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to the scientific community. JEAF contains a collection of libraries that provide
all the basic functionalities of the evolutionary algorithm, represented in the
figure with the block Operators. Outside JEAF we have developed a decoding
library and a simulation library. For the purpose of obtaining the fitness value
for the different configurations, the modular robots are simulated using Gazebo
due to its real dynamics coverage. Detailed realistic models of the four types of
modules established in the previous sections have been produced for these simu-
lation. The decoding library is in charge of transforming the tree representation
of an individual to a robotic unit in Gazebo, where it is run for a fixed number of
steps, returning the selected fitness measure to the algorithm. In this version, the
control is completely distributed over themodules,andthetreerepresentation
of each individual contains the control parameters of each module that make the
robot act in the simulator.
4 Experiments
The evolutionary design system has been tested in a classical problem for mod-
ular systems: obtaining a robot able to cover the maximum distance across a
flat surface [9] [10]. To this end, we have used the following actuator modules:
telescopic, slider, rotational (axis) and rotational (hinge). In addition, we use a
rectangular base module as an initial structure.
In this experiment, to reduce the dimensionality of the search space, the con-
trol adjustment consists in obtaining the optimal offset of the sinusoidal signal
that controls each module, being the frequency and amplitude fixed. The robots
are placed in the Gazebo simulated environment with, at least, one module in
contact with the ground and each morphology is simulated during four cycles of
the sinusoidal control signals. The fitness is calculated as the distance travelled
in the X direction minus the absolute distance travelled in the Y direction. This
way, we are rewarding the robotic unit that covers the maximum distance in a
straight line without lateral displacement. It must be remembered that we are
using a real dynamics simulation, and, consequently, unstable morphologies will
obtain poor results. Related with this, to avoid the effects of robot instability
in the first cycle when it is placed on the ground, we have excluded the first
movement from the fitness calculation.
As commented in the previous section, the modules were designed in Gazebo
in order to have realistic parameters and to be physically reproducible. The
weight of the base, slider and telescopic modules is 400 g and their actuators
have a force of 20 N, while the weight of the rotational modules is 200 g and
their actuators' torque is 2 Nm. All of the modules have a friction coecient of
0.8. The base has 12 connection ports: 4 on the top side corner, 4 on the bottom
side corner, two on one end of the right side (parallel to the X axis) and two
more on the opposite side. The slider module has two connection bays on its
ends with five connection ports each and four connection ports on the mobile
part. The telescopic and the rotational modules have two bays in their ends with
five connections each. Finally, the hinge module has two connectors.
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