Page 427 - Introduction to AI Robotics

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The HIMM updating scheme is simple where: Localization and Map Making
3
g r[3][10] i d = g r[3][10]+ i d
= 3 + 3 = 6
At t 3 , the sonar returns a value of 8.5 units. The robot has moved to the

side and rotated; it is now 6.7 units from the grid element with an of 5 .
In this case g r[3][10] i d is in Region II for the Bayesian and Dempster-Shafer
sonar models, and is not affected by the HIMM model at all.
The probability score for the Bayesian model is computed using Eqn. 11.2
instead of Eqn. 11.1:

( R R r ) ) + (
P (sjE ) m= p t y
2
( 10 6:7 ) 15 5 ) + (
= 10 15 = :50 0
2
ccupied
P (sjO ) = 1:0 P (sjE ) m :0 0: p50=0 t:50 = y 1
The result happens to be an almost even probability that g r[3][10] i d is oc-
cupied. This probability is then substituted into Bayes rule (Eqn. 11.6) with
the previously stored probability:

)
jO)P (Ojs t 0
) =
P (s t 3
) jE)P (E j )
P (Ojs t 3
P (s t 3 jO)P (Ojs t 0 P (s t 1 +s t 0
(0 :50)(0 :72)
=
(0
(0 :50)(0 :72)+ :50)(0 :28)
= 0:72
) = 1 ) :28 = 0
P (Ejs t 3 P (Ojs t 3
The Dempster-Shafer belief function is computed using Eqn. 11.9, yielding
ccupied
)
m(O ) = 0:0; (E m m= 0:50) ; p (dontknow t m y ) = 0:50) . The differ-
m
ence between the probability and belief function is that the :E score p t y
was assigned to P (sjOccupied ) in the Bayesian method and to m(dontknow )
in the Dempster-Shafer. The combination is shown in Fig. 11.16c, and pro-
duces:
(0 :86)(0 :5)
m(O ) = = :76 0
ccupied
1:0 (0 :86)(0 :5)