This paper studies the inverse kinematics (IKs) of a space robot with a controlled-floating base. Different from the traditional space robot which has a free-floating base, the momentum conservation is no longer satisfied so that the degrees-of-freedom (DOFs) and redundancy of the robot obviously increase, and motion limits exist for both base and manipulator. To deal with such a problem, a gradient projection of weighted Jacobian matrix (GPWJM) method is proposed. The Jacobian matrix is derived considering the additional DOFs of the base, and the trajectory tracking by the end-effector is chosen as the main task. A clamping weighted least norm scheme is introduced into the derived Jacobian matrix to avoid the motion limits, and the singular-robustness is enhanced by the damping least-squares. The convergence and accuracy analysis indicates the calculation of damping factor; while the verification of motion limits avoidance indicates the inequality constraint of clamping velocity. Finally, the effectiveness of the proposed GPWJM method is investigated by the numerical simulation in which a planar 3DOF manipulator on a 3DOF base is taken as a demo.
Issue Section:
Research Papers
References
1.
Agrawal
, S. K.
, Pathak
, K.
, Franch
, J.
, Lampariello
, R.
, and Hirzinger
, G.
, 2009
, “A Differentially Flat Open-Chain Space Robot With Arbitrarily Oriented Joint Axes and Two Momentum Wheels at the Base
,” IEEE Trans. Autom. Control
, 54
(9
), pp. 2185
–2191
.2.
Huang
, P.
, Wang
, D.
, Meng
, Z.
, and Guo
, J.
, 2015
, “Adaptive Postcapture Backstepping Control for Tumbling Tethered Space Robot–Target Combination
,” J. Guid. Control Dyn.
, 39
(1
), pp. 1
–7
.3.
Xu
, W.
, Zhang
, J.
, Liang
, B.
, and Li
, B.
, 2016
, “Singularity Analysis and Avoidance for Robot Manipulators With Non-Spherical Wrists
,” IEEE Trans. Ind. Electron.
, 63
(1
), pp. 277
–290
.4.
Xu
, W.
, Peng
, J.
, Liang
, B.
, and Mu
, Z.
, 2016
, “Hybrid Modeling and Analysis Method for Dynamic Coupling of Space Robots
,” IEEE Trans. Aerosp. Electron. Syst.
, 52
(1
), pp. 85
–98
.5.
Xu
, W.
, Yan
, L.
, Mu
, Z.
, and Wang
, Z.
, 2015
, “Dual Arm Angle Parameterization and Its Applications for Analytical Inverse Kinematics of Redundant Manipulators
,” Robotica
, 34
(12
), pp. 1
–20
.6.
Kemal Ozgoren
, M.
, 2013
, “Optimal Inverse Kinematic Solutions for Redundant Manipulators by Using Analytical Methods to Minimize Position and Velocity Measures
,” ASME J. Mech. Rob.
, 5
(3
), p. 031009
.7.
Colomé
, A.
, and Torras
, C.
, 2015
, “Closed-Loop Inverse Kinematics for Redundant Robots: Comparative Assessment and Two Enhancements
,” IEEE/ASME Trans. Mech.
, 20
(2
), pp. 944
–955
.8.
Whitney
, D. E.
, 1969
, “Resolved Motion Rate Control of Manipulators and Human Prostheses
,” IEEE Trans. Man-Mach. Syst.
, 10
(2
), pp. 47
–53
.9.
Wolovich
, W. A.
, and Elliott
, H.
, 1984
, “A Computational Technique for Inverse Kinematics
,” 23rd IEEE
Conference Decision Control
, Las Vegas, NV, Dec. 12–14, Vol. 23
, pp. 1359
–1363
.10.
Wampler
, C. W.
, 1986
, “Manipulator Inverse Kinematic Solutions Based on Vector Formulations and Damped Least Squares Methods
,” IEEE Trans. Syst., Man, Cybern.
, 16
(1
), pp. 93
–101
.11.
Nakamura
, Y.
, and Hanafusa
, H.
, 1986
, “Inverse Kinematics Solutions With Singularity Robustness for Robot Manipulator Control
,” ASME J. Dyn. Syst. Meas. Control
, 108
(3
), pp. 163
–171
.12.
Buss
, S. R.
, and Kim
, J.-S.
, 2005
, “Selectively Damped Least Squares for Inverse Kinematics
,” J. Graphics Tools
, 10
(3
), pp. 37
–49
.13.
Choi
, Y.
, 2008
, “Singularity-Robust Inverse Kinematics Using Lagrange Multiplier for Redundant Manipulators
,” ASME J. Dyn. Syst., Meas. Control
, 130
(5
), p. 051009
.14.
Sciavicco
, L.
, and Siciliano
, B.
, 1988
, “A Solution Algorithm to the Inverse Kinematic Problem for Redundant Manipulators
,” IEEE J. Rob. Autom.
, 4
(4
), pp. 403
–410
.15.
Seraji
, H.
, 1989
, “Configuration Control of Redundant Manipulator: Theory and Implementation
,” IEEE Trans. Rob. Autom.
, 5
(4
), pp. 472
–490
.16.
Baillieul
, J.
, 1985
, “Kinematic Programming Alternatives for Redundant Manipulators
,” IEEE
International Conference on Robotics and Automation
, Mar. 25–28, Vol. 2
, pp. 722
–728
.17.
Karpińska
, J.
, and Tchoń
, K.
, 2012
, “Performance-Oriented Design of Inverse Kinematics Algorithms: Extended Jacobian Approximation of the Jacobian Pseudo-Inverse
,” ASME J. Mech. Rob.
, 4
(2
), p. 021008
.18.
Liëgeois
, A.
, 1977
, “Automatic Supervisory Control of the Configuration and Behavior of Multibody Mechanisms
,” IEEE
Trans. Syst., Man, Cybern., 7
(12
), pp. 868
–871
.19.
Maciejewski
, A. A.
, and Klein
, C. A.
, 1985
, “Obstacle Avoidance for Kinematically Redundant Manipulators in Dynamically Varying Environments
,” Intl. J. Rob. Res.
, 4
(3
), pp. 109
–117
.20.
Hollerbach
, J.
, and Suh
, K. C.
, 1987
, “Redundancy Resolution of Manipulators Through Torque Optimization
,” IEEE J. Rob. Autom.
, 3
(4
), pp. 308
–316
.21.
Mansard
, N.
, Khatib
, O.
, and Kheddar
, A.
, 2009
, “A Unified Approach to Integrate Unilateral Constraints in the Stack of Tasks
,” IEEE Trans. Rob.
, 25
(3
), pp. 670
–685
.22.
Nakamura
, Y.
, Hanafusa
, H.
, and Yoshikawa
, T.
, 1987
, “Task-Priority Based Redundancy Control of Robot Manipulators
,” Int. J. Rob. Res.
, 6
(2
), pp. 3
–15
.23.
Chiaverini
, S.
, 1997
, “Singularity-Robust Task-Priority Redundancy Resolution for Real-Time Kinematic Control of Robot Manipulators
,” IEEE Trans. Rob. Autom.
, 13
(3
), pp. 398
–410
.24.
Flacco
, F.
, De Lucca
, A.
, and Khatib
, O.
, 2012
, “Prioritized Multi-Task Motion Control of Redundant Robots Under Hard Joint Constraints
,” IEEE/RSJ
International Conference on International Robotic Systems
, Oct. 7–12, pp. 3970
–3977
.25.
Chan
, T. F.
, and Dubey
, R. V.
, 1995
, “A Weighted Least-Norm Solution Based Scheme for Avoiding Joint Limits for Redundant Joint Manipulators
,” IEEE Trans. Rob. Autom.
, 11
(2
), pp. 286
–292
.26.
Xiang
, J.
, Zhong
, C.
, and Wei
, W.
, 2012
, “A Varied Weights Method for the Kinematic Control of Redundant Manipulators With Multiple Constraints
,” IEEE Trans. Rob.
, 28
(2
), pp. 330
–340
.27.
Raunhardt
, D.
, and Boulic
, R.
, 2007
, “Progressive Clamping
,” IEEE
International Conference on Robotics And Automation
, Apr. 10–14, pp. 4414
–4419
.28.
Huang
, S.
, Peng
, Y.
, Wei
, W.
, and Xiang
, J.
, 2014
, “Clamping Weighted Least-Norm Method for the Manipulator Kinematic Control: Avoiding Joint Limits
,” 33rd Chinese Control Conference
, July 28–30, pp. 8309
–8314
.29.
Xiang
, J.
, Zhong
, C.
, and Wei
, W.
, 2010
, “General-Weighted Least-Norm Control for Redundant Manipulators
,” IEEE Trans. Rob.
, 26
(4
), pp. 660
–669
.Copyright © 2017 by ASME
You do not currently have access to this content.
