21

CHAPTER 2

AGENT BASED FUZZY LOGIC ROBOT NAVIGATION

AND OPTIMAL PATH PLANNING

2.1 INTRODUCTION

A pertinent problem in autonomous navigation is the need to cope

with the large amount of uncertainty that is inherent of natural environments

and responds reactively to unforeseen events as soon as they are perceived.

Moreover, uncertainty can occur in sensory data caused by environmental

features, and errors in the measurement interpretation process. Fuzzy logic

has features that make it an adequate tool to address this problem.

Applications in mobile robot navigation have been adopting fuzzy logic

approaches over the last two decades. However, this approach tries to prove

that it is enough just for the areas of highest danger coefficients to cause the

robot to change direction, which consequently reduces the number of fuzzy

rules that control the robot motion. The efficiency of the system is improved

by reducing the distance travelled by the robot to reach its goal position. The

proposed navigator consists of a Fuzzy-Based Collision Avoidance, pit

detection sensor and color sensor. The effectiveness of the proposed method

is verified by a series of simulations and real time implementation using

microcontroller in unknown environment.

Some important characteristics of fuzzy logic are as outlined by

Zadeh (1965).

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Exact reasoning is viewed as a limiting case of approximate

reasoning.

Everything is a matter of degree.

Knowledge is interpreted as a collection of elastic, fuzzy

constraints on a collection of variables.

Inference is viewed as a process of propagation of elastic

constraints.

Any logical system can be “fuzzified.”

2.2 FUZZY SETS AND MEMBERSHIP FUNCTIONS

It should be reiterated that membership functions are subjective

measures for linguistic terms and are not probability functions. There are

many types of membership functions. Some of the more common ones

are triangular MFs, trapezoidal MFs, Gaussian MFs, and generalized bell

MFs. The figure below shows the definitions and graphs of these MFs

(Figure.2.1)

Figure 2.1 Types of Membership Functions

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2.3 DEFUZZIFICATION

Defuzzification is the process of producing a quantifiable result in

fuzzy logic, given fuzzy sets and corresponding membership degrees. It is

typically needed in fuzzy control systems. These will have a number of rules

that transform a number of variables into a fuzzy result, that is, the result is

described in terms of membership in fuzzy sets.

A common and useful defuzzification technique is center of

gravity. First, the results of the rules must be added together in some way.

The most typical fuzzy set membership function has the graph of a triangle.

Now, if this triangle were to be cut in a straight horizontal line somewhere

between the top and the bottom, and the top portion were to be removed, the

remaining portion forms a trapezoid. The first step of defuzzification typically

"chops off" parts of the graphs to form trapezoids (or other shapes if the initial

shapes were not triangles). In the most common technique, all of these

trapezoids are then superimposed one upon another, forming a single

geometric shape. Then, the centroid of this shape, called the fuzzy centroid.

The x coordinate of the centroid is the defuzzified value. Formed by weighing

each functions in the output by its respective maximum membership value

(Figure 2.2)

Figure 2.2 Defuzzification

24

*

( ).

( )

C

C

z z

zz

* (.5) (.9)

.5 .9

a bz

2.4 PROPOSED SYSTEM

The proposed system has adopted methods such as following white

or magnetic lines using adequate sensors, and others. However, if the purpose

is to build robots with robust control that can be in any area of application

without having to engineer the area itself, the robot should be armed with

more intelligence, and should have its autonomy increased. Fuzzy logic has

features that make it an adequate tool to address this problem.

This approach divides the space into three categories range wise

and into six categories direction wise. However, this approach proved that it is

enough just for the areas of highest danger coefficients to cause the robot to

change direction, which consequently reduces the number of fuzzy rules that

control the robot motion. In the end, an optimization technique is applied for

the purpose of improving the system performance, where efficiency is

improved by reducing the distance traveled by the robot to reach its target. In

this system the robot will navigate in an unknown environment using fuzzy

logic. Sensors have been used to detect both the static and dynamic obstacles,

pits and the colors. The range depends on the type of sensors. Use of multi

agent approach and multi-agent optimal path planning make the system more

efficient in unknown environment.

2.4.1 System Structure

Figure 2.3 shows the integration of a microcontroller (89C52) with

the features of the robot. This architecture uses totally 5 sensors out of which

three proximity sensors are used to detect the obstacles, one to detect the color

and the other one to detect the pit in the navigation path. Two stepper motors

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are used to navigate the robot which will be simulated by the stepper motor

driver agent.

Figure 2.3 Integration of microcontroller

2.4.2 Decision Making System

The four principal components of the fuzzy decision-making

systems are:

a) The Fuzzification interface: determines input and output

variables and maps them into linguistic variables that are to be

displayed on as universe of discourse.

b) The knowledge base: is a part of expert systems that contains

the domain knowledge. Membership functions and control

rules are decided by the experts at this point, based on their

knowledge of the system.

c) The decision-making logic: treats a fuzzy set as a fuzzy

proposition. One fuzzy proposition can imply another, and

two or more fuzzy propositions can be associated by a Boolean

connectivity relation to infer a final fuzzy proposition.

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d) The defuzzification: interface converts the fuzzy output into a

crisp (nonfuzzy) value.

Figure 2.4 Basic configuration of fuzzy decision making system (FDMS)

Figure 2.4 represents the basic configuration of fuzzy decision

making system. Here fuzzy or crisp input is converted in to linguistic values

through fuzzification interface and processed by knowledge base and decision

is made using fuzzy logic. The outputs in the form of linguistic values are

converted into crisp values using defuzzification interface.

2.4.3 Definitions of Fuzzy Sets for Robot

Figure 2.5(a) represents the membership functions for the set

“range”. The laser scans in a range of tens of meters. Each obstacle detected

has a depth variable from the robot near (N), medium (M) and far (F). This

depth or range data has a different membership in each of the three range

subsets. The range universe of discourse is discretized into 8 parameters or

levels with 3 fuzzy sets, where parameters and membership functions are

chosen heuristically (Levine et al 1999).

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Figure 2.5(a) The Membership function for the set “range”

Figure 2.5(b) The Membership function for the set “direction”

Figure 2.5(b) represents the membership function for the set

“direction”. The sensor scans from –90 degree to +90 degree. This scope is

divided in six Subsets: Large Negative (LN), Medium Negative (MN), Zero

Negative (ZN), Zero Positive (ZP), Medium Positive (MP), and Large

Positive (LP); where each subset has a membership function.

2.4.4 Fuzzy Rules for Robot Navigation and Defuzzification

Each rule in the fuzzy knowledge base corresponds to a fuzzy

relation. There are rules that contain single premises of the form “IF X THEN

Y”. However, rules with multiple premises are more widely used, such as “IF

X AND Y THEN Z”. For an autonomous robot navigating among stationary

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obstacle in an unknown environment, it would be computationally expensive

to produce 3*6=18 rules as well as inefficient to divert the robot from its

trajectory for each fired rule. Hence, this thesis considers the zones of highest

risk which happen to be combinations of Near and Zero Negative as follows

(Shou-tao Li and Yuan-chun Li 2006):

1. If the range is near and angle is Zero Positive, then distance is

Medium and angle of deviation is Zero Negative

2. If range is near and angle is Zero Negative, then distance is

Medium and angle of deviation is Zero Positive.

3. If range is Medium and angle is Zero Positive, then distance is

near and angle of deviation is Zero Negative.

4. If range is Medium and angle is Zero Negative, then distance

is near and angle of deviation is Zero Positive.

The laser range finder upon detecting an obstacle, returns range and

orientation information to the fuzzy logic. A “Get Membership” routine is

applied iteratively to get different range and direction memberships. The

specified fuzzy rules are applied afterwards. In a crisp system, the intersection

of two sets contains the element that is common to both sets. This is

equivalent to the common logical AND operation. In conventional fuzzy

logic, the AND operator is supported by taking the minimum of the truth

membership grades. Range Outputs and Deviation Outputs from all the fired

rules are respectively multiplied in a Maximum relation so that final outputs

are converted back into crisp values. Here the technique inductive reasoning

is used for defuzzification (Miller 1998).

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2.5 IMPLEMENTATION DETAILS

This system consists of two layers which constitute four task-

oriented agents. Each agent is composed of two functional layers, the

Hardware Layer and the Component Layer. The Hardware Layer is a

collection of modules communicating with the robot's hardware devices such

as the camera, infrared sensors and motors. One module can be shared by two

or more agents, which reduces redundancy in coding. The development tools

used is C language and Keil software, which is a part of Microsoft turbo C

and 89C52 IC. We have used 89C52 microcontroller as a controller circuit in

which the proximity sensors, stepper motor driver and the voice chip driver

were connected. Vector field histogram (VFH) algorithm is used for path

planning.

2.5.1 Multi Agent Systems

The architecture is composed of three systems (Figure 2.6). Each

system competes for two available resources: motion and vision. The Pilot is

responsible for all the motions of the robot. It selects these motions to carry

out commands from the Navigation system and to avoid obstacles. The Vision

system is responsible for identifying and tracking landmarks (including the

goal). Finally, the Navigation system is responsible for choosing higher level

robot motions to move the robot to a specified goal. This requires requesting

the Vision system to identify and track landmarks and to build a map of the

environment and requesting the Pilot to move the robot toward the goal

position or toward some intermediate target position. From this two

observations were made. First, these three systems must cooperate mutually to

achieve the overall task of reaching the goal landmark position. For instance,

the Pilot needs the Vision system to identify obstacles and it needs the

Navigation system to select a path to the goal. Second, the systems are also

competing - there are some trade-offs between them. For example, both the

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Pilot and the Navigation system compete for the Vision system. The Pilot

needs vision for obstacle avoidance, while the Navigation system needs vision

for landmark detection and tracking.

The Navigation system is implemented as a multi agent system.

This system is composed of six agents with the following responsibilities

(Madhur Ambastha et al 2005) and (Kolushev 1998)

Keep the target located with maximum precision and reach it

(Target Tracker)

Keep the risk of losing the target low (Risk Manager)

Recover from blocked situations (Rescuer)

Keep the error in the distance to landmarks low (Distance

Estimator)

Keep the information on the map consistent and up to date

(Map Manager).

Figure 2.7 depicts the simplified diagram representing the multi-

agent system using an interface agent. The agents basically interact with the

other components of the system by manipulating information on the interface

agent. The information on the interface agent may represent facts,

assumptions, and deductions made by the system during the course of solving

a problem. An agent is a partial problem solver which may employ a different

problem-solving strategy and try to contribute to the solution by viewing the

information on the interface agent. The system has four independent agents:

Fuzzy Collision Detector, pit detection agent, color sensor and Drive

Controller. All the four agents are allowed to read / write information on the

interface agent. Each one of the four agents basically executes their tasks

independently using information on interface agent and posts any result back

to the interface agent.

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Figure 2.6 Robot architecture

Figure 2.7 Multi agent system for robot navigation

Interface

Agent

Collision detection agent

Pit detection agent

Color sensor agent

Drive Controller agent

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2.5.2 Fuzzy-Based Collision Avoidance

Fuzzy Collision Detector is a fuzzy-based collision avoidance

controller, which is responsible for the safety of the robot used in this work.

The fuzzy logic controller has one input fuzzy set for the sensor value and

three output fuzzy sets for linear-distance, velocity and turn-angle. Each set is

defined by one or more membership functions that map numeric values onto

linguistic membership terms. The fuzzy-based agent is fed with sensor values

as input, acquired from a set of infrared proximity detectors. The values are

fuzzified with designated linguistic terms (near, medium, and far). Among

three output fuzzy sets, the turn-angle fuzzy set has been uniquely defined.

The angle lies between -30°and 30° as a default value. The total angle of 60°

is divided into six amplitudes represented by six membership functions, and

each of which is associated with the following linguistic terms: positive-left

(PL), negative-left (NL), positive-center (PC), negative-center (NC), positive-

right (PR), and negative-right (NR). Figure 2.8 shows the six linguistic terms

on the partitioned turn-angle fuzzy set. Once the input is fuzzified and all the

output fuzzy sets are defined by appropriate linguistic terms, the fuzzy

inference engine looks for a match between the input and the outputs.

Figure 2.8 Partitioned turn angle fuzzy set

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2.5.2.1 Pit Detection Sensor

An apparatus and method for uniquely detecting pits on a smooth

surface by irradiating an area of the surface separately sensing radiation

scattered from the surface in the near-specular region is indicative of a pit and

in the far-specular region indicative of a flaw. It produces signals that are

representative of normalizing the near-specular signal with respect to the far-

specular signal to indicate a pit; and discriminating the near-specular

components of the normalized signal representative of surface pits by Prassler

et al (2001).

2.5.2.2 Color Sensor

The proximity color sensor application development kits combine

ready-to-use integrated color sensor modules with detailed application

information. The kits are designed to provide a quick and easy way for

engineers to discover how color detection, measurement and control

Capabilities can be integrated into their applications. Proximity offers these

application kits in versions for transitive and reflective color sensing

applications. Applications for proximity color sensor can be divided into three

categories:

1. Color detection: Identifying the presence or absence of a

specific color

2. Color measurement: Identifying a color based on its red, green

and blue components

3. Color control: Using the color sensor as part of a closed-loop

feedback system to produce and maintain a required color.

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2.5.2.3 Drive Controller Agent

This agent primarily holds responsibility for the robot's actuator via

the device driver that controls motors through the stepper control module. The

Drive Controller monitors the interface agent uses the navigational

information for locomotion. The agent is made of modules responsible for the

motor initialization and termination, the communication between layers, and

the maneuvering of the robot. A decent number of motion parameters such as

velocity, acceleration, turn-angle, straight distance, and driving duration are

arranged for achieving flexible movements (Bogdanov and Kolushev 1997).

2.5.2.4 Interface Agent

The interface agent operates as a central repository for all shared

information and a communication medium for all the agents. Rather than co-

ordinating all the agents, the role of interface object is Multi-agent Optimal

Path Planning for Mobile Robots in Environment with Obstacles by using the

information from the other agents.

2.5.3 Multi-agent Optimal Path Planning

Multi-agent robot system has some transport subsystem, which

consists of several mobile robots. Problem of controlling such mobile robot

group can be divided into two main parts:

Optimal global (general) task decomposition into subtasks, and

their optimal distribution between separate robots in the group.

Path planning, control and movement correction for each

mobile robot.

In this work a novel approach to path planning and motion

programming for mobile robots is proposed. The method is based on graph

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optimization algorithms. Novelty of the developed multi-agent path planning

algorithm is as follows:

All mobile robots are considered as dynamic obstacles.

Graphic representation of common environment models is

used for path planning.

Each edge of the graph has two weights: distance and motion

time (speed).

Weights of edges can be modified during path planning.

The quickest path is planned (time optimization).

Expert rules for speed and path correction are synthesized to

provide collision avoidance.

Using graph of possible paths, algorithms were developed for of

robot path planning abstract to environment model, thus improving their

application capacity. These algorithms provide global optimality while

planning the path according to various given optimum criteria: least motion

time, least path length, etc. Multi-agent path planning algorithm also provides

robots collision avoidance. The algorithm automatically plans safe robot

paths, which do not intersect each other in time-space continuum. Simulation

results proved effectiveness of synthesized algorithms.

2.5.3.1 Vector Field Histogram (VFH) Algorithm

The VFH method uses a two-dimensional Cartesian histogram grid

as a world model. This world model is updated continuously with range data

sampled by on-board range sensors. The VFH method subsequently employs

a two-stage data-reduction process in order to compute the desired control

commands for the vehicle. In the first stage the histogram grid is reduced to a

one-dimensional polar histogram that is constructed around the robot's

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momentary location. Each sector in the polar histogram contains a value

representing the polar obstacle density in that direction. In the second stage,

the algorithm selects the most suitable sector from among all polar histogram

sectors with a low polar obstacle density, and the steering of the robot is

aligned with that direction.

Obstacle avoidance is one of the key issues for the successful

applications of mobile robot systems. All mobile robots feature some kind of

collision avoidance, ranging from primitive algorithms that detect an obstacle

and stop the robot short of it in order to avoid a collision, through

sophisticated algorithms, that enable the robot to detour obstacles. Usually,

this procedure requires the robot to stop in front of the obstacle, take the

measurements, and only then resume motion. Obstacle avoidance (also called

reflexive obstacle avoidance or local path planning) may result in non-optimal

paths, since no prior knowledge about the environment is used.

VFH Algorithm – Principles

1. A two-dimensional Cartesian histogram grid is continuously

updated in real-time with range data sampled by the on-board

range sensors.

2. The histogram grid is reduced to a one-dimensional polar

histogram that is constructed around the temporary location of

the robot. The polar histogram is the most significant

distinction between the Virtual Force Field (VFF) and the

VFH method as it allows a spatial interpretation (called polar

obstacle density) of the robot's instantaneous environment.

3. Consecutive sectors with a polar obstacle density below

threshold are called "candidate valleys." The candidate valley

closest to the target direction is selected for further processing.

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4. The direction of the center of the selected candidate direction

is determined and the steering of the robot is aligned with that

direction.

5. The speed of the robot is reduced when approaching obstacles

head-on

2.6 EXPERIMENTATION RESULT

To verify the result, a demo was run in various numbers of

obstacles (Figure 2.9). The navigation technique described was implemented

as a C program and interfaced with the microcontroller using keil. For the

test, we have just specified the start point, the target point and velocity of the

point robot. Different navigation tests have been done in real time, Figure 2.10

shows the result of robot navigation in cluttered environments. The

environment is totally unknown, path generated when there is no obstacle

between the robot and the goal and from a densely populated environment

with obstacles. Table 1.1 shows the robot response time for known and

unknown environment.

0

0.5

1

1.5

2

2.5

0 20 40 60 80 100 120

Time steps

Nu

mb

er

of

part

icle

s

Figure 2.9(a) Few number of obstacles

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0

0.5

1

1.5

2

2.5

0 50 100 150 200 250 300 350

Time steps

Nu

mb

er

of

part

icle

s

Figure 2.9(b) Medium number of obstacles

0

0.5

1

1.5

2

2.5

3

3.5

4

0 200 400 600 800 1000 1200

Time steps

Num

ber

of p

artic

les

Figure 2.9(c) Large number of obstacles

Figure 2.10 Path generated when there is no obstacle between the robot

and the goal and from a densely populated environment

with obstacles

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Table 2.1 Response time for known and unknown environment

Fuzzy and VFH

Memory

(Kb)

Time in sec for

Known

environment

Time in sec

for Unknown

environment

10 0.6 5

20 0.8 4.3

30 0.9 3.7

40 1.0 3.2

50 1.1 2.8

60 1.3 2.6

70 1.5 2.5

80 2.0 2.5

90 2.4 2.4

100 2.7 2.2

110 3.0 2

120 3.3 1.9

130 3.3 1.9

2.7 CONCLUSION

The multi-agent and multi-agent optimal path planning approach

provides an extra level intelligence. These techniques deal with the real-time

navigation of a mobile robot in a totally unknown environment. It applies

fuzzy reasoning to endow a mobile robot with ability of the human being to

reason and perceive danger. Based on fuzzy logic, a collision free technique

has been developed that partitions a robot space into eighteen zones of

danger, where just four of them trigger the fuzzy rules. This development had

been validated in different unknown environments cluttered with static and

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dynamic obstacles and has proven to give the robot, a means of safely

reaching the target. Thus using the different types of sensors the navigation

has been successful even in an unknown environment and the goal has been

reached by the robot without any collisions. The system can be enhanced

further in the future by introducing image processing technique using a

wireless camera to store the navigation path which will be helpful to judge the

navigation path. Also we can implement high range sensors which are capable

of detecting obstacles made up of any material.