Mobile robot control system design based on fuzzy neural networks, страница 2

Let us consider procedure of the fuzzy neural network design on an example of the "beacons-gate" task. The gate is formed by two active beacons M1 and M2 (Fig. 1). Obviously this task is similar to the task of a motion direct to a beacon, but the robot must move along a straight line between the beacons.

Fig. 1. Pass of the gate

There are initial positions for which the motion trajectory will pass very near from one of beacons and the robot can bring down the beacon. To prevent this collision the robot has to rotate around of the nearest beacon initially and then pass in the gate.

From analysis of all possible situations, the eight fuzzy rules was designed for the "beacons-gate" task [4]:

g₁, g₂ – angles towards the first beacon and to the second beacon accordingly, r₁, r₂ – distances to the first beacon and the second beacon accordingly, K – number of the active beacons, DV equals to zero when the robot has to move along a straight line and the DV does not equals to zero when the desired motion is an arc.

The TSK fuzzy neural network structure corresponding to the described rules is show in Fig 2.

Fig. 2. The TSK fuzzy neural network structure

The network presented in figure 2 has one output neural. The full structure of the fuzzy neural network consists of the two independent similar networks. The output of the first network defines a desirable value of the parameter d. In the second network, the output defines a desirable value of the parameter. The TSK fuzzy network contains two parametrical layers (the first layer and the third layer), their parameters are determined at training. The parameters of the first layer are unknown coefficients of a membership function (nonlinear parameters ); the parameters of the third layer are called linear weights . In the example "beacons-gate" the eight fuzzy rules and the three input variables are used. The total number of the network parameters is 104, from which 32 are linear weights, the others 72 are parameters of the nonlinear part of the conditions.

In Wang-Mendel fuzzy neural network Mamdany-Zadeh conclusion model is used with the defuzzification in relation to the average center [5]

,                                                                                                                                                                                      (5)

where parametersare the center of the membership function of the k-th conclusion fuzzy rule,  is the value of the membership function of the k-th conclusion fuzzy rule. The Wang-Mendel fuzzy neural network structure corresponding to the rules for the "beacons-gate" task is show in Fig 3.

Fig. 3. The Wang-Mendel fuzzy neural network structure

This network contains four layers. The first layer and the third layer are parametrical. The unknown parameters of the first layer are the membership function coefficients (), the unknown parameters of the third layer are the weights.