Fuzzy Logic Control in Autonomous Robotics:

Investigating the Motorola MC68HC12 on a Line Following Robot

 

David Olsen

Department of Electrical and Computer Engineering

University of Minnesota Duluth

1023 University Drive

Duluth, MN 55812.  USA

 

Faculty Advisor: Dr. Marian S. Stachowicz

 

Abstract

 

Autonomous robot systems require complex control systems.  Fuzzy Logic, a mathematical system developed by Professor Lotfi Zadeh, helps to reduce the complexity of modeling nonlinear problems.  In the 1990s, Motorola developed the MC68HC12 microcontroller with native Fuzzy Logic instructions.  This research determined the effectiveness of the MC68HC12’s Fuzzy Logic instructions for robotic control.  This research involved designing a robotic platform using the MC68HC12 and testing binary logic control systems against Fuzzy Logic control systems.  The research analyzed the two systems using four criteria:   (1) the size of memory required to develop the control system, (2) the ease of writing the control software, (3) how well the control system managed the functions of the robot, and (4) the overall processing power of the system.  The results showed that Fuzzy Logic uses less memory than binary logic and is much easier to design, although more difficult to program initially.  Fuzzy Logic can control more functions of the robot and has greater processing capabilities.  The power, ease of use, and small size of Fuzzy Logic instructions make Fuzzy Logic a practical solution to autonomous robotic control systems.

Keywords: Fuzzy Logic, robotics, control systems, HC12

 

1. Introduction

 

The expansion of robotics and microcontrollers into the facets of everyday life increases the need to develop efficient control systems.  A non-traditional approach to control system design is the use of Fuzzy Logic.

   Fuzzy Logic extends from the traditional crisp boundaries of Aristotelian logic (true or false) to include the concept of partial truth – having truth-values between ‘completely true’ and ‘completely false.’  Dr. Lotfi Zadeh of University of California Berkeley first introduced these fuzzy methods in 1965 [1].  These methods allow the engineer to use natural language to describe and implement the control system.  Fuzzy Logic uses linguistic values to represent part of the range an ordinary crisp variable may assume [2].  For example, a variable t, that represents temperature, may vary from 0 oC to 100oC.  A linguistic value, COLD may be used to represent temperatures from 0oC to 10 oC while other linguistic values represent other ranges.  Fuzzy Logic makes it possible to solve complex, ill-defined problems where there is a large degree of expert knowledge or the solution is easy to describe linguistically [3]. 

   Applications of Fuzzy Logic are appearing in many industries.  Fuzzy Logic enables designers to model complex systems more quickly and effectively than traditional approaches.  Consumer appliances, automobile engines, transmissions, and industrial systems are all using Fuzzy Logic techniques.

   Motorola’s HC68HC12 (HC12) microcontroller incorporates several Fuzzy Logic primitives directly in its instruction set.  The instruction set contains the Fuzzy Logic operations of trapezoidal membership, rule evaluation, and weighted average defuzzification.  The microcontroller also includes other instructions that are helpful in Fuzzy Logic applications such as MIN / MAX instructions and table lookups [4].  Motorola’s HC12 allows the development of low-level applications that can utilize the unique features of Fuzzy Logic.

   The goal of this project is to design and build an autonomous line following robot based on Fuzzy Logic techniques.  The robot uses the Motorola HC68HC12 microcontroller.  This project involves investigating the HC12’s Fuzzy Logic instruction set and analyzing its ability to control an autonomous robot.  The robot in this project serves as a test bed for several pieces of software.  These software programs include initial test scripts, several control system based on traditional logic, and several control systems based on fuzzy systems.  The best classical logic and fuzzy control systems are compared in various tests.  These tests involved the robot following a black line on the floor.

 

2. Fuzzy Logic on the HC12

 

As stated in the introduction, Motorola designed the HC12 with advanced capabilities to handle Fuzzy Logic calculations.  The HC12 contains four instructions that are specific to Fuzzy Logic.  These instructions are:

 

  • MEM                      Evaluates the trapezoidal membership functions
  • REV/REVW           Performs unweighted/weighted MIN-MAX rule evaluation
  • WAV                      Performs weighted average defuzzification

 

   The following section describes the basics of Fuzzy Logic on the Motorola HC12.  This section will only serve as an introduction to fuzzy programming on the HC12 and is not a replacement for the manufacture’s documentation.  This section assumes that the reader has some knowledge of Fuzzy Logic.

 

2.1 fuzzy logic basics

 

The design of a Fuzzy Logic interface for the HC12 consists of two parts.  First, the user must design a knowledge base that contains the membership functions and the rule set.  The second part is the inference kernel that takes the system inputs and produces the system outputs based on the knowledge base [5].  Figure 1 shows the basic structure of the Fuzzy Logic system.  

Figure 1: Block diagram of a fuzzy logic system [5].

 

2.2 fuzzification strategy (MEM)

 

Fuzzification is the process by which system inputs are evaluated to determine the degree at which they belong to a particular fuzzy set, on a scale from 00 to FF in hexadecimal [5].  The MEM instruction evaluates trapezoidal membership functions.  These functions define the fuzzy set, the foundation of Fuzzy Logic.  A fuzzy set is a set without a crisp, clearly defined boundary.  It can contain elements with only a partial degree of membership.  For example, the membership function for COLD could equal FF for temperatures below 7oC and slope down to 00 toward 10oC.  The MEM instruction compares the system input against the membership function to determine the degree of truth of a fuzzy input. 

   The y-axis in Figure 2 represents the degree of truth from completely false (00) to completely true (FF).  The x-axis represents the range of input values for the particular system input.  The MEM function works by finding the y-value, given a system input (x-value) and the membership function.  MEM returns the percentage of truth (y-axis value) for the particular fuzzy set.  The result is a set of fuzzy values that describe characteristics of input variables in the system. 


                Figure 2: Trapezoidal membership function.  The x-axis represents the input range and the y-axis represents the degree of truth [5].

 

   To define a trapezoidal membership function for the HC12, you need four values: (1) the start of the trapezoid, (2) the first slope, (3) second slope, and (4) the end point of the trapezoid.  Figure 2 labels these points and shows the memory representation.  The user should define the trapezoidal in memory as follows:

 

      LABEL_MF    DC.B  $40,$D0,$08,$04

 

   The program should use a descriptive label because the programmer will need this label during fuzzification.  For example, COLD_MF could represent a membership function of the fuzzy set COLD where the postfix _MF reminds the programmer that this variable represents a membership function.  A trapezoidal definition is needed for each membership function.

 

2.3 rule definition and evaluation (REV/REVW)

 

Rule evaluation is how Fuzzy Logic performs calculations.  The fuzzy values produced by the MEM function are passed through the rule list to find the fuzzy output.  The two types of rules that the HC12 allows are weighted (REVW), where each rule can have a different weights; and un-weighted, (REV) were all rules have equal weight.  An example of a rule list:

 

   If temperature is COLD and wind is HIGH, then heat is on HIGH.

   If temperature is WARM and wind is LOW, then heat is on LOW.

   If temperature is HOT and wind is LOW, then heat is OFF.

 

   After the fuzzy inputs are evaluated with REV/REVW, the system’s fuzzy outputs indicate the degree to which an output should have a specific value.  These outputs must then undergo defuzzification before their values are useful.  Creating the rule list is actually very simple.  The antecedents (left side of the rule) are the fuzzy inputs created by the MEM instruction (e.g., a temperature reading evaluated with the COLD, WARM and HOT membership functions).  The consequents (right side of the rule) are the fuzzy outputs of the system.  During REV, each antecedent is joined using the fuzzy and operator (MIN).  This minimum value is compared to the current fuzzy output of each consequent using the fuzzy or operator (MAX), and the maximum of these two values is stored in each consequent (fuzzy output).  In other words, the overall “truth” of a rule is stored in the fuzzy outputs and if a subsequent rule is “truer,” then the fuzzy outputs are updated to reflect this new value.

   The rule list is stored in memory as a list of pointers to fuzzy inputs (antecedents), a reserved separator value, a list of pointers to fuzzy outputs (consequents), and then another separator.  Each rule follows this pattern and the rule list is terminated by an end rule reserved value.

 

   RULE_LIST        DC.B   P_TisCold, P_WisHigh, SEPARATOR, P_HeatHigh, SEPARATOR

                     DC.B   P_TisWarm, P_WisLow, SEPARATOR, P_HeatLow, SEPARATOR

 

2.4 defuzzification strategy (WAV)

 

The final step in the Fuzzy Logic calculation is defuzzification, when the raw fuzzy outputs are evaluated to create a composite system output.  Unlike the input, the fuzzy output membership function is not trapezoidal but a singleton.  This singleton indicates one system output value for each fuzzy output.  The output membership singletons are arraigned in memory in the same order as their corresponding fuzzy outputs.  WAV calculates a sum of products of each fuzzy output value times its singleton value and a sum of all of the fuzzy output values.  The first sum is divided by the second using EDIV to produce an overall value that is the defuzzified output of the system.  Defuzzification creates a weighted average system output based on the truth of the fuzzy outputs.

 

2.5 fuzzy inference kernel

 

The inference kernel contains all of the instructions that make up the fuzzy system.  The kernel utilizes the knowledge base to create a system output from given system inputs [5].  All of the fuzzy instructions require proper initialization of the accumulators, index registers, and fuzzy values.  These details are beyond the scope of this paper and can be found in the manufacture’s documentation.  The sample program listing, Appendix A, also includes comments on developing the fuzzy kernel.

 

   Readers wanting more information are encouraged to refer to the “Fuzzy Logic Support” chapter in the Motorola 68HC12 CPU12 Reference Manual for a detailed explanation of the Fuzzy Logic instruction set.

 

3. Control Software

 

To test if Fuzzy Logic is a superior solution to the problems of autonomous robotic control, this project involved creating two control systems.  The first system uses traditional logic to control the system.  This system does not use any of the microcontrollers embedded Fuzzy Logic functions.  The second robot relies solely on the HC12’s Fuzzy Logic instructions.  This second system uses Fuzzy Logic for all of its control processing.  Both control systems only used the HC12’s onboard RAM area (512 bytes) for program storage.

 

3.1 traditional control system

 

The traditional control system does not use an of the Fuzzy Logic instructions on the HC12.  It relies on testing each input as true or false and then uses an if-else programming structure to determine the correct system output.  Because of the limited size of RAM available for programming, the binary robot relies on an external chip to convert the analog signals from the sensors to a binary, on or off, form.  The control structure is simplified to reduce the necessary amount of memory needed for storage.  The traditional control system uses the following rules:

 

  • Center sensor on                  Go Straight
  • Left sensor on                      Turn Right
  • Right sensor on                    Turn Left
  • No sensors on                      Stop

 

   The motor control of this system is limited to one speed for straight, left, and right.  Because the system relies on an external chip to convert the analog sensor values, it is unable to detect when the sensor is partially on the line.  While this simplifies programming, it reduces the effective resolution of the sensors.

 

3.2 fuzzy control system

 

The small amount of RAM also limits the fuzzy control system.  However, the fuzzy instructions are able to handle far more control system computations than the traditional system in a similar amount of memory.  First, the fuzzy system uses the analog values from the sensors.  This gives the fuzzy robot the benefit of being able to tell exactly when the sensor is leaving the line and to be more robust to changes in the environment.  Second, this system has three levels of speed for each direction.  This gives the fuzzy control system improved turning ability. 

   The fuzzy control system takes the analog value from the sensors and assigns a level of “truth” to a fuzzy value.  This control system used two fuzzy membership functions for each sensor: ON and OFF, to create a total of six fuzzy input values.

   Fuzzy control systems are based on “rules.”  The control system uses these rules to evaluate the fuzzy values and create a fuzzy output.  Table 1 shows the rules based upon the truth of the fuzzy input values and the corresponding fuzzy outputs used in this control system.  In the table, there are ON and OFF fuzzy values for each of the three sensors.  The system combines the “truth” of the three fuzzy inputs for each rule using the fuzzy MIN operator.  This minimum value is stored in the fuzzy outputs unless the outputs already have a greater value stored from a previous rule.  The system finds the output that best fit the fuzzy inputs.

 

Table 1.  Fuzzy Rule List.  This table shows the rule list that evaluates the output speed and direction given the fuzzy input variables.  This rule list is evaluated using the REV instruction on the MC68HC12.

Fuzzy Inputs

Fuzzy Outputs

Left

Center

Right

Speed

Direction

Off

Off

Off

Stop

Line Finder

On

Off

Off

Slow

Hard Left

On

On

Off

Medium

Left

On

On

On

Slow

Line Finder

Off

On

Off

Fast

Straight

Off

On

On

Medium

Right

Off

Off

On

Slow

Hard Right

On

Off

On

Stop

Line Finder

 

4. Hardware Implementation

 

This project uses a custom robot designed to test the various control systems.  This robot has a line sensor and two motors.  The robot can also handle IR distance sensors, but the distance sensors are not uses in the testing portion of this project.

 

4.1 base and motors

 

The test robot consists of a plywood base and uses differential steering.  The motors are two servos, modified to allow continuous revolution.  Servos are useful for small robots because the servo has an integrated motor controller and it provides adequate torque for a small robot [6].  Ball casters support the front and back of the robot.  This allows the robot to turn on its center.  A rechargeable battery pack powers the motors, line sensor, and the microcontroller.

 

4.2 line sensor

 

The custom line sensor is a collection of three IR phototransistor, transmitter pairs that sense when the robot in centered on the line, to the left, and to the right.  These sensors feed analog data into the HC12’s A/D ports for processing.  The analog values represent the IR reflectivity of the surface below the line sensor at three points.  Because the sensor contains IR transmitters, sensor works without ambient lighting.

 

5. Testing

 

The two robot control systems were tested on a variety of tracks.  These tracks were created by placing black electrical tape on a wooden, carpeted, and cement floor.  The tracks included a straight line, a 45-degree angle turn, a 90-degree angle turn, and a 12-inch radius oval shaped ring.  The lighting level was kept constant throughout the trials.  The testing measurements include a qualitative description of the robots ability to stay on the line without “wiggle” or overcorrection.

 


6. Results

 

For each of the test tracks, both robots maintained control and followed the line.  The traditional control system did have more “wiggle” as it moved down the straight section.  This robot was unable to center itself on the line and instead zigzagged down the line.  The fuzzy robot system was able to quickly find and hold the true course of the line.  The fuzzy robot system also made fewer corrections during the turns in the oval test track.  The traditional robot had to correct its course many more times during the oval turns.  The fuzzy robot system had a much smoother course throughout the track.  Neither robot was unable to make any of the turns in the test.

   In addition to comparing at the performance of the two different control systems, this project also looks at the memory requirements, the ease of writing the control software, and the processing power of the system.  For the two systems tested, the Fuzzy Logic system used more memory.  However, it also processed significantly more information and gave results with finer resolution.  Achieving this same level of processing using the traditional system would have made the traditional system’s memory requirements much larger.  

   The fuzzy system is initially more difficult to program because the syntax of the instructions and the format of the knowledge base in memory is unclear.  However, it is much easier to modify the fuzzy control system to changes in the environment or system outputs because only the membership functions need to change.  For the traditional system, the entire logic of the control system may need to be modified.  It is more intuitive to program in Fuzzy Logic because of the ease of creating a linguistic solution to the control problem.  This intuitive nature makes Fuzzy Logic easier to program than traditional logic for complex control problems.

 

7. Conclusion

 

Fuzzy Logic represents a tremendous advancement in autonomous robotic control systems.  The Motorola MC68HC12’s instruction set will make designing fuzzy solutions on microcontrollers much easier than in the past.  Fuzzy Logic is well suited for complex control problems like autonomous control, but it may be too difficult for simple control systems.  The HC12’s fuzzy instructions simplify the design cycle for control system designers and provide an alternative to traditional control methodologies.  The fuzzy system developed by Motorola is a very powerful set of instructions that will have a dramatic impact on control systems in many industries.

 

8. References

 

[1]   Reuss, Robert F, et al.  “Fuzzy Logic Control in a Line Following Robot.” http://www.cs.unr.edu/~simon/fuzzy/fuzzylogic.htm [01/22/2002].

[2]   Kandel, Abraham, et al.  Fuzzy Control Systems.  Boca Raton: CRC Press, 1994.

[3]   Stachowicz, M.S. and Beall, L., "Fuzzy Logic Package for Mathematica®", Wolfram Research, Inc., 2000.

[4]   M. S. Stachowicz and C. Carroll, "Intelligent Systems on Motorola's Microcontroller:  A Team Design Workshop," Proceedings of the 2000 International Conference on Engineering Education, Taiwan, August 14 -18, 2000.

[5]   Motorola Semiconductor, CPU12 Reference Manual. Motorola Inc., 1999.

[6]   McComb, Gordon. The Robot Builder’s Bonanza.  New York: MCGraw-Hill, 2001. 

 


Appendix A. Example Fuzzy Assembly Listing

 

The follow code example lists the overall structure of an assembly program for the HC12 that utilizes Fuzzy Logic.  This simplified example takes two system inputs, temperature and wind speed; and produces one system output, heat.  Input variables, stored in $0800 and $0801, have been scaled from 0016 to ff16.  The range of the heat output is from 0016 to ff16.  Refer to section 2 for details on the Fuzzy Logic operators. 

 

         ORG $0900      ;Memory location for Fuzzy Knowledge Base

 

                        ;###  Fuzzy Constants ###

MARKER   EQU  $FE              ;Used to separate rule sections

ENDRO    EQU $FF              ;Used to finish the rule list

                        ;### Relative Pointers ###

P_COLD   EQU  $00              ;Pointers to the relative locations of the fuzzy

P_WARM   EQU  $01              ;Input and Output variables

P_HOT    EQU  $02

P_CALM   EQU  $03

P_WINDY  EQU  $04

P_NoHt   EQU  $05

P_LowHt  EQU  $06

P_MedHt  EQU  $07

P_HiHt   EQU  $08

                        ;###  Membership Functions ###

COLD_MF  DC   $00,$76,$00,$05  ;Temperature Membership functions

WARM_MF  DC   $56,$AC,$07,$07  ;Point 1, Point 2, Slope 1, Slope 2

HOT_MF   DC   $8C,$FF,$07,$00

CALM_MF  DC   $00,$60,$00,$07  ;Wind Membership functions

WINDY_MF      DC   $50,$FF,$07,$00

                        ;###  Output Singletons ###

No_Heat_FS    DC   $00               ; The Fuzzy system will take the weighted average

Low_Heat_FS   DC   $56               ; of these values based on the truths of the

Med_Heat_FS   DC   $AC               ; corresponding Fuzzy output variables

High_Heat_FS  DC   $FF

                        ;### Fuzzy Variables ###

COLD_FI  DS   $01              ;These instructions reserve bytes for the Fuzzy

WARM_FI  DS   $01              ;  input and output variables.

HOT_FI   DS   $01              ;(NOTE: This variable ordering is what determines the

CALM_FI  DS   $01              ;       relative locations stored above and can be the

WINDY_FI DS   $01              ;     same ordering as the membership functions.)

NoHeat_FO     DS   $01              

LowHeat_FO    DS   $01

MedHeat_FO    DS   $01

HHeat_FO DS   $01

                        ;### RULE Definitions ###

RULE_START       

         DC   P_COLD,P_WINDY,MARKER,P_HiHt,MARKER      ;This section defines the rule list

         DC   P_COLD,P_CALM,MARKER,P_MedHt,MARKER      ;The rules are defined as relative

         DC   P_WARM,P_WINDY,MARKER,P_MedHt,MARKER     ;pointers to the locations of

         DC   P_WARM,P_CALM,MARKER,P_LowHt,MARKER      ;Fuzzy input and output variables.

         DC   P_HOT,P_WINDY,MARKER,P_LowHt,MARKER      ;MARKER and ENDRO are constants

         DC   P_HOT,P_CALM,MARKER,P_NoHt,ENDRO         ;$FE, $FF respectively

 

         org $0803      ; Memory starting location for Inference Kernel

                        ;### Fuzzification for temperature data ###

         LDX  #COLD_MF   ; First of three membership function for temperature

         LDY  #COLD_FI   ; Location of first fuzzy input variable for temperature

         LDAA $0800            ; Location of temperature data in system

         LDAB #$03       ; Number of membership functions for temperature

TEMPFUZZ:     MEM              ; This loop will process each of the three membership functions

         DBNE B,TEMPFUZZ ; and create the three fuzzy input variables

        

                        ;### Fuzzification for wind data ###

         LDX  #CALM_MF   ; First of two membership function for wind

         LDY  #CALM_FI   ; Location of fuzzy wind (These last two lines are optional because

                        ; Accumulator X and Y already have the correct values)

         LDAA $0801            ; Location of wind data in system

         LDAB #$02       ; Number of membership functions for wind

WINDFUZZ:     MEM              ; This loop will process each of the two membership functions

         DBNE B,WINDFUZZ ; and create the two fuzzy input variables

 

                        ;### RULE EVALUATION ###

RULE:    LDAB #$04       ; First you must clear out the fuzzy output variables

CLEAROUT:     CLR  1,Y+

         DBNE B,CLEAROUT

         LDY  #COLD_FI   ; Point at start of Fuzzy Input variables

         LDX  #RULE_START      ; Point at start of rule list

         LDAA #$FF       ; Must load AA with $FF

         REV           

                        ;### DEFUZZIFICATION ###

         LDX  #No_Heat_FS      ; Point to singleton positions

         LDY  #NoHeat_FO ; Point to Fuzzy Output locations

         LDAB #$04       ; Number of Fuzzy Outputs

         WAV            ; Calculate sums for weighted average

         EDIV           ; Final divide step

         TFR  Y,D        ; Move the results to A:B

         STAB $0802            ; Store system outputs