IEEE Robotics & Automation Magazine - March 2012 - 68

Results
Second Round
Third Round
Fourth Round

5 m Boundary
Target Triangle
First Round
100

Wind Direction
3

Northing (m)

80
60
2
40
20

0
−20

100

40
60
Easting (m)
(a)

100

120

100

120

Wind Direction
3

80
Northing (m)

60
2
40
20

0
−20

40
60
Easting (m)
(b)

0°
330°

30°

300°

60°

270°

90°

120°
3

240°
1
150°

210°
180°
(c)
Wind

Edge 2

Edge 1

Edge 3

Figure 6. A comparison of the traveled path tracked by (a) GPS
and (b) theodolite measurements. In the third plot (c) compass
data are depicted in comparison to the target headings of the
triangle edges. The boat traveled in clockwise direction.

measurements with respect to position and allows the
comparison of transect data sets over time. Examples of
the data collected during the transect missions are presented in the "Analysis of Sampled Data Sets" section.
68

IEEE ROBOTICS & AUTOMATION MAGAZINE

MARCH 2012

Controller Dynamics
The performance of the line-following controller was
evaluated experimentally. The data set was recorded
while the ASV traveled along a predefined equilateral triangle of 100-m side length for a total of four rounds. During this test, the line-following controller was utilized as
presented in the "Software Design" section. The target
velocity was set to 0.7 m/s for all rounds, i.e., the speed
used during the transect sampling missions. The three
corner points of the triangle shown in Figure 6 define
lines that were sent to the line-following controller. The
target triangle and the traveled path of the boat can be
seen in Figure 6(a).
From the plotted data, it is evident that the controller
converges to the desired line. The stability of the controller
was proved by Samson and Ait-Abderrahim [23]. The
plotted data shows smooth and quick transitions between
different segments of the path. While the boat is rotating
on the spot (i.e., on all three corners of the triangle) to
point toward the new target point, the position is not
actively controlled and thus the boat drifts due to wind.
Table 1 shows the average distance and the standard deviation from the target lines of the triangle accumulated over
the four rounds.
In addition to the internal GPS measurements, an external system has been used to track the boat position. A
laser-based theodolite by Leica (TS15) capable of tracking
a prism to a distance of up to 2 km with an accuracy of
4.5 mm has been set up at the shore as an external positioning system. A calibration procedure has been applied
to estimate the transformation from the local frame of the
theodolite to the global reference frame. It is based on the
libpointmatch library [24] that implements an iterative
closest point (ICP) algorithm.
Figure 6(a) and (b) show the recordings of the GPS
locations and the theodolite measurements, respectively.
From the theodolite measurements, it can be seen that the
desired path is achieved, despite the noise on the GPS signals. Furthermore, the plots show a 5-m boundary area
that the boat should not leave to achieve the desired precision for the biological sampling missions. The GPS
measurements show an RMS error of 1.29 m with respect
to the theodolite measurements. It is important to note

*
Table 1. Average lateral error from target lines
and the corresponding standard deviation.
Triangle Side

Average
Error (m)

Standard
Deviation (m)

First triangle edge

0.62

1.49

Second triangle edge

0.04

1.98

Third triangle edge

À1.63

2.69

Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - March 2012