Abstract
In this paper, possibilities for workspace enlargement and joint trajectory optimization of a (6 + 3)-degree-of-freedom kinematically redundant hybrid parallel robot are investigated. The inverse kinematic problem of the robot can be solved analytically, which is a desirable property of redundant robots, and is implemented in the investigations. A new method for detecting mechanical interferences between two links which are not directly connected is proposed for evaluating the workspace. Redundant degrees-of-freedom are optimized in order to further expand the workspace. An approach for determining the desired redundant joint coordinates is developed so that a performance index can be minimized approximately when the robot is following a prescribed Cartesian trajectory. The presented approaches are readily applicable to other kinematically redundant hybrid parallel robots proposed by the authors.
Issue Section:
Special Papers
References
1.
Briot
, S.
, and Bonev
, I. A.
, 2008
, “Accuracy Analysis of 3-DOF Planar Parallel Robots
,” Mech. Mach. Theory.
, 43
(4
), pp. 445
–458
. 2.
Duchaine
, V.
, and Gosselin
, C. M.
, 2008
, “Investigation of Human-robot Interaction Stability Using Lyapunov Theory
,” 2008 IEEE International Conference on Robotics and Automation
, Pasadena, CA
, May 19–23
, IEEE, pp. 2189–2194.3.
Duchaine
, V.
, St-Onge
, B. M.
, Gao
, D.
, and Gosselin
, C.
, 2012
, “Stable and Intuitive Control of An Intelligent Assist Device
,” IEEE Trans. Haptics
, 5
(2
), pp. 148
–159
. 4.
Badeau
, N.
, Gosselin
, C.
, Foucault
, S.
, Laliberte
, T.
, and Abdallah
, M. E.
, 2018
, “Intuitive Physical Human-Robot Interaction: Using a Passive Parallel Mechanism
,” IEEE Robot. Automat. Mag.
, 25
(2
), pp. 28
–38
. 5.
Kong
, X.
, and Gosselin
, C. M.
, 2002
, “Kinematics and Singularity Analysis of a Novel Type of 3-CRR 3-DOF Translational Parallel Manipulator
,” Int. J. Robot. Res.
, 21
(9
), pp. 791
–798
. 6.
Gosselin
, C.
, Kong
, X.
, Foucault
, S.
, and Bonev
, I.
, 2004
, “A Fully Decoupled 3-dof Translational Parallel Mechanism
,” Parallel Kinematic Machines in Research and Practice, 4th Chemnitz Parallel Kinematics Seminar
, Chemnitz, Germany.
, Apr. 20–21
, pp. 595–610.7.
Stewart
, D.
, 1965
, “A Platform With Six Degrees of Freedom
,” Proc. Inst. Mech. Eng.
, 180
(1
), pp. 371
–386
. 8.
Fichter
, E. F.
, 1986
, “A Stewart Platform-based Manipulator: General Theory and Practical Construction
,” Int. J. Robot. Res.
, 5
(2
), pp. 157
–182
. 9.
Husty
, M. L.
, 1996
, “An Algorithm for Solving the Direct Kinematics of General Stewart-Gough Platforms
,” Mech. Mach. Theory.
, 31
(4
), pp. 365
–379
. 10.
Dasgupta
, B.
, and Mruthyunjaya
, T.
, 2000
, “The Stewart Platform Manipulator: A Review
,” Mech. Mach. Theory.
, 35
(1
), pp. 15
–40
. 11.
Merlet
, J.-P.
, 2006
, Parallel Robots
, Vol. 128
, Springer Science & Business Media
.12.
Gosselin
, C.
, and Angeles
, J.
, 1990
, “Singularity Analysis of Closed-Loop Kinematic Chains
,” IEEE. Trans. Rob. Autom.
, 6
(3
), pp. 281
–290
. 13.
Zlatanov
, D.
, Fenton
, R. G.
, and Benhabib
, B.
, 1994
, “Singularity Analysis of Mechanisms and Robots Via a Motion-Space Model of the Instantaneous Kinematics
,” Proceedings of the 1994 IEEE International Conference on Robotics and Automation
, San Diego, CA
, May 8–13
, IEEE, pp. 980–985.14.
Conconi
, M.
, and Carricato
, M.
, 2009
, “A New Assessment of Singularities of Parallel Kinematic Chains
,” IEEE Trans. Robot.
, 25
(4
), pp. 757
–770
. 15.
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
. 16.
Wu
, J.
, Li
, T.
, Wang
, J.
, and Wang
, L.
, 2013
, “Performance Analysis and Comparison of Planar 3-dof Parallel Manipulators With One and Two Additional Branches
,” J. Int. Robot. Syst.
, 72
(1
), pp. 73
–82
. 17.
Wu
, J.
, Chen
, X.
, Wang
, L.
, and Liu
, X.
, 2014
, “Dynamic Load-Carrying Capacity of a Novel Redundantly Actuated Parallel Conveyor
,” Nonlinear Dyn.
, 78
(1
), pp. 241
–250
. 18.
Wu
, J.
, Zhang
, B.
, and Wang
, L.
, 2016
, “A Measure for Evaluation of Maximum Acceleration of Redundant and Nonredundant Parallel Manipulators
,” ASME J. Mech. Rob.
, 8
(2
), p. 021001
.19.
Liang
, D.
, Song
, Y.
, Sun
, T.
, and Dong
, G.
, 2016
, “Optimum Design of a Novel Redundantly Actuated Parallel Manipulator with Multiple Actuation Modes for High Kinematic and Dynamic Performance
,” Nonlinear Dyn.
, 83
(1–2
), pp. 631
–658
. 20.
Sun
, T.
, Liang
, D.
, and Song
, Y.
, 2017
, “Singular-Perturbation-Based Nonlinear Hybrid Control of Redundant Parallel Robot
,” IEEE. Trans. Ind. Electron.
, 65
(4
), pp. 3326
–3336
. 21.
Cha
, S.-H.
, Lasky
, T. A.
, and Velinsky
, S. A.
, 2007
, “Singularity Avoidance for the 3-RRR Mechanism Using Kinematic Redundancy
,” Proceedings 2007 IEEE International Conference on Robotics and Automation
, Rome, Italy
, Apr. 10–14
, IEEE, pp. 1195–1200.22.
Ebrahimi
, I.
, Carretero
, J. A.
, and Boudreau
, R.
, 2007
, “3-PRRR Redundant Planar Parallel Manipulator: Inverse Displacement, Workspace and Singularity Analyses
,” Mech. Mach. Theory.
, 42
(8
), pp. 1007
–1016
. 23.
Gosselin
, C.
, Laliberté
, T.
, and Veillette
, A.
, 2015
, “Singularity-Free Kinematically Redundant Planar Parallel Mechanisms with Unlimited Rotational Capability
,” IEEE Trans. Robot.
, 31
(2
), pp. 457
–467
. 24.
Gosselin
, C. M.
, and Schreiber
, L.-T.
, 2016
, “Kinematically Redundant Spatial Parallel Mechanisms for Singularity Avoidance and Large Orientational Workspace
,” IEEE Trans. Robot.
, 32
(2
), pp. 286
–300
. 25.
Reveles
, D.
, and Wenger
, P.
, 2016
, “Trajectory Planning of Kinematically Redundant Parallel Manipulators by Using Multiple Working Modes
,” Mech. Mach. Theory.
, 98
, pp. 216
–230
. 26.
Gosselin
, C.
, and Schreiber
, L.-T.
, 2018
, “Redundancy in Parallel Mechanisms: A Review
,” ASME Appl. Mech. Rev.
, 70
(1
), p. 010802
. 27.
Wen
, K.
, Harton
, D.
, Laliberté
, T.
, and Gosselin
, C.
, 2019
, “Kinematically Redundant (6 + 3)-dof Hybrid Parallel Robot with Large Orientational Workspace and Remotely Operated Gripper
,” 2019 International Conference on Robotics and Automation (ICRA)
, Montreal, Canada
, May 20–24
, IEEE, pp. 1672–1678.28.
Baron
, N.
, Philippides
, A.
, and Rojas
, N.
, 2020
, “A Robust Geometric Method of Singularity Avoidance for Kinematically Redundant Planar Parallel Robot Manipulators
,” Mech. Mach. Theory.
, 151
, p. 103863
. 29.
Wen
, K.
, and Gosselin
, C.
, 2019
, “Kinematically Redundant Hybrid Robots with Simple Singularity Conditions and Analytical Inverse Kinematic Solutions
,” IEEE Robot. Autom. Lett.
, 4
(4
), pp. 3828
–3835
. 30.
Siciliano
, B.
, 1990
, “Kinematic Control of Redundant Robot Manipulators: A Tutorial
,” J. Int. Robot. Syst.
, 3
(3
), pp. 201
–212
. 31.
Wen
, K.
, Nguyen
, T. S.
, Harton
, D.
, Laliberté
, T.
, and Gosselin
, C.
, 2020
, “A Backdrivable Kinematically Redundant (6 + 3)-Degree-of-Freedom Hybrid Parallel Robot for Intuitive Sensorless Physical Human–robot Interaction
,” IEEE Trans. Robot.
, pp. 1
–17
.32.
Schreiber
, L.-T.
, and Gosselin
, C.
, 2017
, “Passively Driven Redundant Spherical Joint with Very Large Range of Motion
,” ASME J. Mech. Rob.
, 9
(3
), p. 031014
. 33.
Zhao
, J.-S.
, Chu
, F.
, and Feng
, Z.-J.
, 2008
, “Symmetrical Characteristics of the Workspace for Spatial Parallel Mechanisms With Symmetric Structure
,” Mech. Mach. Theory.
, 43
(4
), pp. 427
–444
. 34.
Zhao
, J.-S.
, Chu
, F.
, and Feng
, Z.-J.
, 2010
, “Singularities Within the Workspace of Spatial Parallel Mechanisms With Symmetric Structures
,” Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci.
, 224
(2
), pp. 459
–472
. 35.
Bonev
, I. A.
, Zlatanov
, D.
, and Gosselin
, C. M.
, 2002
, “Advantages of the Modified Euler Angles in the Design and Control of PKMs
,” Proceedings of the Parallel Kinematic Machines International Conference
, Chemnitz, German
, Apr. 23–25
, pp. 199–215.36.
Salisbury
, J. K.
, and Craig
, J. J.
, 1982
, “Articulated Hands: Force Control and Kinematic Issues
,” Int. J. Robot. Res.
, 1
(1
), pp. 4
–17
. 37.
Merlet
, J.-P.
, 2006
, “Jacobian, Manipulability, Condition Number, and Accuracy of Parallel Robots
,” ASME J. Mech. Des.
, 128
(1
), pp. 199
–206
. 38.
Cardou
, P.
, Bouchard
, S.
, and Gosselin
, C.
, 2010
, “Kinematic-Sensitivity Indices for Dimensionally Nonhomogeneous Jacobian Matrices
,” IEEE Trans. Robot.
, 26
(1
), pp. 166
–173
. 39.
Chang
, P. H.
, 1987
, “Analysis and Control of Robot Manipulators with Kinematic Redundancy
,” Technical Report 1022 (MIT AI Lab., 1987)
.Copyright © 2021 by ASME
You do not currently have access to this content.
