IEEE Robotics & Automation Magazine - September 2015 - 69

7

i2 (Half-Periods)

6

2

5
1.5

4
3

1

2
0.5
1
(a)
0

0

5

10

15

20

25

30

35

0

i1 (Amplitude)
(a)

3
2.5
2
1.5
1
0.5
0
6

4
i2

2

0 0

10

20

30
(b)

i1

(b)
Figure 4. An area index. (a) The heatmap. (b) The Kriging
reconstruction.

located in areas of the design space where there are high values
of the parameters. In fact, for sinusoidal paths, high values represent the limit capability of a vehicle performing the path-following task. However, it is clear that different performances
have been measured, simply comparing the worst performance values achieved for the area index in (10, 7) with {(25,
5), (30, 5), (35, 5)}, design points that, on the contrary, lead to
higher values for the Hausdorff distance. This highlights the
complementary information gathered from different performance indices and the importance of defining and exploiting
more performance indices and a suitable compound index.
The problem of predicting output at unverified parameter
sets is addressed by a classical Kriging reconstruction of a suitable portion of the parameter space. Such a reconstruction is
computed on a 50 # 50 grid starting from the performance
indices computed on 44 design points: the performance value
corresponding to the line i = ^0, 0h is also assigned to the sets
of design points "^0, ih, i = 1, f, 7 , and "^i, 0 h, i =
5, f, 35 , . A classical algorithm with a Gaussian correlation
model and maximum likelihood estimation for its parameters
has been adopted (see [19]) and the best linear unbiased predictor for the regression model, the one that minimizes the
variance of the prediction error, is chosen. Figures 3(b) and

Figure 5. The CNR-ISSIA vehicles employed in the test campaign.
(a) The Charlie USV is 2.40 m # 1.70 m, and it weighs about
250 kg. (b) The Shark is 0.90 m # 0.75 m, it is 0.60-m high, and
it weighs about 40 kg. (Photos courtesy of CNR-ISSIA.)

4(b) report the reconstructions for both Hausdorff and area
indices and the black lines show that i 2 was set as a discrete
parameter in the beginning. It is worth noticing that due to a
restricted number of experiments that can be executed in simulations and, especially, at sea, prediction is the main tool for
assessing the performance of a vehicle performing experiments when a class of paths is chosen. Significant changes in
the predicted values are not expected when varying the regression model, but further investigations on the sensitivity to the
model are planned to validate this assumption.
Experiments with DeepRuler
Real experiments employing DeepRuler were performed in
the Canale di calma di Pra, Genova, Italy, using two different
National Research Council of Italy-Institute of Intelligent
Systems for Automation (CNR-ISSIA) vessels: 1) the Charlie
USV and 2) the Shark unmanned semisubmersible vehicle
(USSV). Both robots are shown in Figure 5.
The two vehicles were required to perform path-following
experiments on sinusoidal paths which differed in amplitude.
For each vehicle, the experiment parameters, i.e., the working
area, the robot feedback structure (containing the variables
needed to compute the selected metrics), and the features of
September 2015

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Table of Contents for the Digital Edition of IEEE Robotics & Automation Magazine - September 2015
