Page 411 - Introduction to AI Robotics

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11
Localization and Map Making
rule. It specifies the combined probability mass assigned to each C k , where
C is the set of all subsets produced by A \ B. The rule is:
P m(A i )m(B j )
A i \B j =C k ;C k 6=;
(11.9) m(C k ) P =
1 A i \B j =; m(A i )m(B j )
where the focal elements of B 1 an ed B l 2 ar ee: l
B 1 e = l A = fA 1 ; i g : : : ; A
B 2 e = l B = fB 1 ; j : g : : ; B

The computation is repeated k times, once for every distinct subset that
emerged from the orthogonal sum, and results in
l
B 3 = em(C 1 ); (C 2 ); m (C : k ) : : m
For the case of any occupancy grid, there are only three possible focal ele-
ments (Occupied, Empty,and dontknow). Dempster’s rule reduces to:

P
m(A i )m(B j )
ccupied
A i \B j =O
m(O ) P =
ccupied
1 m(A i )m(B j )
A i \B j =;
P
p i )m(B j )
m(A
A i \B j =E m t y
m(E ) P =
mpty
1 m(A i )m(B j )
A i \B j =;
m(A i )m(B j )
P
A i \B j =dontknow
m(don 0 tknow ) P =
1 m(A i )m(B j )
A i \B j =;
11.4.4 Weight of conflict metric
Normalizing contradictory evidence may produce a justifiable measure of
evidence, but a robot needs to be aware of such discordances. Instead, the
renormalization term can be viewed as a measure of the conflict between the
pair of belief functions. The larger the area assigned to ;, the more disagree-
ment between the two beliefs about the FOD. Shafer defines such a measure
in the weight of conflict metric, C : 126 o n
1 X
;
(11.10) C (B 1 o e 2 n B ); her e = = e m 1 (A i l )m 2 (B j ) l o g (
w
l )
1
A i \B j =;
n
o,and as ! 1:0,
C takes oa value between 0 and 1;as ! 0:0, C ! 0:0 n
1a
.
C ! o It is additive, which means that the conflict from summation of
n