Page 169 - Introduction to Autonomous Mobile Robots

Chapter 4
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In the following two sections, we present specific feature extraction techniques based on
the two most popular sensing modalities of mobile robotics: range sensing and visual
appearance-based sensing.

4.3.1 Feature extraction based on range data (laser, ultrasonic, vision-based ranging)
Most of today’s features extracted from ranging sensors are geometric primitives such as
line segments or circles. The main reason for this is that for most other geometric primitives
the parametric description of the features becomes too complex and no closed-form solu-
tion exists. Here we describe line extraction in detail, demonstrating how the uncertainty
models presented above can be applied to the problem of combining multiple sensor mea-
surements. Afterward, we briefly present another very successful feature of indoor mobile
robots, the corner feature, and demonstrate how these features can be combined in a single
representation.

4.3.1.1 Line extraction
Geometric feature extraction is usually the process of comparing and matching measured
sensor data against a predefined description, or template, of the expect feature. Usually, the
system is overdetermined in that the number of sensor measurements exceeds the number
of feature parameters to be estimated. Since the sensor measurements all have some error,
there is no perfectly consistent solution and, instead, the problem is one of optimization.
One can, for example, extract the feature that minimizes the discrepancy with all sensor
measurements used (e.g,. least-squares estimation).
In this section we present an optimization-based solution to the problem of extracting a
line feature from a set of uncertain sensor measurements. For greater detail than is pre-
sented below, refer to [14, pp. 15 and 221].

Probabilistic line extraction from uncertain range sensor data. Our goal is to extract a
line feature based on a set of sensor measurements as shown in figure 4.36. There is uncer-
tainty associated with each of the noisy range sensor measurements, and so there is no
single line that passes through the set. Instead, we wish to select the best possible match,
given some optimization criterion.
More formally, suppose n ranging measurement points in polar coordinates
,
x = ( ρ θ ) are produced by the robot’s sensors. We know that there is uncertainty asso-
i
i
i
ciated with each measurement, and so we can model each measurement using two random
,
variables X = ( P Q ) . In this analysis we assume that uncertainty with respect to the
i i i
P
actual value of and Q is independent. Based on equation (4.56) we can state this for-
mally:
,
,
,
[
E P P ] = E P[]E P[] ∀ i j = 1 … n (4.62)
⋅
i j i j