Optimization schemes for learning the forward and inverse kinematic equations with neural network

Learning in networks has traditionally been posed as an optimization problem. The number of optimization variables equals the number of weights in the network. This has given neural-network-training, which usually requires iterative techniques, a reputation for being very slow. In this paper various techniques of optimizing criterion function to train neural-network (the gradient method, variable-metric, conjugate-gradient) are investigated. These techniques are modified somewhat by the use of a one dimensional search to improve robustness and to accelerate convergence. In this comparative study we used these algorithms to learn the forward and the inverse coordinate transformation of two degrees freedom (DOF) robot arm. The simulations show that the variable-metric combined with a one dimensional optimization provides a variety of benefits learning speed and minimizes the iteration number. The result shows better learning of forward and inverse kinematic robot model and significant reduction of learning time was obtained.

[1]  Robert A. Jacobs,et al.  Increased rates of convergence through learning rate adaptation , 1987, Neural Networks.

[2]  P. J. Werbos,et al.  Backpropagation: past and future , 1988, IEEE 1988 International Conference on Neural Networks.

[3]  David G. Luenberger,et al.  Introduction to Linear and Nonlinear Programming , 1973 .

[4]  Sukhan Lee,et al.  Robot kinematic control based on bidirectional mapping neural network , 1990, 1990 IJCNN International Joint Conference on Neural Networks.

[5]  Raymond L. Watrous.  Learning Algorithms for Connectionist Networks: Applied Gradient Methods of Nonlinear Optimization , 1988 .

[6]  A. Guez,et al.  Accelerated convergence in the inverse kinematics via multilayer feedforward networks , 1989, International 1989 Joint Conference on Neural Networks.

[7]  L. E. Scales,et al.  Introduction to Non-Linear Optimization , 1985 .

[8]  W. C. Miller,et al.  A new acceleration technique for the backpropagation algorithm , 1993, IEEE International Conference on Neural Networks.

[9]  Bing J. Sheu,et al.  Optimization schemes for neural network training , 1994, Proceedings of 1994 IEEE International Conference on Neural Networks (ICNN'94).

[10]  J. Guo,et al.  A solution to the inverse kinematic problem in robotics using neural network processing , 1989, International 1989 Joint Conference on Neural Networks.