A FUZZY LOGIC APPROACH IN ROBOTIC MOTION CONTROL

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1 International Journal of Neural Networks and Applications, 4(1), 2011, pp A FUZZY LOGIC APPROACH IN ROBOTIC MOTION CONTROL Parvinder Bangar 1 and Manisha 2 1 Astt. Prof., Deptt. of ECE, NECS's, Group of Institutions, Karnal, parvinder.bangar@gmail.com 2 Sr. Lecturer, Deptt. of ECE, KITM, Karnal, manishabangar@gmail.com Abstract: Fuzzy logic is indeed the next frontier in building automation. As it is just an emerging technology, so to use fuzzy logic in a meaningful fashion, the automation system software needs to be built from the ground up with this functionality in mind. Not only must the language used to define the rules be well integrated into the operation of the software, but the distinction between conventional control agents and fuzzy control must be clearly delineated. This article represents the basic ideas and the fundamental procedure for use of fuzzy logic in automatic motion control of robotic navigation. Key Words: Robotic navigation, fuzzy sets, motion control, membership function, fuzzy inference system, fuzzification, defuzzification. INTRODUCTION Born in 1921, Dr. Lotfi Zadeh is considered the founder of the field of fuzzy logic[1]. He graduated in 1942 from the University of Tehran, Iran, with a degree in Electrical Engineering, and later traveled to America to attend MIT (1946) and Columbia University (1949), where he taught system theory[1]. He proposed the concept of Fuzzy Logic (FL) presented not as a control methodology, but as a way of processing data by allowing partial set membership rather than crisp set membership or non-membership. WHAT IS FUZZY LOGIC & HOW IS IT DIFFERENT FROM CONVENTIONAL CONTROL METHODS? FL is a problem-solving control system methodology that lends itself to implementation in systems ranging from simple, small, embedded micro-controllers to large, networked, multichannel PC or workstation-based data acquisition and control systems [1,2]. It can be implemented in hardware, software, or a combination of both [8]. FL provides a simple way to arrive at a definite conclusion based upon vague, ambiguous, imprecise, noisy, or missing input information. FL s approach to control problems mimics how a person would make decisions, only much faster. FL incorporates a simple, rule-based IF X AND Y THEN Z approach to a solving control problem rather than attempting to model a system mathematically. The FL model is empirically based, relying on an operator s experience rather than their technical understanding of the system. For example, rather than dealing with temperature control in terms such as SP =500F, T <1000F, or 210C <TEMP <220C, terms like IF (process is too cool) AND (process is getting colder) THEN (add heat to the process) or IF (process is too hot) AND (process is heating rapidly) THEN (cool the process quickly) are used. These terms are imprecise and yet very descriptive of what must actually happen. Consider what you do in the shower if the temperature is too cold: you will make the water comfortable very quickly with little trouble. FL is capable of mimicking this type of behavior but at very high rate. FUZZY LOGIC TERMINOLOGY The discussion so far does not adequately prepare us for reading and understanding most books and articles about fuzzy logic, because of the terminology used by sophisticated authors. Following are explanations of some terms, which should help in this regard. Dr. Zadeh initially established this terminology when he originated the fuzzy logic concept[1,2]. Fuzzy The degree of fuzziness of a system analysis rule can vary between being very precise, in which case we would not call it fuzzy, to being based on an

2 78 International Journal of Neural Networks and Applications opinion held by a human, which would be fuzzy. Being fuzzy or not fuzzy, therefore, has to do with the degree of precision of a system analysis rule. A system analysis rule need not be based on human fuzzy perception. For example, you could have a rule, If the boiler pressure rises to a danger point of 600 Psi as measured by a pressure transducer, then turn everything off. That rule is not fuzzy. As the complexity of a system increases, it becomes more difficult and eventually impossible to make a precise statement about its behavior, eventually arriving at a point of complexity where the fuzzy logic method born in humans is the only way to get at the problem. Fuzzy Sets A fuzzy set is almost any condition for which we have words: short men, tall women, hot, cold, new buildings, accelerator setting, ripe bananas, high intelligence, speed, weight, spongy, etc., where the condition can be given a value between 0 and 1. Example 1: A woman is 6 feet, 3 inches tall. In my experience, I think she is one of the tallest women I have ever met, so I rate her height at.98. This line of reasoning can go on indefinitely rating a great number of things between 0 and 1. Figure 1: Membership Function Structure (Transition of Degree of Membership from 0 to 1 of Various Components is Shown) Degree of Membership The degree of membership is the placement in the transition from 0 to 1 of conditions within a fuzzy set. If a particular building s placement on the scale is a rating of.7 in its position in newness among new buildings, then we say its degree of membership in new buildings is.7. In fuzzy logic method control systems, degree of membership is used in the following way. A measurement of speed, for example, might be found to have a degree of membership in too fast of.6 and a degree of membership in no change needed of.2. The system program would then calculate the center of mass between too fast and no change needed to determine feedback action to send to the input of the control system. Summarizing Information Human processing of information is not based on two-valued, off-on, either-or logic. It is based on fuzzy perceptions, fuzzy truths, fuzzy inferences, etc., all resulting in an averaged, summarized, normalized output, which is given by the human a precise number or decision value which he or she verbalizes, writes down or acts on. It is the goal of fuzzy logic control systems to also do this. The input may be large masses of data, but humans can handle it. The ability to manipulate fuzzy sets and the subsequent summarizing capability to arrive at an output we can act on is one of the greatest assets of the human brain. This characteristic is the big difference between humans and digital computers. Emulating this human ability is the challenge facing those who would create computer based artificial intelligence. It is proving very, very difficult to program a computer to have human-like intelligence. Fuzzy Variable Words like red, blue, etc., are fuzzy and can have many shades and tints. They are just human opinions, not based on precise measurement in angstroms. These words are fuzzy variables. If, for example, speed of a system is the attribute being evaluated by fuzzy, fuzzy rules, then speed is a fuzzy variable. Linguistic Variable Linguistic means relating to language, in our case plain language words. Speed is a fuzzy variable. Accelerator setting is a fuzzy variable. Examples of linguistic variables are: somewhat fast speed, very high speed, real slow speed, excessively high accelerator setting, accelerator setting about right, etc. A fuzzy variable becomes a linguistic variable when we modify it with descriptive words, such as somewhat fast, very high, real slow, etc.

3 A Fuzzy Logic Approach in Robotic Motion Control 79 The main function of linguistic variables is to provide a means of working with the complex systems mentioned above as being too complex to handle by conventional mathematics and engineering formulas. Universe of Discourse Let us make women the object of our consideration. All the women everywhere would be the universes of women. If we choose to discourse about (talk about) women, then all the women everywhere would be our universe of Discourse. Universe of Discourse then, is a way to say all the objects in the universe of a particular kind, usually designated by one word, that we happen to be talking about or working with in a fuzzy logic solution. Fuzzy Algorithm An algorithm is a procedure, such as the steps in a computer program. A fuzzy algorithm, then, is a procedure, usually a computer program, made up of statements relating linguistic variables. FUZZY RULES Human beings make decisions based on rules. Even though, we may not be aware of it, all the decisions we make are based on computer like if-then statements[3]. If the weather is fine, then we may decide to go out. If the forecast says the weather will be bad today, but fine tomorrow, then we make a decision not to go today, and postpone it till tomorrow. Rules associate ideas and relate one event to another. Fuzzy machines, which always tend to mimic the behavior of man, work the same way. Only this time the decision and the means of choosing that decision are replaced by fuzzy sets and the rules are replaced by fuzzy rules. Fuzzy rules also operate using a series of if-then statements. For instance, X then A, if y then b, where A and B are all sets of X and Y. Fuzzy rules define fuzzy patches, which is the key idea in fuzzy logic. A machine is made smarter using a concept designed by Bart Kosko called the Fuzzy Approximation Theorem (FAT). The FAT theorem generally states a finite number of patches can cover a curve as seen in the figure below. If the patches are large, then the rules are sloppy. If the patches are small then the rules are fine. Rules are usually expressed in the form: IF variable IS set THEN action For example, an extremely simple temperature regulator that uses a fan might look like this: IF temperature IS very cold THEN stop fan IF temperature IS cold THEN turn down fan IF temperature IS normal THEN maintain level IF temperature IS hot THEN speed up fan FUZZY CONTROL SYSTEM Fuzzy controllers are very simple conceptually. They consist of an input stage, a processing stage, and an output stage [4,5]. The input stage maps sensor or other inputs, such as switches, thumbwheels, and so on, to the appropriate membership functions and truth values. The processing stage invokes each appropriate rule and generates a result for each, then combines the results of the rules. Finally, the output stage converts the combined result back into a specific control output value. The most common shape of membership functions is triangular, although trapezoidal and bell curves are also used, but the shape is generally less important than the number of curves and their placement[4]. From three to seven curves are generally appropriate to cover the required range of an input value, or the universe of discourse in fuzzy jargon. Figure 2: Fuzzy Inference Unit (the Main Components of FIU are Shown in Figure) As discussed earlier, the processing stage is based on a collection of logic rules in the form of IF-THEN statements, where the IF part is called the antecedent and the THEN part is called the consequent. Typical fuzzy control systems have dozens of rules.

4 80 International Journal of Neural Networks and Applications Each step of the FIU is described in the following sections. Fuzzification Fuzzification is the first step in the fuzzy inferencing process. This involves a domain transformation where crisp inputs are transformed into fuzzy inputs. Crisp inputs are exact inputs measured by sensors and passed into the control system for processing, such as temperature, pressure, rpm s, etc.. Each crisp input that is to be processed by the FIU has its own group of membership functions or sets to which they are transformed. This group of membership functions exists within a universe of discourse that holds all relevant values that the crisp input can possess. Figure 1 shows the structure of membership functions within a universe of discourse for a crisp input. The shape of the membership function should be representative of the variable. However the computing resources available also restrict this shape. Complicated shapes require more complex descriptive equations or large lookup tables. Figure 3 shows examples of possible shapes for membership functions. Figure 3: (i) Shape of Membership Functions (the Most of the Applications use one of the Above Shown MF Shapes i.e. Bell, Singleton or Trapezoidal) too few membership functions for a given application will cause the response of the system to be too slow and fail to provide sufficient output control in time to recover from a small input change. This may also cause oscillation in the system. (ii) too many membership functions may cause rapid firing of different rule consequents for small changes in input, resulting in large output changes, which may cause instability in the system. Industry standard consists of 3 to 9 membership functions. These membership functions should also be overlapped. No overlap reduces a system based on Boolean logic[7]. Overlap Ratio= Overlap Scope / adjacent mf scope (1) Overlap Robustness=area of summed overlap / max. area of summed overlap (2) Rule Evaluation, Min. / Max. Inference Rule Evaluation consists of a series of IF-Zadeh Operator-THEN rules. A decision structure to determine the rules requires familiarity with the system and its desired operation. This knowledge often requires the assistance of interviewing operators and experts. There is a strict syntax to these rules. This syntax is structured as: IF antecedent 1 ZADEH OPERATOR antecedent 2... THEN consequent 1 ZADEH OPERATOR consequent 2... The antecedent consists of: input variable IS label, and is equal to its associated fuzzy input or truthvalue µ(x). The consequent consists of: output variable IS label; its value depends on the Zadeh Operator which determines the type of inferencing used. There are three Zadeh Operators, AND, OR, and NOT. The label of the consequent is associated with its output membership function. The Zadeh Operator is limited to operating on two membership functions, as discussed in the fuzzification process. Zadeh Operators are similar to Boolean Operators. Defuzzification Defuzzification involves the process of transposing the fuzzy outputs to crisp outputs. There are a variety of methods to achieve this; however this discussion is limited to the process used in this thesis design. A method of averaging is utilized here, and is known as the Center of Gravity method or COG, it is a method of calculating centroids of sets. The output membership functions to which the fuzzy outputs are transposed are restricted to being singletons. This is so to limit the degree of calculation intensity in the micro controller. The fuzzy outputs are transposed to their membership functions similarly as in fuzzification. With COG the singleton values of outputs are calculated using a weighted average. The crisp output is the result and is passed out of the FIU for processing elsewhere in the program of the controller.

5 A Fuzzy Logic Approach in Robotic Motion Control 81 CrispOutput [ ] Singleton position i() fuzzy outputi on axis i = Y i ( fuzzy outputi ) CASE STUDY The FL application in autonomous vehicle navigation is in motion control of vehicle[6]. Main requirements can be categorized as Regarding Basic Behavior Well-defined objective Well defined preconditions Simple computation with little state Examples Go to position, follow corridors, cross door, avoid obstacles Tolerate uncertainty In sensor data In prior knowledge In robot parameters Fuzzy Rules (a) IF Target-Left Out-of-reach THEN Turn-Left (b) IF Target-Right Out-of-reach THEN Turn-Right (c) IF Target-Left Out-of-reach THEN Turn-Right (d) IF Target-Left Out-of-reach THEN Turn-Left (e) IF Target-Ahead THEN Go-Straight Examples of fuzzy rules and applications for different situations and applicable rule sets can be shown as follows: Example 1: Inexact Prior Knowledge Figure 5: Example Showing the Motion Control of an Autonomous Vehicle using Fuzzy IF-THEN Rules Fuzzy Rules IF obstacle_close IF obstacle_close THEN avoid THEN cross Example 2: Unexpected Obstacles Figure 4: Qualitative Design Showing Motion Control for an Autonomous Vehicle Navigation Fuzzy Predicts (a) Target-Left: θ positive (b) Target-Right: θ negetive (c) Target-Ahead: θ small (d) Out of Reach: d smaller than Rmin Figure 6: Fuzzy Rules Example Showing the Motion Control of an Autonomous Vehicle using Fuzzy IF-THEN Rules IF obstacle_close IF obstacle_close THEN avoid THEN reach

6 82 International Journal of Neural Networks and Applications USES OF FUZZY LOGIC IN AUTONOMOUS ROBOTICS Realization of basic motion behavior [6] Coordination of behaviors [6] Environment modeling [9,10] Learning basic and complex behaviors Perceptual interpretation and sensor fusion [9,10] Anchoring symbolic representations to sensor data Flexible planning and execution [9,10] CONCLUSION From a slow beginning, fuzzy logic grew in applications and importance, until now it is a significant concept worldwide. Intelligent beings on the other side of our galaxy and throughout the universe have probably noted and defined the concept. Personal computer based fuzzy logic control is pretty amazing. It lets novices build control systems that work in places where even the best mathematicians and engineers, using conventional approaches to control, cannot define and solve the problem. In conclusion, it is well said that, REFERENCES [1] Al, M. Jamishi et: Fuzzy Logic and Control-Software and hardware Applications. [2] Kaur, Dr. Devinder, Konga, Elisa and Konga, Esa, University of Toledo: IEEE Journals: Fuzzy traffic Light Controller. [3] Kosko, Bart: Fuzzy Thinking. [4] Nakamura, K: Preference Relations on a Set of Fuzzy Utilities as a Basis for Decision Making. [5] Zimmerman,H.J: Fuzzy Set Theory and its Applications. [6] Fuzzy Logic from wikipedia- the free encyclopedia. URLhttp:// logic. [7] Fuzzy Logic Tutorial: Fuzzy Logic for just plain folks.url [8] Soffiotti, Alessandro: Fuzzy Logic Techniques for Autonomous Vehicle Navigation, URL aass.oru.se/ fuzzy logic application. [9] Mamdani controller: Fuzzy Logic Algorithm, URL fuzzy.htm [10] Fuzy Logic Applications, URL fuzzy_appl.10.htm The expressive power of fuzzy logic determines not so much what can be said, but what can be left unsaid. [Levesque & Brachman, 1985]