Page 426 - Introduction to AI Robotics

11.6 Comparison of Methods
(1 :0)(0 :46) 409
m(dontknow ) = = :46 0
1:0 0:0
Therefore, the updated belief at g r[3][10] i d is:
ccupied
(11.15) m(O ) :54 ; (E m) =m :0; (dontknow m t =) y :46 0 = 0 0
p
The HIMM updating is governed by Eqn. 11.11, below. Since g r[3][10] i d is
in the HIMM occupied region, the increment term I is I + = . 3

g r[3][10] i d = g r[3][10]+ i d I +
= 0 + 3 = 3

Step 4: Repeat Steps 2 and 3 for each new reading.
At t 2 , the robot has translated forward. The sonar reading is 6.0. The grid
element is now 6.0 units away with an = . g r[3][10] i d still falls in Region 0
I for all three updating methods. The application of Eqn. 11.1 produces a
=
probability of P (sjOccupied ) :69 ; (sjE P ) =m :31 , a p belief tfunction of 0 0
y
ccupied
)
m(O ) = 0:69 ; (E m m= 0:0; ( pdontknow t m y) = 0:31 ,and a HIMM
increment of +3.
Updating the grid produces an increase in the occupancy score, as would
be expected, given two direct sonar observations of an object. The Bayesian
updating is:

)
jO)P (Ojs t 1
P (s t 2
) =
P (Ojs t 2
) jE)P (E j )
P (s t 2 jO)P (Ojs t 1 P (s t 2 +s t 1
(0 :69)(0 :54)
=
(0
(0 :69)(0 :54)+ :31)(0 :46)
= 0:72
) = 1 ) :28 = 0
P (Ejs t 2 P (Ojs t 2
The Dempster-Shafer updating generates a higher occupancy score, which
can also be seen from Fig. 11.16b. The final score is:
(0
(0
(0 :54)(0 :69)+ :46)(0 :69)+ :54)(0 :31)
ccupied
m(O ) =
1:0 0:0
= 0:86
(0 :46)(0 :31)
m(dontknow ) = = :14 0
1:0 0:0
mpty
m(E ) = 0:0