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Bi-criteria velocity minimization of robot manipulators using LVI-based primal-dual neural network and illustrated via PUMA560 robot arm

Published online by Cambridge University Press:  05 June 2009

Yunong Zhang*
Affiliation:
Department of Electronics and Communication Engineering, Sun Yat-Sen University, Guangzhou 510275, China
Kene Li
Affiliation:
Department of Electronics and Communication Engineering, Sun Yat-Sen University, Guangzhou 510275, China
*
*Corresponding author. E-mail: ynzhang@ieee.org

Summary

In this paper, to diminish discontinuity points arising in the infinity-norm velocity minimization scheme, a bi-criteria velocity minimization scheme is presented based on a new neural network solver, i.e., an LVI-based primal-dual neural network. Such a kinematic planning scheme of redundant manipulators can incorporate joint physical limits, such as, joint limits and joint velocity limits simultaneously. Moreover, the presented kinematic planning scheme can be reformulated as a quadratic programming (QP) problem. As a real-time QP solver, the LVI-based primal-dual neural network is developed with a simple piecewise linear structure and high computational efficiency. Computer simulations performed based on a PUMA560 manipulator model are presented to illustrate the validity and advantages of such a bi-criteria velocity minimization neural planning scheme for redundant robot arms.

Type
Article
Copyright
Copyright © Cambridge University Press 2009

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References

1.Sciavicco, L. and Siciliano, B., Modelling and Control of Robot Manipulators (Springer-Verlag, London, UK, 2000).CrossRefGoogle Scholar
2.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, 385394 (2008).CrossRefGoogle Scholar
3.Meghdari, A., Naderi, D. and Eslami, S., “Optimal stability of a redundant mobile manipulator via genetic algorithm,” Robotica 24, 739743 (2006).CrossRefGoogle Scholar
4.Ozbay, U., Sahin, H. T. and Zergeroglu, E., “Robust tracking control of kinematically redundant robot manipulators subject to multiple self-motion criteria,” Robotica 26, 711728 (2008). (doi:10.1017/S0263574708004293)CrossRefGoogle Scholar
5.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, 157173 (2001).CrossRefGoogle Scholar
6.Klein, C. A. and Huang, C.-H., “Review of pseudoinverse control for use with kinematically redundant manipulators,” IEEE Trans. Syst. Man Cybern. B 13 (3), 245250 (1983).CrossRefGoogle Scholar
7.Deo, A. S. and Walker, I. D., “Minimum effort inverse kinematics for redundant manipulators,” IEEE Trans. Robot. Autom. 13 (5), 767775 (1997).CrossRefGoogle Scholar
8.Gravagne, I. A. and Walker, I. D., “On the structure of minimum effort solutions with application to kinematic redundancy resolution,” IEEE Trans. Robot. Autom. 16 (6), 767775 (2000).CrossRefGoogle Scholar
9.Lee, J., “A structured algorithm for minimum l∞-norm solutions and its application to a robot velocity workspace ananlysis,” Robotica 19, 343352 (2001).CrossRefGoogle Scholar
10.Wang, J., Hu, Q. and Jiang, D., “A Lagrangian network for kinematic control of redundant manipulators,” IEEE Trans. Neural Netw. 10 (5), 11231132 (1999).CrossRefGoogle Scholar
11.Mao, Z. and Hsia, T. C., “Obstacle avoidance inverse kinematics solution of redundant robots by neural networks,” Robotica 15, 310 (1997).CrossRefGoogle Scholar
12.Zhang, Y., Ge, S. S. and Lee, T. H., “A unified quadratic programming based on dynamical system approach to joint torque optimization of physically constrained redundant manipulators,” IEEE Trans. Syst. Man Cybern. B 34 (5), 21262132 (2004).CrossRefGoogle ScholarPubMed
13.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), 199206 (1999).CrossRefGoogle Scholar
14.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), 98105 (2001).CrossRefGoogle ScholarPubMed
15.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), 269276 (1999).CrossRefGoogle Scholar
16.Wang, J., “Recurrent neural networks for computing pseudoinverses of rank-deficient matrices,” SIAM J. Sci. Comput. 18 (5), 14791493 (1997).CrossRefGoogle Scholar
17.Xia, Y. and Wang, J., “A dual neural network for kinematic control of redundant robot manipulators,” IEEE Trans. Syst. Man Cybern. B 31 (1), 147154 (2001).Google ScholarPubMed
18.Xia, Y., “A new neural network for solving linear programming problems and its application,” IEEE Trans. Neural Netw. 7, 525529 (1996).Google ScholarPubMed
19.Allotta, B., Colla, V. and Bioli, G., “Kinematic control of robots with joint constraints,” ASME J. Dyn. Syst. Meas. Control 121 (3), 433442 (1999).CrossRefGoogle Scholar
20.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), 923931 (2002).CrossRefGoogle Scholar
21.Zhang, Y., Wang, J. and Xia, Y., “A dual neural network for redundancy resolution of kinematically redundant manipulators subject to joint limits and joint velocity limits,” IEEE Trans. Neural Netw. 14 (3), 658667 (2003).CrossRefGoogle ScholarPubMed
22.Zhang, Y. and Wang, J., “A dual neural network for convex quadratic programming subject to linear equality and inequality constraints,” Phys. Lett. A 298 (4), 271278 (2002).CrossRefGoogle Scholar
23.Wang, J. and Zhang, Y., “Recurrent Neural Networks for Real-Time Computation of Inverse Kinematics of Redundant Manipulators,” In: Machine Intelligence: Quo Vadis? (Sincak, P., Vascak, J. and Hirota, K., eds.) (World Scientific, Singapore, 2004). pp. 299319.CrossRefGoogle Scholar
24.Bouzerdoum, A. and Pattison, T. R., “Neural network for quadratic optimization with bound constraints,” IEEE Trans. Neural Netw. 4 (2), 293304 (1993).CrossRefGoogle ScholarPubMed
25.Zhang, Y., “A set of nonlinear equations and inequalities arising in robotics and its online solution via a primal neural network,” Neurocomputing 70, 513524 (2006).CrossRefGoogle Scholar
26.Zhang, Y. and Ma, S., “Minimum-Energy Redundancy Resolution of Robot Manipulators Unified by Quadratic Programming and its Online Solution,” Proceedings of the 2007 IEEE International Conference on Mechatronics and Automation, Harbin, China (2007) pp. 3232–3237.Google Scholar
27.Qiu, C., Cao, Q. and Miao, S., “An on-line task modification method for singularity avoidance of robot manipulators,” Robotica 27 (4), 539546 (2008).CrossRefGoogle Scholar
28.Donelan, P. S., “Singularity-theoretic methods in robot kinematics,” Robotica 25, 641659 (2007).CrossRefGoogle Scholar
29.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), 654662 (2002).CrossRefGoogle ScholarPubMed
30.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.Google Scholar
31.Zhang, Y., Cai, B., Zhang, L. and Li, K., “Bi-criteria velocity minimization of robot manipulators using a linear variational inequalityes-based primal-dual neural network and PUMA560 example,” Adv. Robot. 22, 14791496 (2008).CrossRefGoogle Scholar
32.Zhang, Y., “Dual Neural Networks: Design, Analysis, And Application to Redundant Robotics,” In Progress in Neurocomputing Research (Kang, G. B. ed.) (Nova Science Publishers, New York, 2007). pp. 4181.Google Scholar
33.Zhang, Y., “On the LVI-Based Primal-Dual Neural Network for Solving Online Linear and Quadratic Programming Problems,” Proceedings of American Control Conference, Portland, OR, USA (2005) pp. 1351–1356.Google Scholar