Page 52 - Concise Encyclopedia of Robotics

Branching
Boolean algebra: theorems
Equation
OR identity
X + 0 = X
AND identity
X * 1 = X
X + 1 = 1
X * 0 = 0
X + X = X
X * X = X Name (if applicable)
( X) = X Double negation
X + ( X) = X
X * ( X) = 0 Contradiction
X + Y = Y + X Commutativity of OR
X * Y = Y * X Commutativity of AND
X + (X * Y) = X
X * ( Y) + Y = X + Y
X + Y + Z = (X + Y) + Z = X + (Y + Z) Associativity of OR
X * Y * Z = (X * Y) * Z = X * (Y * Z) Associativity of AND
X * (Y + Z) = (X * Y) + (X * Z) Distributivity
(X + Y) = ( X) * ( Y) DeMorgan’s theorem
(X * Y) = ( X) + ( Y) DeMorgan’s theorem
on either side of the equal sign are logically equivalent. The second table
shows several logic equations. These are facts, or theorems. Boolean
theorems can be used to analyze complicated logic functions.
See also LOGIC GATE.

BRANCHING
Branching refers to routines, or programs, that have points at which an
intelligent robot controller must select among alternatives.
Consider a robot on an assembly line that makes cars. The robot’s job is
to insert hubcaps in the two right-side wheels. (An identical robot does the
same job on the left side.) Suppose that 20 percent of the cars are fitted with
gold-colored (G) hubcaps; the rest are fitted with silver-colored (S) ones.
The robot should insert hubcaps in the following sequence: SS SS SS SS
GG SS SS SS SS GG SS SS…, and so on. Every fifth pair of hubcaps is gold.
Each time a hubcap pair is to be inserted, the computer must make a
choice. Thus, the routine is at a branch point for every hubcap pair. Every

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