Report on robotic control

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Report on robotic control

  1. 1. Anil Maurya Electrical & Electronics Engineer 1 A REPORT ON ROBOTIC CONTROL USING FUZZY LOGICS BY ANIL MAURYA ELECTRICAL & ELECTRONICS ENGINEER
  2. 2. Anil Maurya Electrical & Electronics Engineer 2 CONTENTS Contents vi List of Figures x List of Tables xii Abstract xiv Chapter 1: Introduction 2 Chapter 2: Fuzzy logics 3 2.1 Fuzzy Set 4 2.2 Fuzzy Inference System 5 Chapter 3: Operation of Fuzzy Logic 11 3.1 Example of Fuzzy Logic 11 3.2 Fuzzy regions 12 3.3 Fuzzy rules 15 3.4 Fuzzification 16 3.5 Defuzzification 16 Chapter 4: Robot Control with Fuzzy Logics 19 4.1 Reactive behaviors using Fuzzy logics 24 4.1.1 Obstacle avoidance 25 4.1.2 Following edge 25 4.1.3 Target steer 26 4.2 Multiple behaviors fusion by fuzzy reasoning 27 Chapter 5: Application of fuzzy logics 30
  3. 3. Anil Maurya Electrical & Electronics Engineer 3 Chapter 6: Conclusion 33 Reference LIST OF FIGURES Chapter 2 Fig. 2.1 Crisp membership function 5 Fig. 2.2 Fuzzy membership function 8 Fig. 2.3 Trapezoidal membership function 10 Fig. 2.4 Gaussian membership function 10 Fig. 2.5 fuzzy logic control 11 Fig. 2.6 fuzzy inference system 12 Chapter 3 Fig. 3.1 Sectional View of fuzzy room cooler 13 Fig. 3.2 Defuzzification condition 17 Chapter 4 Fig. 4.1 Robot motion to reach a target 21 Fig. 4.2 Robot action behavior control 25 Fig. 4.3 Rule for robot behavior 28 List of Tables Chapter 3 Table 3.1 Fuzzy Rules 15 Table 3.2 Fuzzification 16 Chapter 4 Table 4.1 FLC rule table 18
  4. 4. Anil Maurya Electrical & Electronics Engineer 4 ABSTRACT Fuzzy set theory, originally developed by Lotfi Zadeh in the 1960’s, has become a popular tool for control applications in recent years (Zadeh, 1965). Fuzzy control has been used extensively in applications such as servomotor and process control. One of its main benefits is that it can incorporate a human being’s expert knowledge about how to control a system, without that a person need to have a mathematical description of the problem. Many robots in the literature have used fuzzy logic (Song & Tay, 1992), (Khatib, 1986), (Yanetal, 1994) etc. Computer simulations by Ishikawa feature a mobile robot that navigates using a planned path and fuzzy logic. Fuzzy logic is used to keep the robot on the path, except when the danger of collision arises. In this case, a fuzzy controller for obstacle avoidance takes over. Konolige, et al. use fuzzy control in conjunction with modeling and planning techniques to provide reactive guidance of their robot. Sonar is used by robot to construct a cellular map of its environment. Sugeno developed a fuzzy control system for a model car capable of driving inside a fenced-in track. Ultrasonic sensors mounted on a pivoting frame measured the car’s orientation and distance to the fences. Fuzzy rules were used to guide the car parallel to the fence and turn corners (Sugeno et al., 1989). The most known fuzzy models in the literature are Mamdani fuzzy model and Takagi- Sugeno-Kang (TSK) fuzzy model. The control strategy based on Mamdani model has the linguistic expression (Mamdani, 1981).
  5. 5. Anil Maurya Electrical & Electronics Engineer 5 Chapter 1 INTRODUCTION Fuzzy logic was initiated in 1965 by Lotfi A. Zadeh, professor for computer science at the university of California in Berkeley, Fuzzy Logic (FL) is a multivalued logic, that allows intermediate to be defined between conventional evaluations like true/ false, yes /no, high/low etc. notions like rather tall or very fast can be formulated mathematically and processed by computers, in order to apply a more human like way of thinking of the programming of computers. A fuzzy system is an alternative to traditional notions of set membership and logic that has its origins in ancient Greek philosophy. The precision of mathematics owes its success in large part to the efforts of Aristotle and the philosophers who preceded him. In their efforts to devise a concise theory of logic, and later mathematics, the so – called “Laws of thought” were posited. One of these the Law of the Excluded Middle states that every proposition must either is true or false. Even when Parmenides proposed the first version of this law (around 400 B.C) there were strong and immediate objections: for example, Heraclitus proposed that things could be simultaneously True and Not True. It was Plato who laid the foundation for that would become fuzzy logic, indicating that there was a third region (beyond True and False) where these opposites “tumbled about”. Other, more modern philosophers echoed his sentiments, notably Hegel, Marx, and Engels. But it was Lukasiewicz who first proposed a systematic alternative to the bi-valued logic of Aristotle. Even in the present time some Greeks are still outstanding examples for fussiness. Fuzzy logic has emerged as a profitable tool for the controlling and steering of systems and complex industrial processes, as well as for household and entertainment electronics, as well as for the other expert systems and applications like the classification of SAR data.
  6. 6. Anil Maurya Electrical & Electronics Engineer 6 Chapter 2 FUZZY LOGICS FUZZY – “ not clear , distinct , or precise ; blurred ” [Elian Rich] Fuzzy logic is a useful method of learning when mathematical methods are not available and large number of input data is parent. Fuzzy logic 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. It can be implemented in hardware, software or a combination of both. Fuzzy Logic provides a simple way to arrive at a definite conclusion based upon vague, ambiguous, imprecise, noisy or missing input information Fuzzy Logic’s approach to control problems mimics how a person would make decisions, only much faster. Fuzzy logic techniques have been used in image-understanding applications such as detection of edges, feature extraction, classification, and clustering. Fuzzy logic poses the ability to mimic the human mind to effectively employ modes of reasoning that are approximate rather than exact. In traditional hard computing, decisions or actions are based on precision, certainty, and vigor. Precision and certainty carry a cost. In soft computing, tolerance and impression are explored in decision making. The exploration of the tolerance for imprecision and uncertainty underlies the remarkable human ability to understand distorted speech, decipher sloppy handwriting, comprehend nuances of natural language, summarize text, and recognize and classify images. With FL, we can specify mapping rules in terms of words rather than numbers. Computing with the words explores imprecision and tolerance. Another basic concept in Fuzzy logic is the fuzzy if–then rule. Although rule-based systems have a long history of use in artificial intelligence, what is missing in such systems is machinery for dealing with fuzzy consequents or fuzzy antecedents. In most applications, a Fuzzy logic solution is a translation of a human solution. Thirdly, Fuzzy logic can model nonlinear functions of arbitrary complexity to a desired degree of accuracy.
  7. 7. Anil Maurya Electrical & Electronics Engineer 7 Fuzzy logic is a convenient way to map an input space to an output space. Fuzzy logic is one of the tools used to model a multi-input, multi-output system. Soft computing includes Fuzzy logic, neural networks, probabilistic reasoning, and genetic algorithms. Today, techniques or a combination of techniques from all these areas are used to design an intelligence system. Neural networks provide algorithms for learning, classification, and optimization, whereas fuzzy logic deals with issues such as forming impressions and reasoning on a semantic or linguistic level. Probabilistic reasoning deals with uncertainty. Although there are substantial areas of overlap between neural networks, Fuzzy logic, and probabilistic reasoning, in general they are complementary rather than competitive. Recently, many intelligent systems called neuro fuzzy systems have been used. There are many ways to combine neural networks and Fuzzy logic techniques. Before doing so, however, it is necessary to understand basic ideas in the design of Fuzzy logic techniques. In this chapter, we will introduce Fuzzy logic concepts such as fuzzy sets and their properties, Fuzzy logic operators, hedges, fuzzy proposition and rule-based systems, fuzzy maps and inference engine, defuzzification methods, and the design of an Fuzzy logic decision system. 2.1 Fuzzy sets and membership functions Fuzzy sets introduce a certain amount of vagueness to reduce complexity of comprehension. This set consists of elements that signify the degree or grade of membership to a fuzzy aspect. Membership values usually use closed intervals and denote the sense of belonging of a member of a crisp set a fuzzy set. Fuzzy Logics provides the opportunity for modeling conditions that inherently imprecisely defined. Fuzzy techniques in the form of approximate reasoning provide decision support and expert systems with powerful reasoning capabilities. The permissiveness of fuzziness in the human thought process suggests that much of the logic behind thought processing is not traditional two valued logic or even multivalued logic, but logic with fuzzy truths, fuzzy connectiveness, and fuzzy rules of inference. A fuzzy set is an extension of a crisp set. Crisp sets allow only full membership or no membership at all, whereas fuzzy sets allow partial membership. In a crisp set, membership or non- membership of element x in set A is described by a characteristic function µA (x), where µA (x) = 1 if x € A and µA (x) = 0 if x € A. Fuzzy set theory extends this
  8. 8. Anil Maurya Electrical & Electronics Engineer 8 concept by defining partial membership. A fuzzy set A on a universe of discourse U is characterized by a membership function µA (x) that takes values in the interval [0.1]. Fuzzy sets represent commonsense linguistic labels like slow, fast, small, large, heavy, low, medium, high, tall, etc. A given element can be a member of more than one fuzzy set at a time. A fuzzy set A in U may be represented as a set of ordered pairs. Each pair consists of a generic element x and its grade of membership function; that is, A = {(x, µA (x)) | x € U}, x is called a support value if µA (x) > 0. A linguistic variable x in the universe of discourse U is characterized by T (x) = {Tx 1 , Tx 2 …Tx k } and µA (x) = { µx 1 , µx 2 ,…. µx k }, where T(x) is the term set of x that is, the set of names of linguistic value of x, with each Tx i being a fuzzy number with membership function µx i defined on U. For example, if x indicates height, then T(x) may refer to sets such as short, medium, or tall. A membership function is essentially a curve that defines how each point in the input space is mapped to a membership value (or degree of membership) between 0 and 1. As an example, consider a fuzzy set tall. Let the universe of discourse be heights from 40 inches to 90 inches. With a crisp set, all people with height 72 or more inches are considered tall, and all people with height of less than 72 inches are considered not tall. The crisp set membership function for set tall is shown in figure. The corresponding fuzzy set with a smooth membership function is shown in figure. The curve defines the transition from not tall and shows the degree of membership for a given height. We can extend this concept to multiple sets. If we consider a universe of discourse from 40 inches to 90 inches, then, to describe height, we can use three term values such as short, average, and tall. In practice, the terms short, medium, and tall are not used in the strict sense. Instead, they imply a smooth transition. Fuzzy membership functions representing these sets are shown in figure. The Figure shows that a person with height 65 inches will have membership value 1 for set medium, whereas a person with height 60 inches may be a member of the set short and also a member of the set medium; only the degree of membership varies with these sets. Various types of membership functions are used, including triangular, trapezoidal, generalized bell shaped, Gaussian curves, polynomial curves, and sigmoid functions. figure shows trapezoidal membership functions. Triangular curves depend on three parameters a, b, and c and are given by
  9. 9. Anil Maurya Electrical & Electronics Engineer 9 Fig. 2.1 Crisp Membership Function Fig.2.2 Fuzzy Membership Function Fig. 2.3 Trapezoidal Membership Function
  10. 10. Anil Maurya Electrical & Electronics Engineer 10 Trepezoidal Curves dependes on four parameters 2.1 The ∏- shaped membership functions 2.2 Where S(x; a, b, c) represents a membership function defined as 2.3 a, b, and c are the parameters that are adjusted to fit the desired membership data. The parameter b? Is the half width of the curve at the crossover point? The Gaussian and π- shaped membership functions are shown in figures, respectively. Gaussian curves depend on two parameters σ and c and are represented by 2.4
  11. 11. Anil Maurya Electrical & Electronics Engineer 11 Fig. 2.4 Gaussian Membership Function Fig.2.5 π- shaped membership functions 2.2 Fuzzy Inference System The theory of fuzzy logic based system could remain fuzzy till one discovers how to apply it to a problem. Fuzzy Logic has been used in a broad spectrum of applications ranging from domestic like washing machines and cameras, to more sophisticated ones that include turbine control, tracking, data classifiers, etc. Fuzzy Logic by itself does not exhibit intelligence. Invariable systems that use Fuzzy Logic are augmented with techniques that facilitate learning and adaptation to the environment in question. Fig. 2.6 Block diagram of Fuzzy Logic Control A fuzzy inference system (FIS) essentially defines a nonlinear mapping of the input data vector into a scalar output, using fuzzy rules. The mapping process involves input/output membership functions, Fuzzy Logic operators, fuzzy if–then rules, aggregation of output sets, and defuzzification. An FIS with multiple outputs can be considered as a collection of independent multi-input, single-output systems. A general model of a fuzzy inference system (FIS) is shown in Figure. The Fuzzy Logic
  12. 12. Anil Maurya Electrical & Electronics Engineer 12 System maps crisp inputs into crisp outputs. It can be seen from the figure that the Fuzzy Inference System contains four components: the fuzzifier, inference engine, rule base, and defuzzifier. The rule base contains linguistic rules that are provided by experts. It is also possible to extract rules from numeric data. Once the rules have been established, the Fuzzy Inference System can be viewed as a system that maps an input vector to an output vector. The fuzzifier maps input numbers into corresponding fuzzy memberships. This is required in order to activate rules that are in terms of linguistic variables. The fuzzifier takes input values and determines the degree to which they belong to each of the fuzzy sets via membership functions. The inference engine defines mapping from input fuzzy sets into output fuzzy sets. It determines the degree to which the antecedent is satisfied for each rule. If the antecedent of a given rule has more than one clause, fuzzy operators are applied to obtain one number that represents the result of the antecedent for that rule. It is possible that one or more rules may fire at the same time. Outputs for all rules are then aggregated. During aggregation, fuzzy sets that represent the output of each rule are combined into a single fuzzy set. Fuzzy rules are fired in parallel, which is one of the important aspects of an Fuzzy Inference System. In an Fuzzy Inference System, the order in which rules are fired does not affect the output. The defuzzifier maps output fuzzy sets into a crisp number. Given a fuzzy set that encompasses a range of output values, the defuzzifier returns one number, thereby moving from a fuzzy set to a crisp number. Several methods for defuzzification are used in practice, including the centroid, maximum, mean of maxima, height, and modified height defuzzifier. The most popular defuzzification method is the centroid, which calculates and returns the center of gravity of the aggregated fuzzy set. FISs employ rules. However, unlike rules in conventional expert systems, a fuzzy rule localizes a region of space along the function surface instead of isolating a point on the surface. For a given input, more than one rule may fire. Also, in an FIS, multiple regions are combined in the output space to produce a composite region. A general schematic of an Fuzzy Inference System is shown in Figure.
  13. 13. Anil Maurya Electrical & Electronics Engineer 13 Fig. 2.7 Schematic diagram of Fuzzy Inference System
  14. 14. Anil Maurya Electrical & Electronics Engineer 14 Chapter 3 OPERATION OF FUZZY LOGIC We discuss a traditional problem of controlling the speed of a motor based on two parameters temperature and humidity. Such a model fits snug into room coolers that use a tank of water and a fan to increase humidity to bring down temperature. Coolers like these are widely used in tropical high temperature and dry environments. The same could be extended for a wide range of applications. The following description explains how fuzzy logic works and how we model a system to use the concept. The logic explained herein is said to use the Mamdani style of fuzzy inference processing. We assume conventional room cooler implemented using a fan encased in a box with wool or hay that is continuously moistened by a tickle of water. A motorized pump controls the rate of flow of water required for moistening. Two sensors mounted inside the cooler or in the room at strategic locations measure the fan motor speed and the temperature within the room. The fan speed could be varied either by a knob by the user or could be designed to change based on an appropriate parameter sensed (humidity, for instance). The basic aim here is to achieve a smooth control and also save on water, a precious resource. 3.1 Example of Fuzzy Logic The conventional room cooler implemented using a fan encased in a box with wool or hay that is continuously moistened by a tickle of water. A motorized pump controls the rate of flow of water required for moistening. Two sensors mounted inside the cooler or in the room at strategic locations measure the fan motor speed and the temperature within the room. The fan speed could be varied either by a knob by the user or could be designed to change based on an appropriate parameter sensed (humidity, for instance). The basic aim here is to achieve a smooth control and also save on water, a precious resource. For simplicity we assume that to maintain the temperature of the room, only the rate of flow of water needs to be controlled based on the speed of the fan and the temperature.
  15. 15. Anil Maurya Electrical & Electronics Engineer 15 Fig.3 .1 Sectional view of fuzzy room cooler 3.2 Fuzzy regions Two parameters temperature and pressure decide the water flow rate. We define fuzzy terms for temperature as Cold, Cool, Moderate, Warm and Hot, while those for fan speed (measured in rotation per minute) as Slack, Low, Medium, Brisk, fast. Thus temperature in the room could be defined as Cold or Cool or by any of the corresponding fuzzy linguistic variables. Likewise, the fan speed too could be defined by any of the latter variables. The output of the system, which is the water controlled by the motorized pump, could also be defined accordingly by yet another set of fuzzy terms Strong Negative (SN), Negative (N), Low -Negative (LN), Medium (M), Low - Positive (LP), Positive (P) and High – Positive (HP). With real data available we now define profiles for each of these parameters temperature, fan motor speed and flow rate by assigning memberships to their respective values. The shown in the figure depict this relationship for the inputs temperature and fan speed reveals this for the output flow rate.
  16. 16. Anil Maurya Electrical & Electronics Engineer 16 Observe that the regions for each of the sets for both the input parameters, temperature and fan motor speed, as also the output have a common intersection area. For example, we say that when the temperature is 25 degrees, its membership to the fuzzy set moderate is 1 (100%). But as we drift away to 30 degrees, its membership to this set decreases while the same to the set warm starts to increase. Thus when the temperature is 30 degrees it is neither fully moderate nor warm. These profiles have to be carefully designed after studying the nature and desired behavior of the system. (a) Temprature (b) Fan motor speed
  17. 17. Anil Maurya Electrical & Electronics Engineer 17 Water Flow Rate 3.3 Fuzzy rules The fuzzy rules form the triggers of the fuzzy engine. After a study of the system we could write linguistic rules such as – R1: if Temperature is Hot and Fan motor Speed is Slack then Flow – rate is HIGH – POSITIVE. R2: if Temperature is Hot and Fan motor Speed is Low then Flow – rate is HIGH – POSITIVE. R3: if Temperature is Hot and Fan motor Speed is Medium then Flow – rate is POSITIVE. R4: if Temperature is Hot and Fan motor Speed is Brisk then Flow – rate is HIGH – POSITIVE. R5: if Temperature is Warm and Fan motor Speed is Medium then Flow–rate is LOW–POSITIVE. R6: if Temperature is Warm and Fan motor Speed is Medium then Flow – rate is POSITIVE. R7: if Temperature is Cool and Fan motor Speed is Low then Flow – rate is NEGATIVE.
  18. 18. Anil Maurya Electrical & Electronics Engineer 18 R8: if Temperature is Moderate and Fan motor Speed is Low then Flow – rate is MEDIUM. Table 3.1 Table of fuzzy rules 3.4 Fuzzification The fuzzifier forms the heart of the fuzzy engine. Whenever the sensors report values of temperature and fan speed, they are mapped based on their memberships to the respective fuzzy regions they belong to. For instance if at some instance of time t the temperature is 42 degrees and speed 31 rpm, the corresponding membership value and the associated fuzzy regions are mentioned below. Table 3.2 fuzzification From the table, since both temperature and fan speed belong to two regions; it is clear that the rules R3, R4, R5 and R6 are applicable. The rules indicate a conflict. While two of them state the flow – rate should be POSITIVE, the other two states that it should be LOW – POSITIVE and HIGH – POSITIVE respectively.
  19. 19. Anil Maurya Electrical & Electronics Engineer 19 3.5 Defuzzifier The fuzzy outputs LOW – POSITIVE, HIGH – POSITIVE and POSITIVE are to be converted to a single crisp value which can then be delivered to the final actuator of the pump. This process is called defuzzification. Several methods are used to achieve defuzzification, the most common ones being the Centre OF Gravity method and the Composite Maxima method. In both these methods we need to compute the composite region formed by the portions A, B, C and D on the output profile. In case of parameters whose premises are connected by an AND, the minimum of their memberships is first found. This value is used to cut through the profile of the output fuzzy set (done by drawing a horizontal line). This results in a region (area) on the output surface. For cases where an OR relates the premises the maximum membership is taken to work out the output surface. All output surfaces are found to obtain the composite output region. Depending on the application, either the Centre of Gravity or the Composite Maxima of the Region (area) is found and treated as the crisp output. The former method works best for control applications such as the one described herein. The crisp output is the desired flow rate (X – coordinate of the Centroid) and the motorized pump is adjusted accordingly based on this value. Fig. 3.2 Defuzzification condition
  20. 20. Anil Maurya Electrical & Electronics Engineer 20 Defuzzification condition Fig. 3.3 Defuzzification
  21. 21. Anil Maurya Electrical & Electronics Engineer 21 Chapter 4 ROBOTIC CONTROL WITH FUZZY LOGIC The main concept of the study is to coordinate conflicts and competitions among multiple reactive behaviors efficiently by fuzzy sets and a rule base. To achieve this objective, an array of ultrasonic sensors and a vision system are mounted on a robot. The ultrasonic sensors provide distance information between the robot and obstacles for behavior control of the mobile robot, while the vision system identifies some sub goals for determining a good motion direction to avoid robot trap in local region. If a mobile robot moves in unknown environments to reach a specified target without collisions with obstacles, sensors must be used to acquire information about the real world. Using such information, it is very difficult to build a precise world model in real-time for preplanning a collision-free path. On the basis of situational reactive behaviors, behavior based control has been proposed for robot navigation. Since this method does not need building an entire world model and complex reasoning process, it is suitable for robot control in dynamic environments. A key issue in behavior based control is how to coordinate conflicts and competitions among multiple reactive behaviors efficiently. The example in Fig.1 shows that the robot must efficiently weight multiple reactive behaviors, such as avoiding obstacle, following edge, and moving to target and so on, according to range information, when it reaches a target inside a U-shaped object. The usual approach for implementing behavior control is artificial potential fields. A drawback to this approach is that during pre programming much effort must be made to test and to adjust some thresholds regarding potential fields for avoiding obstacle, wandering, and moving to target and so on. In particular, these thresholds frequently depend on Environments. In, we present an approach for fuzzy logic based behavior control of a mobile robot. Unlike behavior control based on artificial potential fields, this method is to compute weights of multiple reactive behaviors in dynamic environments by a fuzzy logic algorithm rather than simply to inhibit some reactive behaviors with lower levels. In this paper, we further present a strategy for fuzzy logic based behavior control of a mobile robot by multi sensor integration. To achieve this objective, an array of ultrasonic sensors and a vision system are mounted on a mobile robot. The ultrasonic sensors provide distance information between the
  22. 22. Anil Maurya Electrical & Electronics Engineer 22 robot and obstacles for robot navigation by reactive behaviors, such as avoiding obstacles and following edges, while the vision system identifies some sub goals for determining a good motion direction to avoid robot trap in local region. This method differs from the fuzzy control approaches for obstacle avoidance in. Since perception and decision units in this method are integrated in one module by the use of the idea of reactive behaviors and are directly oriented to a dynamic environment, this strategy has the better real-time response and reliability. To demonstrate the effectiveness and the robustness of the proposed strategy, we report a lot of simulation results on robot navigation in uncertain environments, such as avoiding obstacle in real-time, decelerating at curved and narrow roads, escaping from a U shaped object and moving to target and so on. Fig.49.1 Robot motion to reach a target
  23. 23. Anil Maurya Electrical & Electronics Engineer 23 Fig. 4.2 Robot motion inside a U – shaped object Fig. 4.3 this graph shows the membership grades for the Fuzzy sets distance and direction In order to acquire information about dynamic environments, 15 ultrasonic sensors are mounted on the THMR-I1 mobile robot [12], as shown in Fig.2. The sonar reflection from a sensor i represents the distance di, measured by the sensor i, between the robot and obstacles in the real world. These ultrasonic sensors are divided into three groups to detect obstacles to the right
  24. 24. Anil Maurya Electrical & Electronics Engineer 24 (sensor i = 1, ..., 6 ), front ( sensor i = 7, ..., 9 ), and left locations ( sensor i = 10, ..., 15 ). Using such information, obviously, it is difficult to build a precise and entire world model in real-time for preplanning a collision-free path. Here, we use the sonar data di (i = 1, ..., 15) to build a simple model for representation of the distances between the robot and obstacles in the real world as follows: Right- obs = Min {di} i = 1, ..., 6 (1) Front- obs = Min {di} i = 7, ..., 9 (2) Left-obs = Min {di) i = 10,…., 15 (3) Where the minimum values, right-obs, front-obs, and left-obs, derived from the sensor data di (i = 1, ..., 15), express the distances between the robot and obstacles to the right, front, and left locations, respectively. The mobile robot is equipped with two wheel encode units to determine its current coordinates. At a start position, a counter is reset to zero. When the robot moves, its current coordinates can be roughly computed by counting the numbers of pulses from the wheel encodes that are attached on driving motors. The THMR-I1 mobile robot with 1.0m length and 0.8m width is equipped with two driving wheels and one driven wheel. The velocities of the driving wheels are controlled by a motor drive unit. (a)
  25. 25. Anil Maurya Electrical & Electronics Engineer 25 (b) Fig. 4.4 Fuzzy logic scheme for perception-action behavior control The input signals to fuzzy logic scheme are the distances between the robot and obstacles to the left, front, and right locations as well as the heading angle between the robot and a specified target, denoted by left-obs, front-obs, right-obs and head- ang, respectively, as shown in Figure. When the target is located to the left side of the mobile robot, a heading angle head-ang is defined as negative; while the target is located to the right side of the mobile robot, a heading angle head-ang is defined as positive, as shown in figure. According to acquired range information, reactive behaviors are weighted by the fuzzy logic algorithm to control the velocities of the two driving wheels of the robot, denoted by left-v and right-v, respectively. The linguistic variables far, med (medium) and near are chosen to fuzzify left-obs, Front- obs and right-obs. The linguistic variables P (positive), 2 (zero) and N (negative) are used to fuzzify head-ang; the linguistic variables fast, med, and slow are used to fuzzy the velocities of the driving wheels left-v and right-v. In analogy to artificial potential fields, the distances between the robot and obstacles serve as a repulsive force for avoiding obstacle, while the heading angle serves as an attractive force for moving to target.
  26. 26. Anil Maurya Electrical & Electronics Engineer 26 Fig. 4.5 describing the various behaviors for robot 4.1 Reactive Behaviors using Fuzzy Logic In order to reach a specified target in a complex environment, the mobile robot at least needs the following reactive behaviors: 1. Obstacle avoidance and decelerating at curved and narrow roads; 2. Following edges; 3. Target steer. Because the real world is a complex, using sensors it is very difficult to acquire precise information about dynamic environments. In this case, a set of fuzzy logic rules is used to describe the reactive behaviors. Now, we only list parts of fuzzy rules from the rule base to explain, in principle, how these reactive behaviors are realized. (In fact, much more fuzzy rules have been used in our navigation algorithms) 4.1.1 Obstacle Avoidance and Decelerating at Curved and Narrow Roads When the acquired information from the ultrasonic sensors shows that there exist obstacles nearby robot or the robot moves at curved and narrow roads, it must reduce its speed to avoid obstacles. In this case, its main reactive behavior is decelerating for obstacle avoidance. We give the first and second of fuzzy rules for realizing this behavior as follows:
  27. 27. Anil Maurya Electrical & Electronics Engineer 27 If (left-obs is near and front-obs is near and right-obs is near and head-ang is any) Then (left-v is fast and right-v is slow). If (left-obs is med and front-obs is near and right-obs is near and head-ang is any) Then (left-v is slow and right-v is fast). Such fuzzy rules represent that the robot only pays attention to obstacle avoidance and moves slowly when it is very close to obstacles or at curved and narrow roads. 4.1.2 Following Edge When the robot is moving to a specified target inside a room, it must reflect following Edge behavior. The first and second rules for describing this behavior are listed as follows: I f (left-obs is far and front-obs is far and right-obs is near and head-ang is P) Then (left-v is med and right-v is med). I f (left-obs is near and front-obs is far and right-obs is far and head-ang is N) Then (left-v is med and right-v is med). These fuzzy rules show that the robot shall follow an edge of an obstacle when the obstacle is very close to the left (or the right) of the robot, and also the target is located to the left (or the right). 4.1.3 Target Steer When the acquired information from the ultrasonic sensors shows that there are no obstacles around robot, its main reactive behavior is target steer. Here, we list the first and second of fuzzy rules for realizing this behavior as follows: I f (left-obs is far and front-obs is far and right-obs is far and head-ang is Z) Then (left-v is fast and right-v is fast). I f (left-obs is far and front-obs is far and right-obs is far and head-ang is N) Then (left-v is slow and right-v is fast).
  28. 28. Anil Maurya Electrical & Electronics Engineer 28 These fuzzy logic rules show that the robot mainly adjusts its motion direction and quickly moves to the target if there are no obstacles around the robot. Table9.1 shows variation in speed with distance
  29. 29. Anil Maurya Electrical & Electronics Engineer 29 Fig.4.6 Graph representing the membership grade of distance as measured by sensor 4.2 Multiple Behaviors Fusion by Fuzzy Reasoning A key issue of behavior-based control is how to efficiently coordinate conflicts and competitions among different reactive behaviors to achieve a good performance. In a priority strategy is used to activate a reactive behavior according to its urgency level. This strategy is highly contentious for robot navigation in complex environments. For example, it is difficult to determine exactly which one of the reactive behaviors, obstacle avoidance, or following edges, or target steer, should be fired when the robot moves through the entrance of the U-shaped object to a target, as shown in Fig. To reach the given target, in fact, all the three reactive behaviors must be efficiently integrated. The following are some deficiencies of the priority strategy noted in our experiments: 1. Much effort must be made to test and to adjust some thresholds or firing reactive behaviors during pre-programming. 2. These thresholds depend heavily on environments, i.e., a set of thresholds, determined in a given environment, and may not be suitable for other environments. 3. Robot motion with unstable oscillations between different behaviors may occur in some cases. This is because just only one behavior could be activated at a given instant and two behaviors with neighbouring priority, e.g., obstacle avoidance and target steer, are fired in turn. In the proposed control strategy, reactive behaviors are formulated by fuzzy sets and fuzzy rules, and these fuzzy rules are integrated in one rule base. The coordination of
  30. 30. Anil Maurya Electrical & Electronics Engineer 30 different reactive behaviors can thus be easily performed by fuzzy reasoning. The following is an illustration of how this problem is dealt with by the Min-Max inference algorithm and the centroid defuzzification method in Eq. For instance, the inputs, left-obs=d1, front-obs=d2, right-obs=d3, head-ang=ſ1, are fuzzified by their membership functions to fire fuzzy rules associated with them simultaneously. Assume that Rule i (see below), formulating the obstacle avoidance behavior, and Rule j, formulating the following edge behavior, is fired according to the fuzzified inputs (in fact, much more fuzzy rules may be activated): Rule i: I f (left-obs is near and front-obs is near and right-obs is near and head-ang is N) Then (left-v is fast and right-v is slow). Rule j: I f (left-obs is near and front-obs is med and right-obs is med and head-ang is N) Then (left-v is med and right-v is med). By fuzzy reasoning and the centroid defuzzification method, both Rule i and Rule j, related to the obstacle avoidance and following edge behaviors respectively, are weighted to determine an appropriate control action, i.e., the velocities, left-v and right-v, of the robot's rear wheels.
  31. 31. Anil Maurya Electrical & Electronics Engineer 31 Fig. 4.7 Behavior fusion by fuzzy reasoning
  32. 32. Anil Maurya Electrical & Electronics Engineer 32 Chapter 5 APPLICATION OF FUZZY LOGICS Product Company Fuzzy logic Air conditioner Hitachi, Matsushita, sharp Prevents overshoot- undershoot temperature oscillation and consumers less on-off power Anti-lock brakes Nissan Controls brakes in hazardous cases based on car speed and acceleration and on wheel speed and acceleration Auto engine NOK/Nissan Controls fuels injection and ignition based on throttle setting, oxygen content, cooling water temperature, RPM Auto transmission Honda, Nissan, Subaru Selects gear ratio based on engine load, driving style, and road conditions Chemical mixer Fuji Electric Mixes chemicals based on plant conditions Copy machine Canon Adjust drum voltage based on picture density, temperature, humidity Cruise control Isuzu, Nissan, Mitsubishi Adjusts throttle setting to set speed based on car speed and acceleration Dryer Matsushita Converts load size, fabric type, and flow of hot air to drying times
  33. 33. Anil Maurya Electrical & Electronics Engineer 33 Elevator control Toshiba Reduces waiting time based on passenger traffic Health management Omron Over 500 fuzzy rules track and evaluate an employee’s health and fitness Microwave Sanyo, sharp, Toshiba Sets and tunes power and cooking strategy Palmtop computer Sony Recognizes handwritten kanji character Paper industry Cellulose do caima, Portugal Pulp production Plasma etching Mitsubhishi electric Sets etch time Refrigerator Sharp Sets defrosting and cooling times based on usage Still camera Canon, Minolta Finds subject anywhere in frame, adjust autofocus Subway control LIFE institute, yokohama Controls the subway during peak hours Television Goldstar (Korea), hitachi, samsug (Korea), sony Adjusts screen color and texture for each frame and stabilizes volume based on viewer’s room location Translator Epson Recognizes, translates word in pencil size unit Toaster Sony Sets toasting time and heat strategy for each bread type Vaccum cleaner Hitachi, matsushita, Toshiba Sets motor-suction strategy based on dust quantity and floor type Video camcorder Canon, Sanyo Adjusts autofocus and lighting
  34. 34. Anil Maurya Electrical & Electronics Engineer 34 Washing machine Goldstar (Korea), hitachi, samsug (Korea), sony Adjusts washing strategy based on sensed dirt level, fabrics type, load size, and water level
  35. 35. Anil Maurya Electrical & Electronics Engineer 35 Chapter 6 CONCLUSION In this project, we use fuzzy logic to realize the reactive behaviors for robot navigation. The method can effectively coordinate conflicts and competitions among multiple reactive behaviors by weighting them and this coordination ability is nearly independent of a dynamic environment due to it robustness. The navigation algorithm has better reliability and real-time response since perception and decision units in the algorithm are integrated in one module and are directly oriented to a dynamic environment. The simulation results show that the proposed method for robot navigation by multi sensor integration can automatically perform avoiding obstacles, decelerating at curved and narrow roads, escaping from a U- shaped object, and moving to target and so on in complex and uncertain environments.
  36. 36. Anil Maurya Electrical & Electronics Engineer 36 Reference 1. McGraw Hill Education Book “Fuzzy Logic System” by Elaine Rich, Kevin Knight, Shivshankar B Nair 2. Zadeh, L. D. (1965). Fuzzy Sets, Information and Control, No 8, pp. 338-365. 3. Gupta, M.M.; Ragade, R. K. & Yager, R.R. (1979). Advances in Fuzzy Set Theory and Applications, North Holland, New York. 4. Dubois, D. & Prade, M. (1979). Fuzzy Sets and Systems: Theory and Applications, Academic Press, New York. 5. Jamshidi, M.; Vadiee, N. & Ross, T. J. (1993). Fuzzy Logic and Control. Software and Hardware Applications, PTR, Prentice Hall, New Jersey, USA. 6. Wei Li: "Fuzzy logic based 'perception action' behavior control of an mobile robot in uncertain environments" IEEE World Congress on Computational Intelligence, in press, 1994. 7. Ivanescu, M., Stoian, V. (1995). Variable Structure Controller for a Tentacle Manipulator. Proceedings of the 1995 IEEE International Conference on Robotics and Automation, Nagoya, Japan, May 21-27, vol. 3, pp. 3155-3160, ISBN: 0-7803- 1967-2. 8. R.A. Brooks, "A robust layered control system for a mobile robot", IEEE J. of Robotics and Automation, RA 2, pp. 14-23, April 1986. 9. Ronald C. Arkin, and Robin R. Murphy, "Autonomous navigation in a manufacturing environment", IEEE Tran. On Robotics and Automation, vo1.6, no.4, pp.445-454, 1990. 10. Wei Li and Kezhong He: "Sensor-based robot navigation in uncertain environments using fuzzy controller" The 1994 ASME International Computers in Engineering Conference, in press, 1994.

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