Page 235 - Introduction to Autonomous Mobile Robots

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(
(
(5.23)
p ni) = p in)p n() Chapter 5
The value of p n() is already available from the current belief state of Dervish, and so
the challenge lies in computing p in( ) . The key simplification for Dervish is based upon
the realization that, because the feature extraction system only extracts four total features
and because a node contains (on a single side) one of five total features, every possible com-
bination of node type and extracted feature can be represented in a 4 x 5 table.
Dervish’s certainty matrix (show in table 5.1) is just this lookup table. Dervish makes
the simplifying assumption that the performance of the feature detector (i.e., the probability
that it is correct) is only a function of the feature extracted and the actual feature in the node.
With this assumption in hand, we can populate the certainty matrix with confidence esti-
mates for each possible pairing of perception and node type. For each of the five world fea-
tures that the robot can encounter (wall, closed door, open door, open hallway-and foyer)
this matrix assigns a likelihood for each of the three one-sided percepts that the sensory
system can issue. In addition, this matrix assigns a likelihood that the sensory system will
fail to issue a perceptual event altogether (nothing detected).
For example, using the specific values in table 5.1, if Dervish is next to an open hallway,
the likelihood of mistakenly recognizing it as an open door is 0.10. This means that for any
node n that is of type open hallway and for the sensor value =open door, p in( ) = 0.10 .
i
Together with a specific topological map, the certainty matrix enables straightforward
computation of p in( ) during the perception update process.
For Dervish’s particular sensory suite and for any specific environment it intends to nav-
igate, humans generate a specific certainty matrix that loosely represents its perceptual con-
fidence, along with a global measure for the probability that any given door will be closed
versus opened in the real world.
Recall that Dervish has no encoders and that perceptual events are triggered asynchro-
nously by the feature extraction processes. Therefore, Dervish has no action update step as
depicted by equation (5.22). When the robot does detect a perceptual event, multiple per-
ception update steps will need to be performed to update the likelihood of every possible
robot position given Dervish’s former belief state. This is because there is a chance that the
robot has traveled multiple topological nodes since its previous perceptual event (i.e., false-
negative errors). Formally, the perception update formula for Dervish is in reality a combi-
nation of the general form of action update and perception update. The likelihood of posi-
tion given perceptual event i is calculated as in equation (5.22):
n

(
(
(
p n i ) = ∫ pn n' ti i , )pn' t – i ) n' ti (5.24)
d
t
–
–
t
t
t
The value of p n'( ) denotes the likelihood of Dervish being at position n' as repre-
t – i
sented by Dervish’s former belief state. The temporal subscript t – i is used in lieu of t – 1