Control of the Kinematic model

We are based on the procedure proposed by Kanayama et al. [1] and Nelson et al. [20] to solve the tracking problem for the kinematic model vdt). Suppose that the desired trajectory qa satisfies (5.5)  

Using the robot local frame (the moving coordinate systan x-y in Fig. 5.2), the error coordinates can be defined as (5.6)  

And the auxiliary velocity control input that achieves tracking for (5.1) is given by (5.7)  

The first approach in the optimization for the fuzzy controller of the mobile robot is to apply our proposed method to obtain the values of fe, (i = 1, 2, 3) for optimal behavior of the controller. 

Once we have found these gain constraints, the second step is to find the values of the membership functions of the fuzzy controller. 

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