Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-21T17:08:02.460Z Has data issue: false hasContentIssue false
  • English
  • Français

State adjustment of redundant robot manipulator based on quadratic programming

Published online by Cambridge University Press:  25 July 2011

Kene Li  and
Yunong Zhang
Kene Li
Affiliation:
School of Information Science and Technology, Sun Yat-sen University, Guangzhou 510006, China Emails: [email protected], [email protected]
Yunong Zhang*
Affiliation:
School of Information Science and Technology, Sun Yat-sen University, Guangzhou 510006, China Emails: [email protected], [email protected]
*
*Corresponding author. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Summary

To achieve desired configuration, a scheme for state adjustment of a redundant robot manipulator with no end-effector task explicitly assigned and referred to as a state-adjustment scheme is proposed in this paper. Owing to the physical limits in an actual robot manipulator, both joint and joint-velocity limits are incorporated into the proposed scheme for practical purposes. In addition, the proposed state-adjustment scheme is formulated as a quadratic program and resolved at the joint-velocity level. A numerical computing algorithm based on the conversion technique of the quadratic program to linear variational inequalities is presented to address the robot state-adjustment scheme. By employing the state-adjustment scheme, the robot manipulator can automatically move to the desired configuration from any initial configuration with the movement kept within its physical limits. Computer simulation and experimental results using a practical six-link planar robot manipulator with variable joint-velocity limits further verify the realizability, effectiveness, accuracy, and flexibility of the proposed state-adjustment scheme.

Keywords

Redundant robot manipulatorState adjustmentPhysical limitsQuadratic programmingNumerical computing algorithm
Type
Articles
Information
Robotica , Volume 30 , Issue 3 , May 2012 , pp. 477 - 489
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Sciavicco, L. and Siciliano, B., Modelling and Control of Robot Manipulators (Springer-Verlag, London, UK, 2000).CrossRefGoogle Scholar
2.Meghdari, A., Naderi, D. and Eslami, S., “Optimal stability of a redundant mobile manipulator via genetic algorithm,” Robotica 24, 739–743 (2006).CrossRefGoogle Scholar
3.Zhang, Y., “On the LVI-based Primal-Dual Neural Network for Solving Online Linear and Quadratic Programming Problems,” Proceedings of the American Control Conference, Portland, OR, USA (2005) pp. 1351–1356.Google Scholar
4.Tang, W. S. and Wang, J., “A recurrent neural network for minimum infinity-norm kinematic control of redundant manipulators with an improved problem formulation and reduced architecture complexity,” IEEE Trans. Syst. Man Cybern. B 31 (1), 98–105 (2001).CrossRefGoogle ScholarPubMed
5.Puga, J. P. and Chiang, L. E., “Optimal trajectory planning for a redundant mobile manipulator with non-holonomic constraints performing push-pull tasks,” Robotica 26, 385–394 (2008).CrossRefGoogle Scholar
6.Ozbay, U., Sahin, H. T. and Zergeroglu, E., “Robust tracking control of kinematically redundant robot manipulators subject to multiple self-motion criteria,” Robotica 26 711–728 (2008).CrossRefGoogle Scholar
7.Allotta, B., Colla, V. and Bioli, G., “Kinematic control of robots with joint constraints,” ASME J. Dyn. Syst. Meas. Control 121 (3), 433–442 (1999).CrossRefGoogle Scholar
8.Mao, Z. and Hsia, T. C., “Obstacle avoidance inverse kinematics solution of redundant robots by neural networks,” Robotica 15, 3–10 (1997).CrossRefGoogle Scholar
9.Zhang, Y. and Wang, J., “A dual neural network for constrained joint torque optimization of kinematically redundant manipulators,” IEEE Trans. Syst. Man Cybern. B 32 (5), 654–662 (2002).CrossRefGoogle ScholarPubMed
10.Zhang, Y., Wang, J. and Xu, Y., “A dual neural network for bi-criteria kinematic control of redundant manipulators,” IEEE Trans. Robot. Autom. 18 (6), 923–931 (2002).CrossRefGoogle Scholar
11.Zhang, Y., “A set of nonlinear equations and inequalities arising in robotics and its online solution via a primal neural network,” Neurocomputing 70, 513–524 (2006).CrossRefGoogle Scholar
12.Zhang, Y., Tan, Z., Yang, Z. and Lv, X., “A Dual Neural Network Applied to Drift-free Resolution of Five-Link Planar Robot Arm,” Proceedings of the 2008 IEEE International Conference on Information and Automation, Zhangjiajie, China (2008) pp. 1274–1279.CrossRefGoogle Scholar
13.Donelan, P. S., “Singularity-theoretic methods in robot kinematics,” Robotica 25, 641–659 (2007).CrossRefGoogle Scholar
14.Padois, V., Fourquet, J.-Y. and Chiron, P., “Kinematic and dynamic model-based control of wheeled mobile manipulators: A unified framework for reactive approaches,” Robotica 25, 157–173 (2001).CrossRefGoogle Scholar
15.Lee, J., “A structured algorithm for minimum l ∞-norm solutions and its application to a robot velocity workspace analysis,” Robotica 19, 343–352 (2001).CrossRefGoogle Scholar
16.Qiu, C., Cao, Q. and Miao, S., “An on-line task modification method for singularity avoidance of robot manipulators,” Robotica 27, 539–546 (2009).CrossRefGoogle Scholar
17.Wang, J., Hu, Q. and Jiang, D., “A Lagrangian network for kinematic control of redundant manipulators,” IEEE Trans. Neural Netw. 10 (5), 1123–1132 (1999).CrossRefGoogle Scholar
18.Ding, H. and Tso, S. K., “A fully neural-network-based planning scheme for torque minimization of redundant manipulators,” IEEE Trans. Ind. Electron. 46 (1), 199–206 (1999).CrossRefGoogle Scholar
19.Ding, H. and Wang, J., “Recurrent neural networks for minimum infinity-norm kinematic control of redundant manipulators,” IEEE Trans. Syst. Man Cybern. A 29 (3), 269–276 (1999).CrossRefGoogle Scholar
20.He, B., “Solving a class of linear projection equation,” Numer. Math. 168, 71–80 (1994).CrossRefGoogle Scholar
21.He, B., “A new method for a class of linear variational inequalities,” Math. Program. 166, 137–144 (1994).CrossRefGoogle Scholar
22.Wang, J., “Recurrent neural networks for computing pseudoinverses of rank-deficient matrices,” SIAM J. Sci. Comput. 18 (5), 1479–1493 (1997).CrossRefGoogle Scholar
23.Zhang, Y., Chen, K. and Ma, W., “MATLAB Simulation and Comparison of Zhang Neural Network and Gradient Neural Network for Online Solution of Linear Time-Varying Equations,” Proceedings of the 2007 International Conference on Life System Modeling and Simulation, Shanghai, China (2007) pp. 450–454.Google Scholar
24.Zhang, Y., Ruan, G., Li, K. and Yang, Y., “Robustness analysis of the Zhang neural network for online time-varying quadratic optimization,” J. Phys. A-Math. Theor. 43, 1–19 (2010) (doi:10.1088/1751-8113/43/24/245202).CrossRefGoogle Scholar