**6. Solution of IKP by using RNN**

This section introduces the basics of ANN architecture and its learning rule. Inspired by the idea of basing the feed forward and back propagation network structure. Fig.14 shows this structure , the Learning rule which is used in this paper is fast momentum back-propagation

Recurrent Neural Network with Human Simulator Based Virtual Reality 111

actual response of the neuron is Ok(n) . Suppose the response yk(n) was produced when x(n) applied to the network. If the actual response yk(n) is not same as **t**k(n) , we may define an error signal as: **e**k = **t**k(n) – **y**k(n). The purpose of error-correction learning is to minimize a cost function based on the error signal **e**k(n). Once a cost function is selected, error-

In case of non-linear neural network, the error surface may have troughs, valleys, canyons, and host of shapes, where as in low dimensional data, contains many minima and so many local minima plague the error landscapes, then it is unlikely that the network will find the global minimum. Another issue is the presence of plateaus regions where the error varies only slightly as a function of weights see and. Thus in presence of many plateaus, training will get slow. To overcome this situation momentum is introduced that forces the iterative

The humanoid manipulator 27-DOF model is built by using VR environment. It is shown in Fig. 15. The simulation of this model is achieved by solution the IKP with analytical model firstly. The data for analytical solution was using to learning FRNN that is shown in previous section with FRNN structure (15-33-27). The inputs are ( I=27 ) six for each two arms and two lags ( three position of end-effecter), one for waist and two for neck. The output of FRNN has dimension (N=27). The outputs are six angles of joint for each the

The initial posture form of humanoid manipulator is shown in Fig. 15. After solution of IKP by FRNN and get the joint angles. The values of joint angle were implemented by forward kinematic solution to get the posture of humanoid manipulator. The interaction between Matlab/Simulink and VR model will used the calculation of IKP by FRNN to implement the

**7. Simulation of the humaniod manipulator based upon virtual reality** 

correction learning is strictly an optimization problem.

process to cross saddle points and small landscapes.

posture. The overall simulation design is shown in Fig. 16.

limbs, one for waist and two for neck.

Fig. 15. Humanoid manipulator in VR.

with delta rule structure of network with dimension ( I-M-N). The inputs are the position of end-effector in (x,y,z) ,the network is single layer with dimension (33) neurons ( this dimension limited by trial and error ). The output dimensions are the angles of rotation and translation displacement in joints.

Fig. 14. FRBP Network with I inputs, one hidden layer of (M) unit and (N) outputs.(The dotted curve lines denote the finite recurrent connection)

The majority of adaptation learning algorithms are based on the fast momentum back propagation the mathematical characterization of a multilayer feed forward network is that of a composite application of functions each of these functions represents a particular layer and may be specific to individual units in the layer, e.g. all the units in the layer are required to have same activation function. The overall mapping is thus characterized by a composite function relating feed forward network inputs to output. That is O=fcomposite (x) . Using ( p ) mapping layers in a ( p+1 ) layer feed forward net yield:

 O=f Lp (f Lp-1 (fL1 (x).) ). Thus the interconnection weights from unit ( k ) in L1 to unit ( I ) in L2 are wL1-L2 . If hidden units have a sigmoidal activation function, denoted f sig .

$$\left\{ O\_{i}^{L2} = \sum\_{k=1}^{Hi} w \right\}\_{ik}^{L1 \to L2} \left\{ f\_{k}^{sig} \left[ \sum\_{j=1}^{I} w\_{kj}^{Lo \to L1} i\_{j} \right] \right\} \tag{15}$$

Above equation illustrates neural network with supervision and composition of non-linear function.The learning is a process by which the free parameters of a neural network are adapted through a continuing process of simulation by the environment in which the network is embedded. The type of learning is determined by the manner in which the parameters changes take place. A prescribed set of well defined rules for the solution of a learning problem is called learning algorithm. The Learning algorithms differ from each other in the way in which the adjustment kj, Δw to the synaptic weight wkj is formulated. The basic approach in learning is to start with an untrained network.

The network outcomes are compared with target values that provide some error. Suppose that **t**k(n) denote some desired outcome (response) for the Kth neuron at time n and let the

with delta rule structure of network with dimension ( I-M-N). The inputs are the position of end-effector in (x,y,z) ,the network is single layer with dimension (33) neurons ( this dimension limited by trial and error ). The output dimensions are the angles of rotation and

Fig. 14. FRBP Network with I inputs, one hidden layer of (M) unit and (N) outputs.(The

The majority of adaptation learning algorithms are based on the fast momentum back propagation the mathematical characterization of a multilayer feed forward network is that of a composite application of functions each of these functions represents a particular layer and may be specific to individual units in the layer, e.g. all the units in the layer are required to have same activation function. The overall mapping is thus characterized by a composite function relating feed forward network inputs to output. That is O=fcomposite (x) . Using ( p )

O=f Lp (f Lp-1 (fL1 (x).) ). Thus the interconnection weights from unit ( k ) in L1 to unit ( I ) in

Above equation illustrates neural network with supervision and composition of non-linear function.The learning is a process by which the free parameters of a neural network are adapted through a continuing process of simulation by the environment in which the network is embedded. The type of learning is determined by the manner in which the parameters changes take place. A prescribed set of well defined rules for the solution of a learning problem is called learning algorithm. The Learning algorithms differ from each other in the way in which the adjustment kj, Δw to the synaptic weight wkj is formulated.

The network outcomes are compared with target values that provide some error. Suppose that **t**k(n) denote some desired outcome (response) for the Kth neuron at time n and let the

(15)

L2 are wL1-L2 . If hidden units have a sigmoidal activation function, denoted f sig .

The basic approach in learning is to start with an untrained network.

1 2 2 1 1 1

*Hi L L I L sig Lo L i k kj j k j ik O w f wi* 

dotted curve lines denote the finite recurrent connection)

mapping layers in a ( p+1 ) layer feed forward net yield:

translation displacement in joints.

actual response of the neuron is Ok(n) . Suppose the response yk(n) was produced when x(n) applied to the network. If the actual response yk(n) is not same as **t**k(n) , we may define an error signal as: **e**k = **t**k(n) – **y**k(n). The purpose of error-correction learning is to minimize a cost function based on the error signal **e**k(n). Once a cost function is selected, errorcorrection learning is strictly an optimization problem.

In case of non-linear neural network, the error surface may have troughs, valleys, canyons, and host of shapes, where as in low dimensional data, contains many minima and so many local minima plague the error landscapes, then it is unlikely that the network will find the global minimum. Another issue is the presence of plateaus regions where the error varies only slightly as a function of weights see and. Thus in presence of many plateaus, training will get slow. To overcome this situation momentum is introduced that forces the iterative process to cross saddle points and small landscapes.
