Page 236 - Introduction to Autonomous Mobile Robots

Mobile Robot Localization

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1 1-2 2 2-3 3 3-4 4

Figure 5.22
A realistic indoor topological environment.

n
because for each possible position n' the discrete topological distance from n' to can
vary depending on the specific topological map. The calculation of p n n'( i , ) is per-
–
t ti t
formed by multiplying the probability of generating perceptual event at position by the
i
n
n'
probability of having failed to generate perceptual events at all nodes between and : n
(
,
⋅
(
⋅
,
,
(
⋅
⋅
,
(
(
p n n' i , ) = p i n ) p ∅ n ) p ∅ n ) … p ∅ n ) (5.25)
–
–
t ti t t t t – 1 t – 2 ti + 1
For example (figure 5.22), suppose that the robot has only two nonzero nodes in its
belief state, {1-2, 2-3}, with likelihoods associated with each possible position:
(
p 1 – 2) = 1.0 and p 2 –( 3) = 0.2 . For simplicity assume the robot is facing east with
certainty. Note that the likelihoods for nodes 1-2 and 2-3 do not sum to 1.0. These values
are not formal probabilities, and so computational effort is minimized in Dervish by avoid-
ing normalization altogether. Now suppose that a perceptual event is generated: the robot
detects an open hallway on its left and an open door on its right simultaneously.
State 2-3 will progress potentially to states 3, 3-4, and 4. But states 3 and 3-4 can be
eliminated because the likelihood of detecting an open door when there is only wall is zero.
The likelihood of reaching state 4 is the product of the initial likelihood for state 2-3, 0.2,
the likelihood of not detecting anything at node 3, (a), and the likelihood of detecting a hall-
way on the left and a door on the right at node 4, (b). Note that we assume the likelihood of
detecting nothing at node 3-4 is 1.0 (a simplifying approximation).
(a) occurs only if Dervish fails to detect the door on its left at node 3 (either closed or
open), 0.6 0.4 +⋅[ ( 1 – 0.6) 0.05⋅ ] , and correctly detects nothing on its right, 0.7.
(b) occurs if Dervish correctly identifies the open hallway on its left at node 4, 0.90, and
mistakes the right hallway for an open door, 0.10.
⋅
⋅
The final formula, 0.2 [⋅ 0.6 0.4 + 0.4 0.05] 0.7 [ 0.9 0.1] , yields a likelihood of
⋅
⋅
⋅
0.003 for state 4. This is a partial result for p 4() following from the prior belief state node
2-3.