In redundant manipulation systems, the end-effector path does not completely determine the trajectories of all the individual degrees of freedom (dof) and the additional dofs can be used to enhance the performance in some sense. The paper deals with utilizing the redundancy to minimize energy consumption. A full linear electromechanical model is used, and the exact energy consumption is calculated. The optimization includes also displacement limits via penalty functions that are included in the cost function. The optimal trajectory is feasible in the sense that it can be obtained by a finite input voltage and all the velocities are continuous. The solution is based on projections that separate the system and the input into two parts. One that is completely determined by the end-effector path and the other that is free for optimization. The important and delicate issue of boundary conditions is resolved accordingly. Simulation results show that redundancy, even with limited joint motion, can lead to a considerable reduction in energy consumption.
Issue Section:
Research Papers
References
1.
Galicki
, M.
, 2004
, “Path Following by the End-Effector of a Redundant Manipulator Operating in a Dynamic Environment
,” IEEE Trans. Rob.
, 20
(6
), pp. 1018
–1025
.10.1109/TRO.2004.8337822.
De Luca
, A.
, and Ferrajoli
, L.
, 2008
, “Exploiting Robot Redundancy in Collision Detection and Reaction
,” International Conference on Intelligent Robots and Systems
, pp. 3299
–3305
.3.
Caccavale
, F.
, Chiavarini
, S.
, and Siciliano
B.
, 1997
, “Second-Order Kinematic Control of Robot Manipulators With Jacobian Damped Least-Squares Inverse: Theory and Experiments
,” IEEE/ASME Trans. Mechatron.
, 2
(3
), pp. 188
–194
.10.1109/3516.6229714.
Larkworthy
, T.
, and Hayes
, G.
, 2009
, “Utilizing Redundancy in Modular Robots to Achieve Greater Accuracy
,” International Conference on Robot Communication and Coordination
, Odense, Denmark, Mar. 31–Apr. 2, pp. 1
–6
.5.
Ohishi
, K.
, Nozawa
, H.
, and Miyazaki
, T.
, 1999
, “Redundant Manipulator Control With Autonomous Consideration Algorithm of Torque Saturation
,” IEEE International Symposium on Industrial Electronics
, 1
, pp. 145
–150
.10.1109/ISIE.1999.8017746.
Nguyen
, L. A.
, Walker
, I. D.
, and DeFigueiredo
, R. J. P.
, 1995
, “Robustness Issues for Kinematically Redundant Manipulator Control
,” IEEE Trans. Syst., Man Cybern.
, 25
(6
), pp. 1010
–1016
.10.1109/21.3842667.
Khatib
, O.
, 1990
, “Motion/Force Redundancy of Manipulators
,” Japan—USA Symposium on Flexible Automation
, Kyoto, Japan
, July 23, pp. 337
–342
.8.
Martin
, D. P.
, Baillieul
J.
, and Hollerbach
, J. M.
, 1989
, “Resolution of Kinematic Redundancy Using Optimization Techniques
,” IEEE Trans. Rob. Autom.
, 5
(4
), pp. 529
–533
.10.1109/70.880679.
Bowling
, A.
, and Harmeyer
S.
, 2010
, Repeatable Redundant Manipulator Control Using Nullspace Quasivelocities
,” J. Dyn. Syst., Meas. Control
, 132
(3
), p. 031007
.10.1115/1.400133410.
Enns
, D.
, 1998
, “Control Allocation Approaches
,” Proceedings of AIAA Guidance, Navigation, and Control Conference
, Boston, MA, Aug. 5.11.
Petersen
, J. A. M.
, and Bodson
, M.
, 2006
, “Constrained Quadratic Programming Techniques for Control Allocation
,” IEEE Trans. Control Syst. Technol.
, 14
(1
), pp. 91
–98
.10.1109/TCST.2005.86051612.
Malysz
, P.
, and Sirouspour
, S.
, 2009
, “Dual-Master Teleoperation Control of Kinematically Redundant Robotic Slave Manipulators
,” IEEE/RSJ International Conference on Intelligent Robots and Systems
, pp. 5115
–5120
.13.
Xiang
, J.
, Zhong
, C.
, and Wei
, W.
, 2010
, “General-Weighted Least-Norm Control for Redundant Manipulators
,” IEEE Trans. Rob.
, 26
(4
), pp. 660
–669
.10.1109/TRO.2010.205065514.
Galicki
, M.
, 2000
, Time-Optimal Controls of Kinematically Redundant Manipulators With Geometric Constraints
,” IEEE Trans. Rob. Autom.
, 16
(1
), pp. 89
–93
.10.1109/70.83319415.
Ma
, S.
, and Watanabe
, M.
, 2004
, “Time Optimal Path-Tracking Control of Kinematically Redundant Manipulators
,” JSME Int. J., Ser. C
, 47
(2
), pp. 582
–590
.10.1299/jsmec.47.58216.
Fahham
, H. R.
, Farid
, M.
, and Khooron
, M.
, 2011
, “Time Optimal Trajectory Tracking of Redundant Planar Cable-Suspended Robots Considering Both Tension and Velocity Constraints
,” ASME J. Dyn. Syst. Meas. Control
, 133
(1), p. 011004
.10.1115/1.400271217.
Ma
, S.
, 1994
, “Local Torque Optimization of Redundant Manipulators in Torque-Based Formulation
,” IEEE International Conference on Industrial Electronics, Control and Instrumentation
, Vol. 2
, pp. 697
–702
.18.
Zhang
, Y.
, and Ma
, S.
, 2007
, “Minimum-Energy Redundancy Resolution of Robot Manipulators Unified by Quadratic Programming and Its Online Solution
,” IEEE International Conference on Mechatronics and Automation. ICMA
, pp. 3232
–3237
.19.
Deo
, A. S.
, and Walker
, I. D.
, 1997
, “Minimum Effort Inverse Kinematics for Redundant Manipulators
,” IEEE Trans. Rob. Autom.
, 13
(5
), pp. 767
–775
.10.1109/70.63123820.
Hirakawa
, A. R.
, and Kawamura
, A.
, 1996
, “Proposal of Trajectory Generation for Redundant Manipulators Using Variational Approach and the Application to Consumed Electrical Energy Minimization
,” IEEE Proceedings of Advanced Motion Control
, pp. 687
–692
.21.
Hirakawa
, A. R.
, and Kawamura
, A.
, 1997
, “Trajectory Planning of Redundant Manipulators for Minimum Energy Consumption Without Matrix Inversion
,” International Conference on Robotics and Automation
, Vol. 3
, pp. 2415
–2420
.22.
Flacco
, F.
, De Luca
, A.
, and Khatib
, O.
, 2012
, “Prioritized Multi-Task Motion Control of Redundant Robots Under Hard Joint Constraints
,” IEEE/RSJ International Conference on Intelligent Robots and Systems
, Vilamoura, Portugal
, pp. 3970
–3977
.23.
Halevi
, Y.
, Carpanzano
, A.
, Montalbano
, G.
, and Koren
, Y.
, 2011
, “Minimum Energy Control of Redundant Actuation Machine Tools
,” CIRP Ann. - Manuf. Technol.
, 60
, pp. 433
–436
.10.1016/j.cirp.2011.03.03224.
Halevi
, Y.
, Carpanzano
, A.
, and Montalbano
, G.
, 2012
, “Minimum Energy Control of Redundant Cartesian Manipulators
,” Proceedings of the 11th Biennial ASME Conference on Engineering Systems Design and Analysis (ESDA)
, Nantes, France
, July 2–4.25.
Jacobson
, D. H.
, Lele
, M. M.
, and Speyer
, J. L.
, 1971
, “New Necessary Conditions of Optimality for Control Problems With State-Variable Inequality Constraints
,” J. Math. Anal. Appl.
, 35
(2
), pp. 255
–284
.10.1016/0022-247X(71)90219-826.
Hartl
, R. F.
, Sethi
, S. P.
, and Vickson
, R. G.
, 1995
, “A Survey of the Maximum Principles for Optimal Control Problems With State Constraints
,” SIAM Rev.
, 37
, pp. 181
–218
.10.1137/103704327.
Aghili
, F.
, 2011
, “Projection Based Control of Parallel Mechanisms
,” ASME J. Comput. Nonlinear Dyn.
, 6
(3), p. 031009
.10.1115/1.400294228.
Halevi
, Y.
, 1989
, “The Optimal Reduced Order Estimator for Systems With Singular Measurement Noise
,” IEEE Trans. Autom. Control
, 34
, pp. 777
–781
.10.1109/9.2941329.
Bryson
, A. E.
, and Ho
, Y. C.
, 1975
, Applied Optimal Control
, Wiley
, New York
.30.
Zagorianos
, A.
, Kontoyannis
, E.
, and Tzafestas
, S.
, 1994
, “Resolved Motion Model Based Predictive Control of Redundant Robots
,” Math. Comput. Simul.
, 37
(2–3
), pp. 195
–205
.10.1016/0378-4754(94)90018-3Copyright © 2014 by ASME
You do not currently have access to this content.
