mv-4920 battlefield data processing theory-ii * generic processing cycle * truth table program *...
TRANSCRIPT
MV-4920 Battlefield Data Processing
Theory-II
* Generic Processing Cycle
* Truth Table Program
* Data Processing Automation
* Input and Output Transforms
* Calculation Levels
Generic Processing Cycle
READ WRITE
DetectorActuator
inpu
t
outp
utProgramDetector Status to
Actuator Commands
1) Read - Reads Detector Content into Input array for the calcualtion phase
2) Process - Execute the program which connects a set of Inputs to a set of Outputs
3) Write - Sends Actuator Commands from calcualtion output array into Actuator
4) Wait - reset go back to step 1
Generic Processing Steps
Detector Readings - Detector name, detector content
Actuator Commands- Actuator Name, Actuator content
Input - Memory Cell Name, Memory Cell Content
Output - Memory Cell Name, Memory Cell Content
Generic Data Structures
The Transform from detector name space to program input name space is done by the Read function
Detector Readings InputREAD
Read ( radix* DetectorNames, radix* Input){
Enable (DetectorNames+I);
For (I=0,I<Number of detector names,I++){*(Input+I) = *(DetectorNames + I);
}
Disable (DetectorNames+I);
return;
} Low level simple assignment example
READ
enable
disable
The Transform from program output to actuator commands is done by the WRITE function
OutputActuator
CommandsWRITE
Write( radix* ActuatorNames, radix* Output){
Enable (ActuatorNames+I);
For (I=0,I<Number of ActuatorNames,I++){
*Output = *(ActuatorNames + I);
}
Disable (ActuatorNames+I);
return;
}Low level simple assignment example
WRITE
enable
disable
Inpu
t
Out
put
Radix InputTable [MaxInput Possibilities]
Radix OutputTable [MaxOutputPossibilities]
TruthTableProgram(Radix Input,Radix Output)
{
while(This<MaxInput Possibilities){
if (Input = = InputTable[this])
{Output = OutputTable[This]; return;}
This = This + 1;
}
return;
}
Generic Truth Table Program
Truth Table ProgramINPUT OUTPUT
Detector names Actuator names
All
pos
sibl
e de
tect
or c
onte
nt s
tate
s
All
pos
sibl
e ac
tuat
or c
omm
ands
1 2 3 …. Dmax 1 2 3 …. Amax
0 0 0 0
1 0 0 0
0 1 0 0
1 1 0 0
0 0 1 0
1 0 1 0
...
0 1 1 0
1 0 0 1
0 1 0 1
1 0 0 0
1 1 1 0
1 1 1 1
...
If this do that
Any calculation doable with a Turing machine can be written as a Truth Table Program.
The program execution steps are trivial.
All the complexity is in the Input and Output tables.
The Input and Output Tables can get very big.
For example suppose besides the immediate detector input the program also considers the past history ie. The memory of the machine. Then the
Input would contain the not just the detector readings but also the the content of all the memory cells.
HOW BIG?
Assume there are Dmax detectors reporting one of “Dc” readings and Mmax memory cells reporting a “0 or 1” each of then the total number of
Configurations is
DcDmax * 2Mmax
Each additional cell will multiply the volume of possibilities by the number of
different contents that can be read from the cell.
If this number of input possibilities requires a response to Amax actuators with “l” levels the total truth table array is
Amax * l * DcDmax * 2Mmax
Some Properties of the Truth Table Program
Simple Surface Seeker Example
Input: 2 detector 2 levels
L R 0 1Output: 1 actuator 3 positions
wheel L N R
Program: Truth TableDetector Name
L R
0 0
0 1
1 0
1 1
Actuator name
Wheel
L
R
L
N
Reason
no target seek left
target right go right
target left go left
target center go straight
L R
L N R
0
1
0
0
0
11
1
00
0
11
11
0
L
R
N
L
R
EXAMPLE: HARDWARE IMPLEMENTATION
OF A TRUTH TABLE PROGRAM
EXAMPLE: LOOKUP Table Implementation
OUTPUT = TRUTHTABLE[INPUT];
How many gates does it take to Implement?
For a system with INmax 2 state inputs and outputs the Total Gates = 2* (INmax +1)* 2INmax
Suppose each set of these gates are a micro meter in size.How big a problem could you fit into a sphere of size R in meters.
Total Gates = 4/3 *1024*R3
T = (2R/c )= 2/c (3 /4*10-24*G)1/3
= (2/c)* 10-6* (3 2 /4)1/3 ((IN+1) 2IN )1/3
= ~ 5* 10-14 ((IN+1) 2IN )1/3
IN= 30 bits T= 3.4x10-10 R = 10 cm
IN = 100 bits T = .004 sec R = 1.2 x106
How fast could a calculation be done ?
Time to for the speed of light to go from the center to the surface and back. T = 2R/c
TRICKS TO REDUCE IMPLEMENTATION COST
* Reduce bits
* use value changes
* some patterns cannot happen
* collect patterns with the same solution
* Add time ( program steps)
* calculate each possibility when it happens
* Hybrid - pre-calculate partial solutions
Truth Table Program solves any problem in real time but complex problems cost a lot what can you do?
* WHAT IS AUTOMATION?
The transfer of what a human does to a machine.
* Automation Steps1) Learn the human operation sequences.
2)Build a machine that automatically executes machine operations
3) Map the human to sequences of machine operations
4) if mapping not complete add machine operations and go to 2.
* We already have a machine that does any calculation we can imagine.
* So what is left to do?
Learn how the human writes the truth table program.
How is the program written?Input and output possibilities are defined by all possible content configurations in the space of input and output cell names.
The programmer visualizes the meaning of an input content configuration possibility.
The programmer decides for each possible input what is the appropriate output and writes this decision into a truth table.
The programmer goes to the next possible content configuration until all possible input configurations are exhausted.
Context and Reason for Program Supplied by Programmer
READ WRITE
inpu
t
outp
utProgramDetector Status to
Actuator Commands
Programmers World Concept
Programmer Writers Process
inpu
t
outp
utProgram
Programmers World Concept
Input
meaning
Output
Meaning
Interpret
detector readings
in terms of
input
Interpret
Meaning of output in terms of
Actuator
commands
decision
Transforming The Program to a Higher Level
READ WRITEou
tput
DETECTOR LEVEL
Program
Programmers World Concept
outp
ut
HIGHER LEVEL
Programin
put
inpu
t
Transform Transform
1) Find a space in which the Problem Solution decision can be made
2) Make the decisions in this space
3) Transform from measurements to Decision Space and add detectors as necessary.
4) Transform from Decision to Command Space and add Actuators as necessary.
Steps to Solve the Intercept Problem at a Higher Level
Select Hunter and Target Object Space. Solution Minimized distance.
Write the Program (Input Hunter and Target Object
Space ,Output Hunter and Target Object Space )
Write the Transform (Readings Detector Space ,
Input Hunter and Target Object Space )
Write the Program (Output Hunter and Target Object
Space ,Commands Actuator Space )
General functions Example Specific
Step 1) Find the Decision SpaceSolution is to close the distance
Hunter PositionXh,Yh,Zh,Th
Target PositionXt,Yt,Zt,Tt
Step 2) Write the Interceptor Truth Table Program(3x3x3 Example)
Output cell names
memory to actuators
0 1 2 0 1 2 0 1 2 0 1 2 … 2
0 0 0 1 1 1 2 2 2 0 0 0 … 2
0 0 0 0 0 0 0 0 0 1 1 1… 2
0 1 2 0 1 2 0 1 2 0 1 2 … 2
0 0 0 1 1 1 2 2 2 0 0 0 … 2
0 0 0 0 0 0 0 0 0 1 1 1… 2
0 0 0 ... 0
T 0 0 0
H 0 0 … 0
B 0 0 0
0 T 0 ... 0
T T 0 0
H T 0 … 0
B T 0 0
0 H 0 ... 0
T H 0 0
H H 0 … 0
B H 0 0
0 0 0 ... 0
0 0 0 T 0 0 H 0 .. 0 T 0 H 0 0 0 000 0
H 0 0 … 0
B 0 0 0
Input cell names
measured memory
X 0 1 2 0 1 2 0 1 2 0 1 2 … 2
Y 0 0 0 1 1 1 2 2 2 0 0 0 … 2
Z 0 0 0 0 0 0 0 0 0 1 1 1… 2
0 1 2 0 1 2 0 1 2 0 1 2 … 2
0 0 0 1 1 1 2 2 2 0 0 0 … 2
0 0 0 0 0 0 0 0 0 1 1 1… 2
0 0 0 ... 0
T 0 0 0
H 0 0 … 0
B 0 0 0
0 T 0 ... 0
T T 0 0
H T 0 … 0
B T 0 0
0 H 0 ... 0
T H 0 0
H H 0 … 0
B H 0 0
…
0 0 0 ... 0
0 0 0 T 0 0 H 0 .. 0 0 0 0 0 T 0 00H 0
0 0 0 … 0
0 0 0 0
All
Pos
sibi
liti
esN
ame
dim
ensi
ons
How is the Intercept program written?
Visualize Next Possible Input Configuration
H1 T1
H2 T2
Calculate the best Move
Predict new position based on constant velocity:
Xh3 = 2*Xh2 - Xh1, Yh3 = 2*Yh2 - Yh1, Zh3 = 2*Zh2 - Zh1
Xt3 = 2*Xt2 - Xt1, Yt3 = 2*Yt2 - Yt1, Zt3 = 2*Zt2 - Zt1
Calculate Hunter’s best velocity Change:
R = (Xh3-Xt3)2 + (Yh3-Yt3)2 + (Zh3-Zt3)2
X = (Xh3-Xt3) /R Y= (Yh3-Yt3) /R Z= (Zh3-Zt3) /R
Calculate desired position
Xhout = Xh3 + X , Yhout = Yh3 + Y , Zhout = Zh3 + Z
Write Output decision H1 T1
H2 T2
H3 Hout T3
Next =Next+1
Step 3 ) Detector Reading to Object Space Transform
Transform( Detector readings| HunterPosition,TargetPosition)In
stan
t H
un
terP
osit
ion
,Tar
getP
osit
ion
Inst
ant D
etec
tor
read
ings
Transform program in Truth Table format
All possible Detector readingsD,Az,El,f,Xh,Yh,Zh
Corresponding
Hunter Position, Target PositionXt,Yt,Zt,Xh,Yh,Zh
How is the Detector Reading to Object Space Transform Programmed?
3) add Additional Detectors for Hunter positioning
4) A
dd A
ddit
iona
l Det
ecto
rs f
or
Tar
get P
osit
ioni
ng
Xh Yh Zh Th
Az
El
GPS receiver
f o
1) paramterize Object Space5)Single Instant Transform Xt=O*cos(el)*cos(az)
Yt=O*cos(el)*sin(az)
Zt=O*sin(el)
O = m*f
2) Find Detector Reading Context
F
D
How is Object Space to Actuator Command Transform Programmed?
Spectrum of Actuator Command
PitchRateYawRate Thrust
1) If the vales Yr,Pr,Th were applied
2) The change in position in Vehicle coordinates in T
F = Th * drag
F = Th * drag
U= F * (1-cos(Pr)/2)
R= F * (1-cos(Yr)/2)
3) Transform from Vehicle to
Object Space Coordinates
X Vehicle F
Y = to U
Z space R
4) The change X, Y, Z
Would result in the position. Desired X, Y, Z from Program
Rev
erse
cal
cula
tion
to g
et A
ctua
tor
Com
man
ds
F
U R
THEORY II SUMMARY
READ WRITE
outp
ut
DETECTOR LEVEL
Program
Programmers World Concept
outp
ut
OBJECT LEVEL
Programin
put
inpu
tTransform Transform
LE
VE
LS
OF
AB
ST
RA
CT
ION