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July 2003 MassMind newsletter

Learning Robotics / CMAC


I've always been interested in artificial life, or more exactly, in machines that are more useful than the standard, stationary manufacturing type things. A small device that can move around in the home and vacuum, polish, or just take out the trash would be a huge win. But so far, it just isn't happening. Why? The recently introduced Roomba "vacuuming" robot has shown that it can be done. There are lots of hobby robots out there that prove that people are capable of complex fabrication. But there is no available design for a "build your own useful household robot."

How much does it take to design and build a little motorized base with a small trash can on its back that follows a florescent line from the bathroom to a charging station next to the the kitchen trash and then meows to be emptied and returns? Or a cheap electric screw driver mounted at a slight angle with a buffing wheel at the bottom so that as it turns it both rubs the floor (wood, tile, etc...) and pushes itself forward. Add a stick to a reversing switch with bumpers front and back so that it will bang back and forth across the room, cover it with a glass bowl and add a small solar panel (ala BEAM robotics) and you can really make mommy proud.

But, they always do end up getting caught on something, run out of power (or just eat batteries) or can't figure out what to do when they encounter something they don't expect. The real need is for something smooth, solar powered or able to find an outlet and most importantly, just a bit smarter.  It looks like that is the hardest part: Roomba makes use of "thousands of lines of code" to do a passable job of covering the living room floor. (see: for more internals)

Conventional neural networks are often too complicated to fit into the limited confines of solar-able processors, and they don't work that great even on large computers. But I've found a couple of simple solutions that can run on tiny processors. The simplest is to replace the hard-coded actions with memories (variables), then when something doesn't go right randomize the memory corresponding to the previous move. A more dense and ultimately more capable memory method is to allow multiple inputs to select different memories by using the processed input bits (environment) as the memory address.

Environmental Memory provides a good example (the code follows this text and is great to look over). The algorithm is similar to David Heiserman's "beta class" machine (original algorithm used last move as part of the address, this version uses just the environment); it rewards moves that result in a "good" environment and punishes moves that result in a "bad" environment or movement in reverse when in a good environment. In this case, the environment is broken down to six bits: 2 feelers, 2 bits to indicate greater light (never both on) and 2 bits to indicate darkness on that cell (also space-limited). A bad environment can be defined as either or both feelers touching or just one dark bit set, or the same move being made over and over in a changing environment. A good environment is free of obstacles, full of light and has some bad environment mixed in to keep things interesting.

; while true
;   lastenvbad flag = badenv flag
;   read senses into environment
;   clear badenv flag
;   if feelers touching or one dark bit set
;       set badenv flag
;   if action = lastmove
;       if address <> environment
;          boring = boring + 1
;          if boring >= boringthreshhold
;             set badenv flag
;   else
;       boring = 0
;   if badenv or (not lastenvbad and reverse)
;       if confidence > 0
;          decrement confidence
;          memory(address) = action/confidence
;   else
;       if confidence < 3 
;          increment confidence
;          if confidence < 3
;             if direction = towards the light
;                increment confidence
;          memory(address) = action/confidence
;   lastmove = action
;   address = environment
;   action/confidence = memory(address)
;   if action not valid or confidence = 0
;       action = random
;       confidence = 0
;   move robot according to action

CMAC: Cerebellar Model Articulation Controller

"CMAC: Brain, Behavior, and Robotics" by James S. Albus published by Byte Books

An extension of the ability to learn is the ability to infer: To generalize experience. This diagram illustrates the idea: An input value is translated via an algorithm (algorithm: A procedure that produces the desired result without concern for the reason why it works) into not one, but several addresses into the memory. The values stored at each of these addresses are summed or averaged to produce a result. The critical part of the input to address translation algorithm is that for slight changes in the input, most of the output addresses will remain the same. As a result, experience recorded for one input will be applied, or generalized, to other inputs that are simular.

In general, you can just take the input, add a seperation value (distance from "d" to "i" in the picture) plus the inverse of the number of outputs desired, store that value, then divide it by the number of outputs and round it off. Repeat this for each output.

function CMACLookUp (int: in) int: out {
int i,sum

	for (i = 0; i > CMAC_OUTPUTS; i++) {
		in += CMAC_INC;
		sum += CMACArray(in / CMAC_OUTPUTS);
	return sum / CMAC_OUTPUTS;

For 4 outputs with a seperation of 4, the asm code would be:

;until 4
; add 17 (seperation * outputs plus 1) to the input.
; shift right twice and use as address.
; lookup output and average into result
; loop

	call :NextAddr
	call :ArrayLookup
	mov out,w
	call :NextAddr
	call :ArrayLookup
	add out,w		;combine the first 2 outputs
	rr out			;and average (recovers C)
	call :NextAddr
	call :ArrayLookup
	mov out2,w
	call :NextAddr
	call :ArrayLookup
	add out2,w		;combine second 2 outputs
	mov w, >> out2		;average second 2
	add out, w		;combine the averages
	rr out			;average the two averages

	add in, #17
	mov w,>>in		;recover "in.8" aka carry while /2
IFDEF WREG			;wreg is FR1 when it shows W and not RTCC
	clc			;clear carry
	rr wreg			;divide W by 2
	clr temp
	add temp,w		;clears carry
	mov w,>>temp

Training is basically the same except that the correction (random or computed) value is spread over the memory addresses as a change. The potential magnitude of the change is based on how good or bad the current environment is, or on the direction and magnatide of the change of fortunes. Better outcomes result in smaller changes, going from bad to worse may produce a larger change. This provides the same sort of "confidence" system employed in our first example, but allows for small "fine tuning" adjustments even during "good times" so that "even better times" might be found. Rather than a single bit for good or bad environment, the amount of change needs to be related to a range of good to bad situations. A situational report is prepared before the training and is saved to look for upward or downward trends.

function CMACtrain (int: in, oldSitRep, newSitRep) void {
int i,training
	training = ( rnd(0)*newSitRep + rnd(0)*(newSitRep - oldSitRep) ) / CMAC_OUTPUTS
	for (i = 0; i > CMAC_OUTPUTS; i++) {
		in += CMAC_INC;
		CMACArray(in / CMAC_OUTPUTS) += training;

For a system of outputs with a spread of 4:

;training is random * sitRep + random * statusChange shifted right twice
;until 4
; add 17 (seperation * outputs plus 1) to the input.
; shift right twice and use as address.
; change array value by training
; loop

It should also be said that the CMAC is probably the upper limit of what can be implemented in a microcontroller like the SX or PIC. In most CMAC systems, there are not one, but many CMACs and most have more than one input or diminsion. In a minimal system with only one CMAC, the input must be a combination of different values rather than just one sensor per CMAC diminsion. If the input is broken into individual bits, then we must realize that there is a difference in the "importance" or "priority" of the bits. and assign the positions of the bits in a usefull way. Low order bits will have little effect on the operation of the unit. High order bit changes in the input will drastically change the experiences the unit draws upon. For example, for a vaccume cleaning bot, the lowest bit could be assigned to a dirt sensor; it doesn't really signal a need to change operation, but it provide some hope that it will learn to find more dirt. The highest bit might be assigned to the status of the battery since the operation of the unit when charged is completly different than its operation when it needs to find a recharge.

See also:


Much more can be said and done on this subject and more informed and much more brilliant writers have and will. But I hope to have inspired a vew hobby robot fans to look into adding a bit more brain, and more AI especially, to their projects.

Best wishes! And thanks for your support.

; PicBot 2.05
; Debugging...
;  long flash = bad environment
;  short flash = picking random move
;  dumps memory at the end of pop cycle

        device PIC16C56, RC_OSC, WDT_ON, PROTECT_OFF
        reset startup
        org 000h

pops = 15       ; pops per cycle
popdur = 50     ; x ontime+offtime
ontime = 1      ; duty cycle = ontime/(ontime+offtime)
offtime = 1
optsleep = 00001111b    ; during sleep - int rtc, max wdt 
optpause = 00001100b    ; bits 0-2 control pause between pops
maxsleep = 20   ; number of looks before wak
ng in unchanging env. 
darkthresh = 30 ; when dark bits come on
boringthresh = 6   ; max identical moves in changing environment

; port assignments...
; Ra0 - 24LC65 clock
; Ra1 - 24LC65 data
; Ra2 - 1381 output
; Ra3 - debug led

; Rb0 - Left Photocell
; Rb1 - Left Feeler
; Rb2 - Right Motor Forward (grounds blue when 1)
; Rb3 - Right Motor Reverse (grounds red when 1)
; Rb4 - Left Motor Forward (grounds red when 1)
; Rb5 - Left Motor Reverse (grounds blue when 1)
; Rb6 - Right Feeler
; Rb7 - Right Photocell

powerpin       = ra.2
leftfeelpin    = rb.1
rightfeelpin   = rb.6

forward   = 01010100b   ; predefined moves
reverse   = 01101000b   ; bits 6,7 always "01"
popleft   = 01000100b   ; bits 0,1 confidence=0
popright  = 01010000b
turnleft  = 01100100b
turnright = 01011000b
backleft  = 01100000b
backright = 01001000b

environment = 15h
action      = 16h
popcnt      = 17h
flags       = 18h

badenv      = flags.0     ; set if something bad in environment
badmove     = flags.1     ; set if something wrong with action
sleeping    = flags.2     ; set if robot was in deepsleep
popping     = flags.3     ; set if in a pop cycle
lastenvbad  = flags.4     ; last environment was bad

temp        = 19h
temp1       = 1Ah
LightL      = 1Bh
LightR      = 1Ch

lastmove    = 1Dh
boring      = 1Eh

statusLED   = ra.3
portspeed   = 25    ; memory dump bit delay

; EEPROM routines modified from Microchip application note AN558
; bitin and bitout routines are coded in-line to permit write and
; read routines to be called without overflowing stack.
statby  = 03h
eeport  = 05h ; port A
eeprom  = 0Ah
bycnt   = 0Bh  
addr    = 0Ch
addr1   = 0Dh
datai   = 0Eh
datao   = 0Fh
txbuf   = 10h
count   = 11h
bcount  = 12h
loops   = 13h
loops2  = 14h
di      = 3
do      = 2
sdata   = 1
sclk    = 0
outmask = 11110100b
inmask  = 11110110b
; wait routine - waits approx loops milliseconds

wait	mov	W, #75
	mov	loops2, W
wait2	nop
	decsz	loops2
	jmp	wait2
	decsz	loops
	jmp	wait
        clr wdt  ; convenient

; generate start bit

bstart	setb	eeport.sdata
	mov	W, #outmask
;*** WARNING: TRIS expanded in two instructions. Check if previous instruction is a skip instruction.
;        tris eeport

	clrb	eeport.sclk
	setb	eeport.sclk
	clrb	eeport.sdata
	clrb	eeport.sclk

; generate stop bit

bstop	clrb	eeport.sdata
	mov	W, #outmask
;*** WARNING: TRIS expanded in two instructions. Check if previous instruction is a skip instruction.
;        tris eeport

	clrb	eeport.sdata
	setb	eeport.sclk
	setb	eeport.sdata
	clrb	eeport.sclk

; transmit byte in txbuf

tx	mov	W, #8
	mov	count, W
txlp	clrb
	snb	txbuf.7
	mov	W, #outmask
;*** WARNING: TRIS expanded in two instructions. Check if previous instruction is a skip instruction.
;        tris eeport

	jmp	txlp1
	setb	eeport.sdata
	jmp	txlp2
txlp1	clrb	eeport.sdata
txlp2	setb	eeport.sclk
	clrb	eeport.sclk
	rl	txbuf
	decsz	count
	jmp	txlp
	setb	eeprom.di
	mov	W, #outmask
;*** WARNING: TRIS expanded in two instructions. Check if previous instruction is a skip instruction.
;        tris eeport

	setb	eeport.sclk
	sb	eeport.sdata
	clrb	eeprom.di
	clrb	eeport.sclk

; receive byte into datai

rx	clr	datai
	mov	W, #8
	mov	count, W
	clrb	statby.0
rxlp	rl	datai
	setb	eeprom.di
	mov	W, #outmask
;*** WARNING: TRIS expanded in two instructions. Check if previous instruction is a skip instruction.
;        tris eeport

	setb	eeport.sdata
	setb	eeport.sclk
	sb	eeport.sdata
	clrb	eeprom.di
	clrb	eeport.sclk
	snb	eeprom.di
	setb	datai.0
	decsz	count
	jmp	rxlp

; get byte from EEPROM into datai

rbyte	call	bstart
	mov	W, #10100000b
	mov	txbuf, W
	call	tx
	mov	W, addr1	; high address
	mov	txbuf, W
	call	tx
	mov	W, addr	; low address
	mov	txbuf, W
	call	tx
	call	bstart
	mov	W, #10100001b
	mov	txbuf, W
	call	tx
	call	rx
	call	bstop

; write byte in datao to EEPROM

wbyte	call	bstart
	mov	W, #10100000b
	mov	txbuf, W
	call	tx
	mov	W, addr1
	mov	txbuf, W
	call	tx
	mov	W, addr
	mov	txbuf, W
	call	tx
	mov	W, datao
	mov	txbuf, W
	call	tx
	call	bstop
	mov	W, #10
	mov	loops, W
	call	wait

; end cryptic microchip instructions
; start parallax instructions

; get environment byte subroutine
leftfeeler   = environment.0
rightfeeler  = environment.1
lightonleft  = environment.2
lightonright = environment.3
darkonleft   = environment.4
darkonright  = environment.5

        clr environment       ; start all bits clear
        sb leftfeelpin        ; set feeler bits
        setb leftfeeler       ; pins low=touching
        sb rightfeelpin       ; env  high=touching
        setb rightfeeler
; read photocells  (hard coded to bits 0 and 7)
        mov lightL, #127        ; max light level
        mov !rb, #11000010b     ; make L photobit an out
        clr rb                  ; short out cap
        mov loops, #10          ;  for few ms
        call wait
        mov !rb, #11000011b     ; make ins again
ploopL  jb rb.0, readR          ; go on when input goes high
        djnz lightL, ploopL     ; loop if still above 0
readR   mov lightR, #127
        mov !rb, #01000011b
        clr rb
        mov loops, #10
        call wait
        mov !rb, #11000011b
ploopR  jb rb.7, readend
        djnz lightR, ploopR
; mask noise
        and lightL, #01111000b
        and lightR, #01111000b
; set environment bits
        csbe lightL, lightR       ; if left > right
        setb lightonleft          ;    set lightonleft flag
        csbe lightR, lightL       ; if right > left
        setb lightonright         ;    set lightonright flag
        csa  lightL, #darkthresh  ; if left <= darkthresh
        setb darkonleft           ;    set darkonleft flag
        csa  lightR, #darkthresh  ; if right <= darkthresh
        setb darkonright          ;    set darkonright flag
; set bad-environment flag
        clrb badenv
        mov w, environment
        and w, #00000011b         ; isolate feelers
        sz                        ; if either touching
        setb badenv               ;    set badenv flag
        mov temp1, environment
        and temp1, #00110000b     ; isolate dark bits
        jz gend                   ; skip if neither dark
        cse temp1, #00110000b     ; skip if both dark
        setb badenv               ; just one, set badenv flag

; sub to validate action byte and set badmove flag
        clrb badmove
        mov temp1, action
        and temp1, #11000000b
        cse temp1, #01000000b
        setb badmove            ; invalid memory
        jnb action.2, ca1
        jnb action.3, ca1
        setb badmove            ; smoke on right
ca1     jnb action.4, ca2
        jnb action.5, ca2
        setb badmove            ; smoke on left
ca2     mov w, action
        and w, #00111100b
        setb badmove            ; no movement

; table of valid moves
getmove jmp pc+w
        retw forward
        retw reverse
        retw popleft
        retw popright
        retw turnleft
        retw turnright
        retw backleft
        retw backright

;debug subs
shortflash  setb ra.3
            mov loops, #30
            call wait
            clrb ra.3
            mov loops, #220
            call wait

longflash   setb ra.3
            mov loops, #200
            call wait
            clrb ra.3
            mov loops, #50
            call wait

;*********** main code here
        mov OPTION, #optpause   ; short delay
        mov !ra, #00000111b     ; 2=1381in 1=eedata 0=eeclk (set to hi-z)
        mov !rb, #11000011b     ; 0,7=photo ins 1,6=feeler ins 2-5 motor outs
        clr ra                  ; clear led out (ra.3)
        clr rb                  ; clear motor outs
        mov  addr1, #00011111b  ; set to top of eeprom        
        jnb statby.3, rest      ; if not waking up from sleep
        jnb powerpin, rest      ;   and power not low
        call getenvironment     ;     initialize variables
        clrb lastenvbad
        clrb popping
        clr action
        clr addr
        clr lastmove
        clr boring
rest    jb popping, nextpop     ; jump if in middle of a pop cycle
        mov popcnt, #maxsleep   ; set up max delay before waking
        jb powerpin, watch      ; become alert if enough power
        setb sleeping           ; otherwise set deepsleep flag
        mov OPTION, #optsleep   ;  long duration (!OPTION for SPASM)
        sleep                   ;  sleep and keep on charging

watch   ; charge until something changes or counter runs out
        jnb sleeping, wakeup       ; if not in deepsleep, continue on
        mov temp, environment
        call getenvironment             ; look around
        jb badenv, wakeup               ; wake if bad environment
        cjne temp, environment, wakeup  ; wake if change in env.
        decsz popcnt                    ; wake if count runs out
        sleep                           ; else sleep and charge

wakeup  mov popcnt, #pops       ; set up pop counter
        clrb sleeping           ; not sleeping anymore
        mov OPTION, #optpause   ; shorten delay (!OPTION for SPASM)


; learn about surroundings and store in eeprom
; eeprom memory layout...
;   7 6 5 4 3 2 1 0    a = motor actions    m = set to "01" if
;   m m a a a a c c    c = confidence 0-3       a valid memory

        movb lastenvbad, badenv    ; save bad flag
        call getenvironment        ; look around

        snb badenv
        call longflash             ; flash if bad environment

; boring detection
        mov temp, action
        and temp, #00111100b       ; compare just action bits 
        cjne lastmove, temp, rstbc      ; if same move
        cje environment, addr, bdend    ;  if env. changed
        inc boring                      ;   boring=boring+1
        csb boring, #boringthresh       ;   if boring>=toomany
        setb badenv                     ;    set badenv flag
        jmp bdend                       ; else
rstbc   clr boring                      ;  boring=0

; update confidence of last move according to success
        jb badenv, decconf     ; decrement last if bad environment 
        jb lastenvbad, incconf ; increment if last environment bad
        mov w, action          ;   (but this one isn't)
        and w, #00101000b      ; check for reverse bits
        jnz decconf            ; decrement if backing up when good
incconf mov temp, action       ; good move, increment
        and temp, #00000011b
        cje temp, #00000011b, evaldone ; no change if max confidence
        inc action          ; increment confidence
        mov temp, action           ; learned photovore behavior
        and temp, #00000011b       ; reward if going to light
        cje temp, #00000011b, wr2ee
        jnb lightonleft, lpvb2
        jnb action.2, wr2ee
        jb  action.5, wr2ee
lpvb2   jnb lightonright, lpvb3
        jnb action.4, wr2ee
        jb  action.3, wr2ee
lpvb3   inc action        

wr2ee   mov datao, action   ; write action
        call wbyte          ;  to eeprom (addr)
        jmp evaldone
decconf mov w, action
        and w, #00000011b
        jz evaldone      ; no change if conf already 0
        dec action       ; decrement confidence
        jmp wr2ee        ; jmp to write        
        mov lastmove, action     ; save last move
        and lastmove, #00111100b ;  minus extra data

; access memory from eeprom
        mov addr, environment
        call rbyte 
        mov action, datai      ; action = memory
        call checkaction
        jb badmove, rmove      ; select random if bad move
        mov w, action
        and w, #00000011b
        jnz move               ; confidence > 0, go with move

; select random move
        call shortflash        ; short flash when picking random

; variable delay based on light
        mov !rb, #11000010b    ; discharge left photo input cap 
        clr rb
        mov loops, #10
        call wait
        mov !rb, #11000011b
        mov temp, #255         ; set max loops
vdelay  jb rb.0, loadrnd       ; go if photo input high
        djnz temp, vdelay      ; loop until temp = 0
loadrnd mov temp, rtcc         ; who knows what
        and temp, #00000111b   ; mask off all but bottom 3
        mov w, temp            ; convert 0-7 into
        call getmove           ;  valid predefined move
        mov action, w          ; get move in action

; move robot with move in action variable
; (bits 2-5 to motors, rest ignored)
        call checkaction        ; validate action
        jb badmove, drstop      ; stop if forbidden move        

        mov temp, #popdur       ; how much
drloop  mov rb, action
        mov loops, #ontime
        call wait
        clr rb
        mov loops, #offtime
        call wait 
        djnz temp, drloop       ; loop until done
        setb popping            ; tell startup we're in a move cycle
        sleep                   ; sleep between pops to save power

nextpop                         ; here if wakes with popping set
        clrb popping            ; end of move cycle
        djnz popcnt, poploop    ; next pop
        mov OPTION, #optsleep   ; long duration (!OPTION for SPASM)

; dump contents of memory to LED then go to sleep
; each byte ...1-0-m0-m1-m2-m3-m4-m5-m6-m7-1-0-0...
        mov temp, addr          ; save current addr
        mov addr, #0            ; start at 0
dumplp  call rbyte              ; get byte
        setb statusLED
        mov loops,#50           ; '1' start bit
Await   mov loops2,#portspeed
Await2  djnz loops2, Await2
        djnz loops, Await
        clrb statusLED
        mov loops,#50           ; '0' start bit
Bwait   mov loops2,#portspeed
Bwait2  djnz loops2, Bwait2
        djnz loops, Bwait
        mov count, #8           ; 8 data bits 
LEDfla2 clrb statusLED
        snb datai.0
        setb statusLED          ; 1 if lsb set
        clr wdt                 ; don't bomb
        mov loops,#50
Cwait   mov loops2,#portspeed
Cwait2  djnz loops2, Cwait2
        djnz loops, Cwait
        rr datai                 ; next bit
        djnz count, LEDfla2
        setb statusLED
        mov loops,#50           ; '1' stop bit
Dwait   mov loops2,#portspeed
Dwait2  djnz loops2, Dwait2
        djnz loops, Dwait
        clrb statusLED
        mov loops, #100         ; 2 '0' stop bits
Ewait   mov loops2,#portspeed
Ewait2  djnz loops2, Ewait2
        djnz loops, Ewait
        inc addr                ; next address
        jnb addr.6, dumplp      ; loop if under 64
        mov addr, temp          ; restore old address
        sleep                   ; rest and charge

; end

/*              CMAC - Cerebellum Model Articulation Controller
                as described in AI Expert, June 1992, pp. 32-41
                and Transactions of ASME, Sept. 1975, pp. 220-227

          \     |                |---|****   |----------|
           \    |                |---|AND *--| x Weight |--+
          \ >---|                |---|****   |----------|  |
X Input1-* X    |                |                         |
          X >---|                |                         |
X Input2-* X    |                |     :                   |
          / >---|                |                         |
           /    |                |                         |
          /     |                |     :                   |
                |  Interconnect  |                         |
          \     |     Matrix     |                         |
           \    |                |     :                   | |-----------|
          \ >---|                |                         +-+           |
Y Input1-* X    |                |---|****   |----------|    |           | Output
          X >---|                |---|AND *--| x Weight |----+  Output   +------->
Y Input2-* X    |                |---|****   |----------|    | Summation |
          / >---|                |                         +-+           |
           /    |                |     :                   | |-----------|
          /     |                |                         |
                |                |                         |
          \     |                |     :                   |
           \    |                |                         |
          \ >---|                |                         |
Z Input1-* X    |                |                         |
          X >---|                |     :                   |
Z Input2-* X    |                |                         |
          / >---|                |                         |
           /    |                |---|****   |----------|  |
          /     |                |---|AND *--| x Weight |--+
                |                |---|****   |----------|

                                                  ^ trainable weight vector
                                       ^ AND gates (eg. dimension=3)
                        ^connection matrix (connects inputs to AND gates)
             ^overlapping input sensors (eg. width=2 inputs/sensor)
         ^inputs (eg. quant=2 bits/dimension)
 ^dimension (eg. 3)

       1. Only one input per dimension can be active (= 1) at any time.
          Input values must be quantized into 1 of "quant" values.

       2. Input sensors overlap and cover to "1 to width" number of inputs.
          Width can vary between 1 to "quant". Low numbers usually work best.

       3. Interconnect matrix is such that each input vector (eg. X,Y,Z)
          activates exactly "width" number of AND gates.

       4. Each AND gate has "dimension" number of inputs.

       5. Output is a summation of weights corresponding to activated AND gates.

       6. Weights are trained using the Delta rule.

       7. CMAC converges very rapidly. Three bit parity example can be solved to
          an accuracy of .001 in about 20 training passes.

       8. All nonlinearity comes from input mapping instead, of sigmoid
          function like FFNNs.

       9. Visualize input vectors as locations in an N-dimensional space.
          The Output is then the value of the function at that location.

      10. Interpolation between multiple outputs can be added to reduce
          effect of quantization.

      11. Once the weights have been trained, the compute_output routine
          can be used alone to determine output quickly.

      12. CMAC can be used to find approximations to N-dimensional nonlinear
          functions like sqrt or distance calculations quickly.

      13. CMAC has been used successfully to linearize transducers or to form
          the inverse function of unknown plant dynamics.

#include <stdio.h>
#include <math.h>

                /* User selectable values */
#define dimension       3               /* input dimensions */
#define quant           2               /* input quantization per dimension */
#define width           2               /* width of input sensors */
#define max_gates       10              /* ==> set to (quant**dimension)+width) */
#define beta            0.4             /* learning rate for weight training */
#define err_limit       0.001           /* maximum error for any input */

#define k1              (quant+width-1) /* intermediate calculation */
#define max(a,b)        ((a>=b)?a:b)    /* max macro */
#define min(a,b)        ((a<=b)?a:b)    /* min macro */

struct  list_of_conns{
           int  n;                      /* number of gates in list */
           int  gate_ptr[(max_gates)];  /* indices of gates */
        } conn[quant][dimension],       /* connections between inputs and gates */
          activated,                    /* list of activated gates */
          *c;                           /* pointer to list_of_conns */

int     n_inputs;                       /* number of possible input vectors */
int     n_sensors;                      /* number of possible input sensors */
int     input[dimension];               /* input vector */
int     nbr_gates = 0;                  /* num of gates used */
int     gate[max_gates];                /* AND gates */
double  weight[max_gates];              /* weight matrix */
double  output, desired, error, total_error;

void form_interconnects();
void compute_output();
void train();

int main()
    register int        i, j, k;
    int                 pass=1;
    double              max_error=err_limit;

    printf("\n\n       CMAC        \n\n");
    printf("cmac: finished interconnects, beginning training.\n");
    while(max_error>=err_limit){                    /* for each pass */
        for(i=0;i<n_inputs;i++){                    /* for each possible input */
            for(k=1,j=0;j<dimension;k*=quant,j++)   /* form input vector */
            for(desired=0,j=0;j<dimension;j++)      /* compute desired output */
              desired=(double)(((int)desired) ^ input[j]); /* parity bit example */
        printf("Pass=%d   \tmax_error=%g\tAvg Err=%g\n",
    printf("cmac: finished training.\n\n");
    for(i=0;i<nbr_gates;i++)                        /* display weights */

void form_interconnects()                       /* generate interconnect lists */
        register int    i, j, k, m, n, p, found;

        for(c = &conn[0][0],i=0; i<quant*dimension; c++,i++)  /* initialization */

        for (k=0; k<width; k++){
            for(i=0;i<n_sensors;i++){  /* for each combination of input sensors */
                for(m=1,j=0; j<dimension; m*=k1,j++)   /* for each dimension */
                    if((((i/m)%k1)%width)!=k){     /* check acceptance criteria */
                        found=0;                     /* rejected, try another */
                if(found==1){                               /* if acceptable */
                    for(m=1,j=0; j<dimension; m*=k1,j++){ /* for each dimension */
                        n=(i/m)%k1;                         /* n=input sensor */
                        for(p=max(0,n-width+1); p<=min(n,(quant-1)); p++){
                            c = &conn[p][j];   /* p=input connected to sensor n */
                    if(nbr_gates > max_gates){
                       printf("cmac: error, maximum number of gates exceeded!\n");
                       exit(3);         /* increase #define max_gates */

void compute_output()                       /* usable during and after training */
        register int g, i, j;

        activated.n=0;                      /* initialization */
        for(g=0;g<nbr_gates;g++)  gate[g]=0;

        for(i=0;i<dimension;i++){           /* for all dimensions */
            c = &conn[input[i]][i];
            for(j=0;j<c->n;j++){            /*increment all gates in list */
                if(((i+1)==dimension)&&(gate[g]==dimension)){ /* if activated */
                                            /* generate list of activated gates */
                    output += weight[g];    /* update output */

void    train()                             /* compute error and modify weights */
        register int    i;

        for(i=0;i<activated.n;i++)          /* using list of activated gates */

See also:

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