IEEE Robotics & Automation Magazine - March 2012 - 69

Speed (m/s)

Depth (m)

Drag Angle (°)

Error (m/s)

that this value depends on the ICP
0.4
procedure that is used to estimate
the transformation between the
0.2
theodolite and GPS measurements.
0
During the test, strong winds
−0.2
blew (average speed: 5 m/s with gusts
of up to 15 m/s). The wind measure−0.4
1
2
3
4
5
6
7
8
9
10
11
12
ments were not acquired online on
Line Segment
the boat, but were available from a
meteorological station close by. The
7. Errors of the measured speed of the boat with respect to the desired target
plot in Figure 6(c) shows the target Figure
speed (0.7 m/s). The speed measurements are provided by the GPS device.
heading along each of the three edges
(solid arrows) and the mean of the
compass measurements (dashed arrows). The shaded areas between different depth levels, the boat stopped, causing a
depict a band Æ3 times the standard deviation. The black transient phase until the desired speed level has been
arrow shows the direction of the wind. Especially on the reached for the next section of the test. The gray areas indiedges 1 and 2, it can be seen that the boat was compensating cate the steady-state phases from which the data have been
for the perturbation caused by wind. The mean heading of extracted for further analysis. To estimate the drag in the
the boat is approximately 10° off from the target heading.
horizontal direction and the drag angle from these meaAlong with the accuracy of the line-following controller, surements, the following equations provide the worst-case
the speed controller has also been evaluated. Figure 7 indi- estimate in which the cable is assumed to be a straight line:
cates the deviation of the actual speed from the target

pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
speed during the triangle test. The numbering of the line
d
2 À d2 ,
:
a
¼
arccos
dx
¼
l
segments corresponds to the chronology of the three edges
l
of the triangle during the four rounds. The box plot shows
The displacement of the probe in the horizontal directhat the median of the speed values is very close to the
desired target value. The large amount of outliers is due to tion with respect to the boat is denoted by dx, l correthe noise level of the speed readings that are provided by sponds to the cable length, d is the depth measured by the
probe, and a denotes the estimated drag angle.
the GPS device.
Table 2 shows the resulting mean values for the four
This evaluation shows that our ASV is capable of very
accurate GPS waypoint navigation in the presence of high steady-state phases that are indicated in Figure 8. From
external perturbations. On the spot, rotations enable these results, several conclusions can be drawn. First, the
smooth transitions between consecutive segments of the expected dependency of the drag behavior on the cable
length evidently occurs. Second, the results showed propath, even if they differ largely in direction.
vide a simple model to estimate a worst-case estimate of
the drag in the horizontal direction, which enables the
Probe Localization
The laboratory experiment described in the "Probe" section has
25
35
shown that the wing configuration
20
28
of the probe support structure sig15
21
nificantly decreases the drag angle.
However, these tests were restricted
10
14
to a cable length of 1 m due to the
5
7
depth of the water channel. To eval0
0
(a)
0.8
uate the drag behavior when using
0.6
longer cable lengths, we have done a
0.4
0.2
series of tests in the lake. Figure 8
0
shows an example of the recorded
0
100
200
300
400
500
600
data. The upper part of the plot
Time (s)
(b)
compares the measured depth of the
probe and the corresponding length
Steady State
Cable Length
Drag Angle
of the cable. The lower plot indicates
Probe Depth
Boat Speed
the speed of the boat when sailing
along a straight line. The target
Figure 8. (a) shows a comparison of cable length and the depth measured by the probe.
speed for the controller has been set (b) shows the travel speed of the boat (GPS measurements). The gray areas indicate the
to 0.6 m/s. During transition steady-state phases.
MARCH 2012

IEEE ROBOTICS & AUTOMATION MAGAZINE

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