KNOWLEDGE-BASED ROBOT VISION SYSTEM FOR AUTOMATED PART HANDLING

South African Journal of Industrial Engineering, May 2008 by Wang, J, van Niekerk, T I, Hattingh, D G, Hua, T

3. CONTINUOUS FUZZY CONTROLLER

Fuzzy logic is one of the fastest-growing technologies in the world since the inception of the computer era. Fuzzy logic is based on natural language, which can model nonlinear functions of arbitrary complexity, and can be further built on the expertise of experts. The fuzzy controller is capable of giving excellent and robust solutions to complicated systems, if adequate, precise, and reliable expertise has been accumulated. Fuzzy pattern recognition is a very active branch in the field of pattern recognition, which may result in systems with high computational efficiency and achieve the desired accuracy. A schematic fuzzy system architecture is illustrated in Figure 3.

To represent the object profile with a closed chain of vectors, locating the corner points, with given tolerance, is the kernel. As far as the corner tracing is concerned, a continuous fuzzy controller was developed in this application on the basis of testing various corners and collecting enough knowledge, which covered all known possibilities of corner appearance.

To judge whether a corner appears, two determinative factors are considered: one is the length of orthogonal vector Len to the base vector vbase from the Mth point; the other is the distance Prj from the project point that is perpendicular to the base vector to the endpoint of vbase; Node, the output of this Continuous Fuzzy Controller (CFC), is the membership of the corner point. Figure 4 illustrates the definition of Len and Prj.

The implementation procedure of the developed CFC algorithm is described as follows:

3.1 Normalization of universe of discourse

For the sake of simplification, x, y, and z are used to represent Len, Prj, and Node respectively. Assuming χ ∈[χ^sub 1^,χ^sub 2^], y ∈ [y^sub 1^,y^sub 2^], and z ∈ [z^sub 1^,z^sub 2^], to confine Len, Prj and Node to [-1, 1], the following normalization formulae are applied:

... (1)

... (2)

... (3)

3.2 Definition of fuzzy set and membership functions

For the normalized input and output variable x, y, and z, five fuzzy sets are defined as: NL, NS, ZE, PS, and PL, which are represented by the symmetric and entirelyoverlapped triangle membership functions A1~A5, B1~B5, C1~C5 respectively. Hence, ] 1 , 1 [- . .x , . = 1 Ai µ . Figure 5 illustrates the membership functions of Len, Prj, and Node.

The five membership functions can be further expressed as:

Negative Large (NL):

... (4)

Negative Small (NS):

... (5)

Zero (ZE):

... (6)

Positive Small (PS):

... (7)

Positive Large (PL):

... (8)

3.3 Fuzzy rule base

Table 1 gives all 25 rules for fuzzy reasoning.

3.4 Fuzzy reasoning methods

According to Table 1, the fuzzy rule set can be described as:

Rule 1 (R1): IF Len is negative large && Prj is negative large, THEN Node is positive large;

Rule 2 (R2): IF Len is negative small && Prj is negative small, THEN Node is positive small;

Rule 24 (R24): IF Len is positive small && Prj is positive large, THEN Node is negative small;

Rule 25 (R25): IF Len is positive large && and Prj is positive large, THEN Node is negative small.