Download presentation
Presentation is loading. Please wait.
Published byFerdinand Richard Modified over 6 years ago
2
A great man who created a complete new mathematics with many practical applications.
3
Fuzzy Logic practical easy examples
4
How to combine various, even conflicting pieces of advise?
Linguistic How to combine various, even conflicting pieces of advise?
5
Examples of Operations on the same variable
A B A B A
6
Example 1: Using Fuzzy Logic for a Line Following Robot
7
Mechanical Design of a very inexpensive Line-Following Robot
In our example below: Line white, background black
8
Basic Motions of a Differential Drive robot
Reminder = Braitenberg Vehicles
9
Calculations for input rules
10
Defuzzifier of the “sum”
Structure of this type of the system: Two Levels, various membership functions in each, shared MIN MIN Defuzzifier of the “sum” Fuzzified inputs MIN MIN MIN Fuzzy values of combined first level groups One input Defuzzifier MIN MAX MIN Level of input membership functions Level of output membership functions Reminder = general simple scheme for Fuzzy Logic
11
Input Membership Functions
Characteristics of two identical sensors We have three membership functions: Black, Gray and White
12
Sample Fuzzy Rule Base – for input rules
Here is an example how you can create your own rules for a robot of your choice. This table decides what to do for every combination of data from both input sensors SR X = don’t know = undetermined The system will “learn” values for these don’knows. Descriptions such as this table: Generalize Truth Table Generalize Karnaugh Map
13
Output Membership Function
Output of the controller can be negative or positive
14
This slide explains how to apply rules for left sensor
We calculate for given measurement for the left sensor For black membership function white black gray For white membership function black Reading the data from left sensor
15
How to apply input rules?
16
How to calculate output?
Here are some examples of rule calculations This calculated 0.7 for SL This calculated 0.2 for F Right sensor Left sensor
17
Calculations for output rules
18
How to calculate Output Membership Function
Calculated in previous slide 0.7 for SL Calculated similarly for SR 0.2 for F Note: this is some kind of weighted sum This is one example of defuzzification that calculates the speed of the motor
19
Structure of this type of the system: Two Levels, various membership functions in each, shared
Sensor L This is fuzzy “strength” of the fuzzy output value SL white SL 0.7 Defuzzifier 0.7 MIN Note: this is some kind of weighted sum gray This is fuzzy “strength” of the fuzzy output value F 0.8 SL F black -20 MIN F white other MIN HL ……. gray Fuzzy values of combined first level groups black Sensor R Level of input membership functions Level of output membership functions speed of the motor
20
To remember The previous slide was only a special case of defuzzification in a sum gate Many other methods and shapes are possible. Remember the general structure of the circuit. There are many variants of this circuit. With many defuzzification methods.
21
Example 2: Using Fuzzy Logic for an Obstacle Avoiding Robot
22
In this example the principles are the same as before, but the way of calculating is somewhat different. We have no table, just we directly write rules. This is just for didactic reasons.
25
Very Basic Control Theory
Read carefully @ Your speed towards a goal or away from an object should be proportional to the distance from If you want to get to a goal in an optimal amount of time you want to move However, you need to decelerate as you grow near the target so you can have more is proportional to distance-to-target Speed is proportional to the distance to target
26
Very Basic Control Theory
@ In systems with momentum (i.e. the real world) we have to worry about more complex acceleration and We can overshoot our target or stop increase your rate of deceleration based on how close you are to a goal or can also integrate over the distance to a goal to create a steady This is the basic idea behind a PID Integral physical derivation of PID can be tricky, we will avoid it for this is a part of an extremely interesting topic! Read carefully
27
IDEA! Heuristic experimental rules
Lets just hack a fuzzy controller together and avoid some math. The formal mathematicians will hate us, but if it works, that may be all that matters! Derive rule of thumb ideas for speed and direction If I am 6 meters from the obstacle, am I far from it?
28
If near, turn more
29
Experimental heuristics in robot design
Try some fuzzy rules… Let us look at adjusting trajectory first then we will look at speed… If an obstacle is near and center, turn sharp right or left. If an obstacle is far and center, turn soft left or right. If an obstacle is near, turn slightly right or left, just in case. Etc… You have to experiment with these rules
30
Degrees of angle Degrees of angle meters
32
Implication of the rules
33
Defuzzification
35
Get closer, turn more Many rules of thumb like this
36
Advise on creating rules
The robot works in continuous time The fuzzy rules should change slightly at each time step. We don’t want the robot to jerk to a new trajectory too quickly. Smooth movements tend to be better. How often we need to update the controller is dependant on how fast we are moving. For instance: If we update the controller 30 times a second and we are moving < 1 kph then movement will be smooth. Ideally, the commands issued from the fuzzy controller should create an equilibrium with the observations. These are just examples. You decide for your robot and your sensors
37
Advise on creating rules
Our robot has momentum We have somewhat implicitly integrated the notion of momentum. This is why we would slow down as we get closer to an obstacle What about more refined control of speed and direction? Use the derivative of speed and trajectory to increase or decrease the rate of change. Thus, if it seems like we are not turning fast enough, then turn faster and visa versa.
40
Remember the general structure
MIN MIN Defuzzifier of the “sum” Fuzzified inputs MIN MIN MIN Fuzzy values of combined first level groups One input Defuzzifier MIN MAX MIN Level of input membership functions Level of output membership functions Reminder = general simple scheme for Fuzzy Logic
41
EXAMPLE 3: Fan control
42
Controller Structure Fuzzification Inference Mechanism Defuzzification
Scales and maps input variables to fuzzy sets Linear or not Single input single output Inference Mechanism Approximate reasoning Deduces the control action Various shapes of membership functions Various operators, not only MIN, MAX and NOT. Defuzzification Convert fuzzy output values to control signals Defuzzification can be a single output linear or nonlinear function with fuzzy input and crisp output Defuzzification can be built-into the “output sum” which can be other function than MAX or SUM or TRUNCATED SUM.
43
Rule Base for Fan Control
Air Temperature Set cold {50, 0, 0} Set cool {65, 55, 45} Set just right {70, 65, 60} Set warm {85, 75, 65} Set hot {, 90, 80} Fan Speed Set stop {0, 0, 0} Set slow {50, 30, 10} Set medium {60, 50, 40} Set fast {90, 70, 50} Set blast {, 100, 80}
44
Defuzzifier of the “sum”
Structure of this type of the system: Two Levels, various membership functions in each, shared MIN MIN Defuzzifier of the “sum” Fuzzified inputs MIN MIN MIN Fuzzy values of combined first level groups One input Defuzzifier MIN MAX MIN Level of input membership functions Level of output membership functions
45
Rules Air Conditioning Controller Example: IF Cold then Stop
default: The truth of any statement is a matter of degree Membership function is a curve of the degree of truth of a given input value Rules Air Conditioning Controller Example: IF Cold then Stop If Cool then Slow If OK then Medium If Warm then Fast IF Hot then Blast
46
Fuzzy Air Conditioner outputs
This is another useful visualization in two-dimensional space. inputs
47
Mapping Inputs to Outputs
48
EXAMPLE 4: Using Fuzzy Logic for a SWERVING ROBOT
This is a more detailed analysis of a simple version of Example 1
49
Motivating Example: Swerving Robot
53
proximity motion We take into account only PROXIMITY
59
DEFUZZIFICATION has many faces
Blended Centroid Largest Centroid Weighted Means
60
Defuzzification
61
Defuzzification: BLENDED CENTROID
63
Defuzzification: Largest Centroid
64
Defuzzification: Weighted Means
65
Back to Swerve Now we also take into account where is open for motion
66
Open can be rightside or leftside
67
Examples for evaluation with PROXIMITY and OPEN
68
evaluation open
69
Variant which uses NOT in a rule
70
Variant which uses hedges in a rule
Hard_Right Very Hard_Right
71
Summary on Fuzzy Controllers for simple robots
72
Advantages of Fuzzy Controllers
Minimal mathematical formulation Can easily design with human intuition Smoother controlling Faster response
73
Few More real-life Applications
ABS Brakes Expert Systems Control Units Bullet train between Tokyo and Osaka Video Cameras Automatic Transmissions
75
Advise based on our previous projects
Fuzzy logic is easy to program Fuzzy logic can be easily combined with any other method from this and next class In particular , there is a very good match to evolutionary ideas. Much software exist, you do not have to write from scratch. You should concentrate on combining ideas and analyzing results. I am not happy if you only give code but do not discuss, analyze and illustrate how it actually works on a robot, its part or your simulated model. With more time, it is good to modify the model step by step based on more experiments on a real robot Look to many examples from my 478, 479, and 510 AER webpages There are also many free books and reports on Internet. All this can be completely formalized, new math created and you can write a MS or PHD on these topics. Every branch of mathematics or calculus can be rewritten This happens always when we deal with something as fundamental as sets and probabilities. The same is in quantum. Quantum Fuzzy logic has been also created.
76
Defuzzifier of the “sum”
Structure of this type of the system: Two Levels, various membership functions in each, shared MIN MIN Defuzzifier of the “sum” Fuzzified inputs MIN MIN MIN Fuzzy values of combined first level groups One input Defuzzifier MIN MAX MIN Level of input membership functions Level of output membership functions
77
Questions and Problems
Draw the complete logic diagram for Example 1. Write software for Example 1. Draw the complete logic diagram for Example 2. Write software for Example 2. Draw the complete logic diagram for Example 3. Write software for Example 3. Draw the complete logic diagram for Example 4.
79
Priyaranga Koswatta Mundhenk and Itti, 2007
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.