IEEE Robotics & Automation Magazine - September 2019 - 45

Optimizing Network Structure
Depending on parameters such as neuron number, layer depth,
size of training data set, and so on, the evaluation of a single
instantiated neural network may be quite costly in terms of
computation time. The approach of Snoek et al., termed Bayesian optimization, provides efficient hyperparameter optimization, thereby lowering the overall cost of producing an efficient
model configuration [32]. In this article, the optimization of the
LSTM network (see the "LSTM" section) was focused on the
number of LSTM blocks in a single layer as well as the learning
rate, the two most important parameters according to [33]. A
range of 10 to 200 was selected for the number of blocks, and a
range of 10 -5 to 10 -1 was selected for the learning rate. The
cost function returned the mean square error (MSE) of the validation samples (10% of the total number of samples used for
training), which provided a means of quantifying the expected
performance of the network. Together with the input selection
stage, the number of parameters in need of tuning has now
been limited to those required for setting the threshold for the
input selection and the upper/lower values of the range in
which hyperparameter optimization is performed.
Simulation Results
We propose using a data-based model, described in the
"LSTM" section, to model the relationship between various
inputs and the predicted linear vessel frame-relative velocities at the next time step. To assess the performance and the
validity of this method, we compare it to two other models:
● KF: Linearized equations of motion are obtained for the
vessel by rotating the position measurements to a vesselparallel coordinate system at each time step. This facilitates
the use of a linear KF observer model for the DP test case
described in this article [34].
● Single-layer feedforward neural network (SLFN): This represents the most basic structure among neural networks used
for regression.
In the case of the KF, we coast through the outage using the
thruster command, wind velocity, and wind angle as inputs.
These measurements are fed to the mathematical model of the
vessel. The individually learned predictive models of the two
machine-learning methods replace the explicit vessel model.
The machine-learning DR methods do not use the vessel
model or sensors to measure the displacement of the vessel.
Vessel and Environment Description
All experiments were conducted in a commercial simulator,
developed by the Norwegian company Offshore Simulator
Centre AS. It features a simulated environment in which a
user may manipulate the wind, waves, and ocean current to
mimic real-life conditions and offers a library of virtual vessels to choose from. For these experiments, a multipurpose
offshore vessel was selected. Table 3 provides its main
dimensions, and Figure 5 shows a view of the simulated
environment with the selected vessel engaged in a DP operation close to a static rig. For the specific simulation study
performed in this article, varying environmental parameters

were applied. The direction of the environmental disturbances is incremented at intervals of 30° from 0° to 360°, relative to the vessel frame. At each fixed direction, a set of
wind and wave magnitudes was applied consecutively, causing increasingly severe weather conditions. Table 4 shows
the wind and wave magnitudes for each of the distinct conditions faced by the vessel at the directions previously specified. A specific weather condition is determined by the
direction of the wind and waves along with their respective
magnitudes. In this test set, each weather condition has a
duration of 14 min; the first 7 min involve a change of both
wind and wave magnitude from the previous weather condition. If all conditions have been run for a single direction,
this period involves a linear transition from one weather
direction to the next one. The entire simulation test set
spans approximately 15 h of vessel maneuvering. The actual
run time is reduced by running the simulation five times
faster than the real time.
A 3-DoF DP controller is applied to perform station
keeping. The controller applies a single PID controller in
each DoF, and the output of the motion controller connects
to a basic generalized inverse-control allocator for distribution of the generalized force vector into individual thruster
commands. Figure 6 shows how the true position compares
to the position with measurement noise added (see the
"Measurement Noise" section). The latter is the raw position output by the dGNSS system when it is operating normally. The noiseless position signal is not used for any
purpose other than visualization.
KF Parameters
A KF was implemented for comparison to a conventional DR
method. It requires model-dependent matrices in addition to
tuning parameters. We list the applied tuning parameters
along with the matrices describing the mass and damping of
the simulated vessel in the following:

Table 3. The dimensions of the simulated vessel.
Description

Value

Length between perpendiculars (Lpp)

82.7 m

Breadth

23.1 m

Displacement

10,180 × 103 kg

Table 4. The parameters of the sea states
simulated at each discrete weather direction.
Significant Wave Height (Hs)

Wind Velocity

2 m/s

4 m/s

7 m/s

11 m/s

SEPTEMBER 2019

IEEE ROBOTICS & AUTOMATION MAGAZINE

IEEE Robotics & Automation Magazine - September 2019

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