Abstract
A primal-dual neural network based on linear variational inequalities (LVI) is presented in this paper, which is used to solve the repetitive motion planning of redundant robots. To do so, a drift-free criterion is exploited. In addition, the physical constraints such as joint limits and joint velocity limits are incorporated into the problem formulation of such a scheme. The scheme is finally reformulated as a quadratic programming (QP) problem and resolved at the velocity-level. Compared to other computational strategies on inverse kinematics, the LVI-based primal-dual neural network is designed based on the QP-LVI conversion and Karush-Kuhn-Tucker (KKT) conditions. With simple piecewise-linear dynamics and global (exponential) convergence to optimal solutions, it can handle general QP and linear programming (LP) problems in the same inverse-free manner. The repetitive motion planning scheme and the LVI-based primal-dual neural network are simulated based on PUMA560 robot manipulator with effectiveness demonstrated.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Zhang, Y.: Analysis and Design of Recurrent Neural Networks and Their Applications to Control and Robotic Systems. Ph.D. Thesis, Chinese University of Hong Kong (2002)
Latash, M.L.: Control of Human Movement. Human Kinematics Publisher, Chicago (1993)
Zhang, Y., Wang, J., Xu, Y.: A Dual Neural Network for Bi-Criteria Kinematic Control of Redundant Manipulators. IEEE Transanctions on Robotics and Automation 18, 923–931 (2002)
Zhang, Y., Ge, S.S., Lee, T.H.: A Unified Quadratic Programming Based on Dynamical System Approach to Joint Torque Optimization of Physically Constrained Redundant Manipulators. IEEE Transanctions on Systems, Man, and Cybernetics 34, 2126–2132 (2004)
Liegeois, A.: Automatic Supervisory Control of the Configuration and Behavior of Multibody Mechanisms. IEEE Transactions on Systems, Man, and Cybernetics 7, 868–871 (1977)
Khatib, O., Bowling, A.: Optimization of the Inertial and Acceleration Characteristics of Manipulators. In: Proceedings of IEEE International Conference on Robotics and Automation, vol. 4, pp. 2883–2889 (1996)
Zhang, Y., Wang, J., Xia, Y.: A Dual Neural Network for Redundancy Resolution of Kinematically Redundant Manipulators Subject to Joint Limits and Joint Velocity Limits. IEEE Transactions on Neural Networks 14, 658–667 (2003)
Zhang, Y., Wang, J.: A Dual Neural Network for Convex Quadratic Programming Subject to Linear Equation and Inequality Constraints. Physics Letters A 298, 271–278 (2002)
De Luca, A., Lanari, L., Oriolo, G.: Control of Redundant Robots on Cyclic Trajectories. In: Proceeding of IEEE International Conference on Robotics and Automation, vol. 1, pp. 500–506 (1992)
Klein, C., Huang, C.: Review of Pseudoinverse Control for Use with Kinematically Redundant Manipulators. IEEE Transactions on Systems, Man, and Cybernetics 13, 245–250 (1983)
Cheng, F.T., Chen, T.H., Sun, Y.Y.: Resolving Manipulator Redundancy Under Inequality Constraints. IEEE Journal of Robotics and Automation 10, 65–71 (1994)
Kinderlehrer, D., Stampcchia, G.: An Introduction to Variational Inequalities and their Applications. Academic, New York (1980)
Ferris, M.C., Pang, J.S.: Complementarity and Variational Problems: State of the Art. SIAM, Philadephia, Pennsylvania (1997)
Xia, Y., Wang, J.: A Recurrent Neural Network for Solving Linear Projection Equations. Neural Networks 13, 337–350 (2000)
He, B., Yang, H.: A Nual Network Model for Monotone Linear Asymmetric Variational Inequalities. IEEE Transactions on Neural Networks 11, 3–16 (2000)
Bazarra, M.S., Sherali, H.D., Shetty, C.M.: Nonlinear Programming – Theory and Algorithms. Wiley, New York (1993)
Li, W., Sweits, J.: A New Algorithm for Solving Strictly Convex Quadratic Programs. SIAM Journal on Optimization 7, 595–619 (1997)
Zhang, Y., Wang, J.: A Dual Neural Network for Constrained Joint Torque Optimization of Kinematically Redundant Manipulators. IEEE Transactions on Systems, Man, and Cybernetics 32, 654–662 (2002)
Bertsekas, D.P.: Parallel and Distributed Computation: Numerical Methods. Prentice-Hall, Englewood Cliffs, New Jersey (1989)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zhang, Y., Lv, X., Li, Z., Yang, Z. (2007). Repetitive Motion Planning of Redundant Robots Based on LVI-Based Primal-Dual Neural Network and PUMA560 Example. In: Li, K., Li, X., Irwin, G.W., He, G. (eds) Life System Modeling and Simulation. LSMS 2007. Lecture Notes in Computer Science(), vol 4689. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74771-0_61
Download citation
DOI: https://doi.org/10.1007/978-3-540-74771-0_61
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74770-3
Online ISBN: 978-3-540-74771-0
eBook Packages: Computer ScienceComputer Science (R0)