**1. Introduction**

During almost three decades, the study on theory and applications of artificial neural network has increased considerably, due partly to a number of significant breakthroughs in research on network types and operational characteristics, but also because of some distinct advances in the power of computer hardware which is readily available for net implementation. In the last few years, recurrent neural networks (RNNs), which are neural network with feedback (closed-loop) connects, have been an important focus of research and development. Examples include bidirectional associative memory (BAM), Hopfield, cellular neural network (CNN), Boltzmann machine, and recurrent back propagation nets, etc.. RNN techniques have been applied to a wide variety of problems due to their dynamics and parallel distributed property, such as identifying and controlling the real-time system, neural computing, image processing and so on.

RNNs are widely acknowledged as an effective tool that can be employed by a wide range of applications that store and process temporal sequences. The ability of RNNs to capture complex, nonlinear system dynamics has served as a driving motivation for their study. RNNs have the potential to be effectively used in modeling, system identification, and adaptive control applications, to name a few, where other techniques may fall short. Most of the proposed RNN learning algorithms rely on the calculation of error gradients with respect to the network weights. What distinguishes recurrent neural networks from static, or feedforward networks, is the fact that the gradients are time dependent or dynamic. This implies that the current error gradient does not only depend on the current input, output, and targets, but rather on its possibly infinite past. How to effectively train RNNs remains a challenging and active research topic.

The learning problem consists of adjusting the parameters (weights) of the network, such that the trajectories have certain specified properties. Perhaps the most common online learning algorithm proposed for RNNs is the real-rime recurrent learning (RTRL), which calculates gradients at time (k) in terms of those at time instant (k-1). Once the gradients are evaluated, weight updates can be calculated in a straightf\_\_Gorward manner. The RTRL algorithm is very attractive in that it is applicable to real-time systems. However, the two main drawbacks of RTRL are the large computational complexity of O(N4) and, even more critical, the storage requirements of O(N3), where N denotes the number of neurons in the network.

Recurrent Neural Network with Human Simulator Based Virtual Reality 91

1. The hierarchic multilayer topology which they are based on is well known and efficient. 2. The use of dynamic neurons allows limiting the number of neurons required for modeling a given dynamic system, contrary to the tapped-delayed networks. 3. The training procedures for properly adjusting the network weights are significantly

The categories of RNN is very difficult where many parameters can be division according to

There are many classes of RNN architectures. All architectures can be best described using the state-space model from systems theory. This state-space model is explain in many references (Cheron et al., 2007) (Cruse, 2006)(Dijk, 1999), the following architectures or

These architectures emerge by applying constraints to the general state-space model. The architectures have been investigated and tested in applications by many researchers. In the following subsections, these specific constraints will be listed and the resulting architectures will be discussed. Each class is presented together with a quick look at some properties and

The architectures treated can be ordered hierarchically since some architecture is special cases of more general architectures. This hierarchy is visualized in Fig.1. The most general architectures are at the left, specific architectures are at the right. The accolades show what

The Fully Recurrent Neural Network (FRNN) is first described here in terms of individual neurons and their connections, as was done in [Williams e.a., 1989]. Then the FRNN is considered as a special case of the general state-space model and a convenient matrix

simpler and faster than those for the fully recurrent networks.

This chapter consists of the following items:

Training algorithms for recurrent neural networks

consideration, therefore the division will explain by:

**2.1 Types of RNN according to the performance of NN** 


architectures are parts of a more general architecture description.

Inverse kinematic For Humanied manipulator with 27-DOFs

Simulation of the humaniod manipulator based upon Virtual Reality

Some Special Recurrent Networks

Solution of IKP by using RNN

classes of architectures are presented:


**2.1.1 Fully recurrent neural networks (FRNN)** 


examples of their application.

notation of the network is given.

Types of RNN.

Conclusion

**2. Types of RNN** 

RNNS are mathematical abstractions of biological nervous systems that can perform complex mappings from input sequences to output sequences. In principle one can wire them up just like microprocessors, hence RNNs can compute anything a traditional computer can compute. In particular, they can approximate any dynamical system with arbitrary precision. However, unlike traditional, programmed computers, RNNs *learn* their behavior from a training set of correct example sequences. As training sequences are fed to the network, the error between the actual and desired network output is minimized using gradient descent, whereby the connection weights are gradually adjusted in the direction that reduces this error most rapidly. Potential applications include adaptive robotics, speech recognition, attentive vision, music composition, and innumerably many others where retaining information from arbitrarily far in the past can be critical to making optimal decisions. Recently, *Echo State Networks* ESNs and a very similar approach, *Liquid State Machines*, have attracted significant attention. Composed primarily of a large pool of hidden neurons (typically hundreds or thousands) with fixed random weights, ESNs are trained by computing a set of weights from the pool to the output units using fast, linear regression. The idea is that with so many random hidden units, the pool is capable of very rich dynamics that just need to be correctly "tapped" by setting the output weights appropriately. ESNs have the best known error rates on the Mackey-Glass time series prediction task.( Abraham, 2005)

Two main methods exist for providing a neural network with dynamic behavior: the insertion of a buffer somewhere in the network to provide an explicit memory of the past inputs, or the implementation of feedbacks. As for the first method, it builds on the structure of feed forward networks where all input signals flow in one direction, from input to output. Then, because a feed forward network does not have a dynamic memory, *tappeddelay-lines* (temporal buffers) of the inputs are used. The buffer can be applied at the network inputs only, keeping the network internally static as in the buffered multilayer perceptron (MLP) or at the input of each neuron as in the MLP with Finite Impulse Response (FIR) filter synapses (FIRMLP). The main disadvantage of the buffer approach is the limited past-history horizon, which needs to be used in order to keep the size of the network computationally manageable, thereby preventing modeling of arbitrary long time dependencies between inputs and outputs it is also difficult to set the length of the buffer given a certain application.

The second method, the most general example of implementation of feedbacks in a neural network is the fully recurrent neural network constituted by a single layer of neurons fully interconnected with each other or by several such layers. Because of the required large structural complexity of this network, in recent years growing efforts have been propounded in developing methods for implementing temporal dynamic feedback connections into the widely used multi-layered feed forward neural networks. Recurrent connections can be added by using two main types of recurrence or feedback: *external* or *internal*. *External recurrence* is obtained for example by feeding back the outputs to the input of the network as in NARX networks; *internal recurrence* is obtained by feeding back the outputs of neurons of a given layer in inputs to neurons of the same layer, giving rise to the so called *Locally Recurrent Neural Networks* (*LRNNs*) ( Francesco et al., 2006 )

The major advantages of LRNNs with respect to the buffered, tapped-delayed feedforward networks and to the fully recurrent networks are:


This chapter consists of the following items:

Types of RNN.

90 Recurrent Neural Networks and Soft Computing

RNNS are mathematical abstractions of biological nervous systems that can perform complex mappings from input sequences to output sequences. In principle one can wire them up just like microprocessors, hence RNNs can compute anything a traditional computer can compute. In particular, they can approximate any dynamical system with arbitrary precision. However, unlike traditional, programmed computers, RNNs *learn* their behavior from a training set of correct example sequences. As training sequences are fed to the network, the error between the actual and desired network output is minimized using gradient descent, whereby the connection weights are gradually adjusted in the direction that reduces this error most rapidly. Potential applications include adaptive robotics, speech recognition, attentive vision, music composition, and innumerably many others where retaining information from arbitrarily far in the past can be critical to making optimal decisions. Recently, *Echo State Networks* ESNs and a very similar approach, *Liquid State Machines*, have attracted significant attention. Composed primarily of a large pool of hidden neurons (typically hundreds or thousands) with fixed random weights, ESNs are trained by computing a set of weights from the pool to the output units using fast, linear regression. The idea is that with so many random hidden units, the pool is capable of very rich dynamics that just need to be correctly "tapped" by setting the output weights appropriately. ESNs have the best known error rates on the Mackey-Glass time series

Two main methods exist for providing a neural network with dynamic behavior: the insertion of a buffer somewhere in the network to provide an explicit memory of the past inputs, or the implementation of feedbacks. As for the first method, it builds on the structure of feed forward networks where all input signals flow in one direction, from input to output. Then, because a feed forward network does not have a dynamic memory, *tappeddelay-lines* (temporal buffers) of the inputs are used. The buffer can be applied at the network inputs only, keeping the network internally static as in the buffered multilayer perceptron (MLP) or at the input of each neuron as in the MLP with Finite Impulse Response (FIR) filter synapses (FIRMLP). The main disadvantage of the buffer approach is the limited past-history horizon, which needs to be used in order to keep the size of the network computationally manageable, thereby preventing modeling of arbitrary long time dependencies between inputs and outputs it is also difficult to set the length of the buffer

The second method, the most general example of implementation of feedbacks in a neural network is the fully recurrent neural network constituted by a single layer of neurons fully interconnected with each other or by several such layers. Because of the required large structural complexity of this network, in recent years growing efforts have been propounded in developing methods for implementing temporal dynamic feedback connections into the widely used multi-layered feed forward neural networks. Recurrent connections can be added by using two main types of recurrence or feedback: *external* or *internal*. *External recurrence* is obtained for example by feeding back the outputs to the input of the network as in NARX networks; *internal recurrence* is obtained by feeding back the outputs of neurons of a given layer in inputs to neurons of the same layer, giving rise to the

The major advantages of LRNNs with respect to the buffered, tapped-delayed feedforward

so called *Locally Recurrent Neural Networks* (*LRNNs*) ( Francesco et al., 2006 )

networks and to the fully recurrent networks are:

prediction task.( Abraham, 2005)

given a certain application.

