An Embedded Type-2 Fuzzy Controller for a Mobile Robot Application

Fuzzy logic systems (FLS) have been used in different applications with satisfactory performance (Wang, 1997). The human perception cannot be modelled by traditional mathematical techniques, thus, the introduction of fuzzy set (FS) theory in this modelling has been suitable (John & Coupland, 2007). When real-world applications are treated, many sources of uncertainty often appear. Several natures of uncertainties would influence the performance of a system. It is independent from what kind of methodology is used to handle it (Mendel, 2001). Type-1 Fuzzy logic systems (T1-FLS) have limited capabilities to directly handle data uncertainties (Mendel, 2007). Once a type-1 membership function (MF) has been defined, uncertainty disappears because a T1-MF is totally precise (Hagras, 2007). Type-2 fuzzy logic systems (T2-FLS) make possible to model and handle uncertainties. These are rule based systems in which linguistic variables are described by means of Type-2 fuzzy sets (T2-FSs) that include a footprint of uncertainty (FOU) (Mendel, 2001). It provides a measure of dispersion to capture more about uncertainties (Mendel, 2007). While T2-FSs have non-crisp MFs, T1-FSs have crisp membership grades (MGs) (John & Coupland, 2007). A representation of the inference model for T2-FLS is depicted in Figure 1 (Mendel, 2007). It begins with fuzzification, which maps crisp points into T2-FSs. Next, inference engine computes the rule base by making logical combinations of antecedent T2-FS, whose results are implicated with consequent T2-FS to form an aggregated output type-2 fuzzy set. Afterwards, Type-Reduction (TR) takes all output sets and performs a centroid calculation of this combined type-2 fuzzy set, which leads to a type-1 fuzzy set called type-reduced set. That reduced set is finally defuzzyfied in order to obtain a crisp output (Mendel, 2001; Karnik & Mendel 2001). The computational complexity of this model is reduced if interval type-2 fuzzy sets are used (Mendel, 2001), it is convenient in the context of hardware implementation in order to make softer the computational effort and sped up the inference time. Type-2 fuzzy hardware is a topic of special interest, since the application of T2-FLS to particular fields that demand mobile electronic solutions would be necessary. Some recent