MA 240  Discrete Mathematics                                    NAME: ________________________________ 

Fall 2005               Instructor:  Jeffrey Horn

HOMEWORK 3:  Combinatorial (Propositional) Logic as Stimulus-Response Brains (Digital Braitenberg Vehicles)
 

Handed out/Assigned:	Monday, September 26, 2005
Due:	Monday, October 3, 2005

(1)  DIGITAL Braitenberg Vehicle 1:

  Assume two inputs and two outputs.  Input is from photo detectors,.  Assume the following detector geometry:

 
So a "01" input vector would mean a light source detected to the right, but nothing center or left, while "11" would mean a light source in the center .  Also assume a finite detector range, defined by an arc (not shown above) with its center at the robot's center.

We have two binary outputs, one for each motor.  LM is left motor, RM is right.  A "0" output means the motor stops, while a "1" means go forward.  (so an output of 01, which is 0 to the left and 1 to the right motor, would result in an arcing turn to the left, while 10 would be a right turn)
 

Here is an example truth table (ie., a "brain") for a strategy to TURN AWAY FROM lights (hopefully!):

 

 

INPUTS			OUTPUTS
LS	RS		LM	RM
0	0		1	1
0	1		0	1
1	0		1	0
1	1		0	1

For each of the following parts of question 1, fill out the truth table (thus determining the indicated strategy), then write out the corresponding boolean expressions for the two outputs, simplify as much as possible (extra credit for any simplification), and finally draw the circuit for each output (i.e., for each motor).  See above example.

 

Boolean expressions:                               LM                                                         RM

                            

Simplified (extra credit):

 

CIRCUITS:                  LM                                                                                                RM

 

 

 

 

 

 


(1A)  Fill in the following blank truth table for a strategy to WORSHIP lights (that is, it seeks light, and when it has light directly in front of it, meaning both LS and RS see light, then it stops):    (you can try out your strategy in the on-line simulator) 

 

INPUTS			OUTPUTS
LS	RS		LM	RM
0	0
0	1
1	0
1	1

 

Boolean expressions:                                                LM                                                            RM

 

Simplified (extra credit):

 

CIRCUITS:                  LM                                                                                                RM

 

 

 

 

 

(2)  DIGITAL Braitenberg Vehicle 2:

This is the same as vehicle 1, except that we add one more sensor bit and one more output bit.   We now have a "predator proximity detector P" that gives us one bit of information.  If P is 0 then there is no predator in front of us.  If P is 1, then there is a predator somewhere within a cone of detection in front of us (finite range).  We also now have another "effector" (output), which is B for "BACKUP".    If the output B is set to 1, then the two motors will interpret a "0" signal as "reverse" instead of "stop".  If B is set to "0" then the the "0"signela to RM or LM will mean the usual "stop".  This will allow the vehicle to back up.   Thus we can now go backwards! 

THE STRATEGY:  Design a vehicle that seeks out light sources, BUT avoids predators.  (If a predator touches your vehicle, it eats it!)

(2 A)  Now fill out the 3-input truth table for the above strategy:

 

(2 B)  Explain in plain English what strategy your truth table above implements:

 

 

 (2 C)  Now try creating the circuits (or giving the boolean expressions, which do NOT have to be minimized) FOR EACH OF THE THREEE OUTPUTS above.
 

      LM:

 

 

 

 

     RM:

 

 

 

 

 

     B: