, P.
, 2007
, “Generation and Application of Prestress in Redundantly Full-Actuated Parallel Manipulators
,” Multibody Syst. Dyn.
, 18
(2
), pp. 259
–275
. 6.
Cheng
, C.
, Xu
, W.
, and Shang
, J.
, 2015
, “Optimal Distribution of the Actuating Torques for a Redundantly Actuated Masticatory Robot With Two Higher Kinematic Pairs
,” Nonlinear Dyn.
, 79
(2
), pp. 1235
–1255
. 7.
Woo
, S. H.
, Kim
, S. M.
, Kim
, M. G.
, Yi
, B.-J.
, and Kim
, W.
, 2017
, “Torque-Balancing Algorithm for the Redundantly Actuated Parallel Mechanism
,” Mechatronics
, 42
, pp. 41
–51
.8.
Kang
, L.
, Kim
, W.
, and Yi
, B.-J.
, 2016
, “Kinematic Modeling, Analysis, and Load Distribution Algorithm for a Redundantly Actuated 4-DOF Parallel Mechanism
,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
, Korea
, pp. 356
–361
. 9.
Wu
, J.
, Li
, T.
, and Xu
, B.
, 2013
, “Force Optimization of Planar 2-DOF Parallel Manipulators With Actuation Redundancy Considering Deformation
,” Proc. Inst. Mech. Eng., Part C
, 227
(6
), pp. 1371
–1377
. 10.
Jiang
, Y.
, Li
, T.
, and Wang
, L.
, 2015
, “Dynamic Modeling and Redundant Force Optimization of a 2-DOF Parallel Kinematic Machine With Kinematic Redundancy
,” Robot. Comput.-Integr. Manuf.
, 32
(Apr.
), pp. 1
–10
. 11.
Zhao
, Y.
, Lu
, L.
, Zhao
, T.
, Du
, Y.
, and Huang
, Z.
, 1998
, “The Novel Approaches for Computing the Dynamic Load-Carrying Capacity of Multiple Cooperating Robotic Manipulators
,” Mech. Mach. Theory
, 34
(4
), pp. 637
–643
. 12.
Huang
, Z.
, and Zhao
, Y.
, 1994
, “The Accordance and Optimization-Distribution Equation of the Over-Determinate Inputs of Walking Machines
,” Mech. Mach. Theory
, 29
(2
), pp. 327
–332
. 13.
Xu
, Y.
, Yao
, J.
, and Zhao
, Y.
, 2012
, “Inverse Dynamics and Internal Forces of the Redundantly Actuated Parallel Manipulators
,” Mech. Mach. Theory
, 51
, pp. 172
–184
. 14.
Wu
, J.
, Wang
, D.
, and Wang
, L.
, 2015
, “A Control Strategy of a Two Degrees-of-Freedom Heavy Duty Parallel Manipulator
,” ASME J. Dyn. Syst. Meas. Control
, 137
(6
), p. 061007
. 15.
Lipiński
, K.
, 2016
, “Modeling and Control of a Redundantly Actuated Variable Mass 3RRR Planar Manipulator Controlled by a Model-Based Feedforward and a Model-Based-Proportional- Derivative Feedforward-Feedback Controller
,” Mechatronics
, 37
, pp. 42
–53
. 16.
Ayas
, M. S.
, and Altas
, I. H.
, 2017
, “Fuzzy Logic Based Adaptive Admittance Control of a Redundantly Actuated Ankle Rehabilitation Robot
,” Control Eng. Pract.
, 59
, pp. 44
–54
. 17.
Rugthum
, T.
, and Tao
, G.
, 2016
, “An Adaptive Actuator Failure Compensation Scheme for a Parallel Manipulator With Parameter Uncertainties
,” IEEE 55th Conference on Decision and Control
, Las Vegas, NV
, Dec. 12–14
, pp. 2013
–2018
.18.
Xuemei
, N.
, Gao
, G.
, Liu
, X.
, and Fang
, Z.
, 2015
, “Decoupled Sliding Mode Control for a Novel 3-DOF Parallel Manipulator With Actuation Redundancy
,” Int. J. Adv. Robot. Syst.
, 12
(5
), pp. 64
–77
. 19.
Escorcia-Hernández
, J. M.
, Chemori
, A.
, Aguilar-Sierra
, H.
, and Monroy-Anieva
, A. J.
, 2020
, “A new Solution for Machining With RA-PKMs: Modelling, Control and Experiments
,” Mech. Mach. Theory
, 150
, pp. 1
–18
. 20.
Shang
, W.
, Cong
, S.
, and Ge
, Y.
, 2013
, “Coordination Motion Control in the Task Space for Parallel Manipulators With Actuation Redundancy
,” IEEE Trans. Autom. Sci. Eng.
, 10
(3
), pp. 665
–673
. 21.
Zhang
, H.
, Fang
, H.
, Zhang
, D.
, Zou
, Q.
, and Luo
, X.
, 2020
, “Trajectory Tracking Control Study of a New Parallel Mechanism With Redundant Actuation
,” Int. J. Aerosp. Eng.
, 2020
(Pt.1
), pp. 1
–14
. 22.
Park
, S.
, Kim
, J.
, Jeong
, J. I.
, Kim
, J
, and Lee
, G.
, 2017
, “Optimal Dimensioning of Redundantly Actuated Mechanism for Maximizing Energy Efficiency and Workspace via Taguchi Method
,” Proc. Inst. Mech. Eng., Part C
, 231
(2
), pp. 326
–340
. 23.
Wu
, J.
, Zhang
, B.
, and Wang
, L.
, 2016
, “Optimum Design and Performance Comparison of a Redundantly Actuated Solar Tracker and Its Nonredundant Counterpart
,” Sol. Energy
, 127
(Apr.
), pp. 36
–47
. 24.
Liu
, H.
, Huang
, T.
, Kecskeméthy
, A.
, Chetwynd
, D. G.
, and Li
, Q.
, 2017
, “Force/Motion Transmissibility Analyses of Redundantly Actuated and Overconstrained Parallel Manipulators
,” Mech. Mach. Theory
, 109
, pp. 126
–138
. 25.
Li
, Q.
, Zhang
, N.
, and Wang
, F.
, 2017
, “New Indices for Optimal Design of Redundantly Actuated Parallel Manipulators
,” ASME J. Mech. Rob.
, 9
(1
), p. 011007
. 26.
Zhang
, F.
, Zhang
, B.
, Zhou
, F.
, Shang
, W.
, and Cong
, S.
, 2020
, “Configuration Selection and Parameter Optimization of Redundantly Actuated Cable-Driven Parallel Robots
,” J. Mech. Eng.
, 56
(1
), pp. 1
–8
. 27.
Chai
, X.
, Zhang
, N.
, He
, L.
, Li
, Q.
, and Ye
, W.
, 2020
, “Kinematic Sensitivity Analysis and Dimensional Synthesis of a Redundantly Actuated Parallel Robot for Friction Stir Welding
,” Chin. J. Mech. Eng.
, 33
(1
), pp. 1
–10
. 28.
Wu
, J.
, Wang
, J.
, Wang
, L.
, and Li
, T.
, 2009
, “Dynamics and Control of a Planar 3-DOF Parallel Manipulator With Actuation Redundancy
,” Mech. Mach. Theory
, 44
(4
), pp. 835
–849
. 
