Tutorial on Range and Bearing Estimation
October 30, 2009
1 Introduction
Estimating the range and bearing from the robot to a landmark object is a necessary component for building
a localization system to determine the robot’s current pose. Specifically the range and bearing information
is used to estimate the likelihood of a hypothetical pose of the robot given a map of the environment. This
document serves as a reference to the Tutorial on a Probabilisitic Measurement Model based on Landmark
Range and Bearing Information1, which describes how to use the range and bearing information to estimate
the likelihood function in the landmark measurement model.
The Probabilistic Measurement Model tutorial specifies a spotted landmark in the camera’s visual stream
as a feature and denotes it by the triple (r, φ, o) where ris the distance (range) from the robot to the
fiducial, φ (-π,π] is the angle (bearing) at which the fiducial was spotted and o{yellow ball, pink fiducial,
green/orange fiducial,...}is its type. The bearing is 0 if the fiducial is directly in the middle of the robot’s
field of view. The bearing is positive if the landmark is to the left and negative if the landmark is the
right of the robot’s view center. This document describes how to determine the rand φfor each feature
(r, φ, o). The estimated rand φin the vector of observed features (1), where nis the number of objects in
view, is then measured against the feature vector of a hypothetical pose to compute the likelihood that a
hypothetical robot pose is the true robot pose.
f(z) = {f1, f2, . . . , fn}=
r1
φ1
t1
,
r2
φ2
t2
,...,
rn
φn
tn
(1)
2 Measuring Landmark Objects
It is recommended that a data-driven procedure is used to learn a function that outputs the predicted range
of landmark objects, each which have known dimensions and appearance, from perceived blob features.
Thus the estimated distance to a landmark will be based on the dimensions of the associated blob(s) as seen
through the robot’s blobfinder. It is necessary to record the blob measurements for each landmark (pink
fiducial, green/orange fiducial, orange/green fiducial, green goal and orange goal) in order to localize within
the environment. If you choose to perform localization on the ball’s location, then it is also necessary to
measure blob dimensions for the yellow ball.
To estimate the range from your robot to a landmark, place each landmark at varying distances from the
robot and record features (e.g., height, width, area) of the perceived blob(s) corresponding to the ob ject,
multiple times at each distance. You should record distances starting at 0 cm, or the closest the robot can
see an object, to at least the entire length of the FC148 field. The result is a set of example input-output
pairs that relate blob features to distance, as seen in Table 1. Note that measurements at far distances will
vary only slightly and may become difficult to distinguish an accurate distance based on blob size.
1/course/cs148/pub/measurement model tutorial.pdf
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