LECTURE 6

Segment-based Localization

Position Measurement Systems

The problem of Mobile Robot Navigation:Where am I?Where am I going?How should I get there?

Perhaps the most important result from surveying the vast body of literature on mobile robot positioning is that to date there is no truly elegant solution for the problem (Johann Borenstien, UMich Ann Arbor). The many partial solutions can roughly be categorized into two groups: relative and absolute position measurements.

Classification of Localization Methods

Relative Odometry: Uses encoders to measure wheel rotation. Is

self contained and is ever ready to provide the vehicle with an estimate of position. Position error grows out of bound

Inertial Navigation: Uses gyroscopes and accelerometers to measure rates of rotation and acceleration. Self contained. Unsuitable for accurate positioning over extended periods of time. High manufacturing and equipment cost.

Classification of Localization Methods

Absolute Active Beacons: Computes the absolute position of the robot by

measuring the direction of incidence of three or more actively transmitted beacons

Artificial Landmark Recognition: Distinctive landmarks placed in known locations. Errors are bounded. Computationally intensive and raises questions for persistent real-time position updates

Today’s Lecture

Classification of Data Points: How do you classify the newly obtained data point to the segments already present in the map

Weighted correction vector: Having classified the data points to segments how to obtain the corrected position of the robot

Quality Measures: Performance evaluate the obtained corrected position. i.e. how correct/probable is the corrected position

Orientation Correction: Having obtained the corrected position is it possible to obtain the correct orientation of the robot

Classification of Data Points

Under the assumption of small position error data points will not usually be too far away from the objects they represent

The target line segment of each point is that segment to which the point is closest in an Euclidean sense

The closest distance is computed by taking the minimum of the distance of the point to the two end-points of the target segment and the perpendicular distance if the perpendicular distance falls between the two endpoints of the line

Weighted Correction of the Image Points to the Target

Let xi, yi be the displacement between the image point and the point resulting from its perpendicular projection onto the infinite line passing through the line segment

Then

di is the distance between the ith range data point and its target segment computed in the manner specified in previous slide. The sigmoid function introduces a soft non-linearity by ensuring that points close to the target segments have a greater voting strength

c(t) = c(0)(1-t/T). In other words the value of c decreases as iterations proceed and less and less points are brought into the correction vector estimate

n

ii

n

iii

dw

xdw

X

1

1

)(

)(

n

ii

n

iii

dw

ydw

Y

1

1

)(

)(

mm

m

cd

ddw

1)(

Weighted Correction of the Image Points to the Target

Then xc = xuc + X, yc = yuc + Y, where xc, xuc the corrected and uncorrected x component of the robot’s position

If the target segments are parallel to one of the two axes of the coordinate frame then the position correction can only be done along the other orthogonal direction. This is called the hallway effect. In other words if the target segment is parallel to x axis then position correction can occur only along y and vice-versa

Quality Measures

How correct are our corrections? The mean-squared error measure: Emse = dist(pi,li)2/n, where

pi is the ith range data point and li is its corresponding target segment and dist is the closest distance between the two

Global minimum of the function occurs at the true position of the robot. Hence higher Emse lesser is the probability that the corrected position is the true position.

Emse is susceptible to outliers

Quality Measures

Classification Factor:

Here c is the neighborhood size, m = 2 is the steepness of the sigmoid, d=dist(pi,li).Higher the classification factor, higher is the probability that the corrected position represents the true position of the robot.

n

imm

m

cfcd

d

nE

1

)1(1

Classification factor peaks at the true position of the robot

Quality Measures Ecf is not a useful measure for comparing two robot’s

positions which are close to one another for their accuracy. Emse does not suffer from this

Hence a combination of both of the form called comparative quantity is used as:

bmse

acf

cqmE

EE

Reference: http://www.cim.mcgill.ca/~mrl/publications.html

“Precise positioning using model based maps”, 1994, IEEE ICRA