Page 174 - Introduction to Autonomous Mobile Robots

159
Perception
This requires direct application of equation (4.60) with A and R representing the
random output variables of and respectively. The goal is to derive the 2 × 2 output
α
r
covariance matrix

σ 2 A σ AR
C = , (4.75)
AR 2
σ σ
AR R
given the 2n × 2n input covariance matrix

(
2
diag σ ) 0
C P 0 ρ
C = = i (4.76)
X 2
(
0 C Q 0 diag σ )
θ
i
and the system relationships [equations (4.73) and (4.74)]. Then by calculating the Jaco-
bian,
∂α ∂α … ∂α ∂α ∂α … ∂α
∂ P ∂ P 2 ∂ P ∂ Q ∂ Q 2 ∂ Q n
1
n
1
F PQ = (4.77)
∂r ∂r … ∂r ∂r ∂r … ∂r
∂ P ∂ P 2 ∂ P ∂ Q ∂ Q 2 ∂ Q n
1
n
1
we can instantiate the uncertainty propagation equation (4.63) to yield C AR :
T
C = F C F (4.78)
AR PQ X PQ
Thus we have calculated the probability C AR of the extracted line α r,( ) based on the
probabilities of the measurement points. For more details about this method refer to [6, 37]

4.3.1.2 Segmentation for line extraction
The previous section described how to extract a line feature given a set of range measure-
ments. Unfortunately, the feature extraction process is significantly more complex than
that. A mobile robot does indeed acquire a set of range measurements, but in general the
range measurements are not all part of one line. Rather, only some of the range measure-
ments should play a role in line extraction and, further, there may be more than one line