Biomedical Engineering Reference
In-Depth Information
For example, the string
{joint(1) [joint(1) forward(1)] clockwise(2)}(3)
produces the robot
in Figure 4.6b, through the development process shown in Figure 6a. Constructed robots do not
have a central controller; rather each joint oscillates independent of the others. In Figure 4.6
large crosses are used to show the location of actuated joints and small crosses show unactuated
joints. The left image shows the robot with all actuated joints in their starting orientation and
the image on the right shows the same robot with all actuated joints at the other extreme of their
actuation cycle. In this example, all actuated joints are moving in phase.
These strings were generated using an L-system. The L-systems are a set of rules like the
'' A
!
B'' and ''B
!
AB'' rules discussed above. However, this time these ''rewrite'' rules are
parametric (i.e., may pass parameters), and have conditions (are executed only when the parameters
meet some conditions).
For example, the L-system to produce the robot in Figure 4.6b consists of two rules with each
rule containing two condition-successor pairs:
P0(
n
):
n
>
2
!
{P0(
n
1)}(
n
)
n
>
0
!
joint
(1) P1(
n
2)
clockwise
(2)
P1(
n
):
n
>
2
!
[P1(
n/
4)]
n
>
0
!
joint
(1)
forward
(1)
If the L-system is started with P0(3), the resulting sequence of strings is produced:
P0(3)
{P0(2)}(3)
{joint(1) P1(4) clockwise(2)}(3)
{joint(1) [P1(1)] clockwise(2)}(3)
{joint(1) [joint(1) forward(1)] clockwise(2)}(3)
which produces the robot in Figure 4.6b.
An evolutionary algorithm was used to evolve individual L-systems, that when executed
produced a build sequence which produced the machine. Approximately half the runs produced
''interesting'' viable results. The two main forms of locomotion found used one or more oscillating
appendages to push along, or had two main body parts connected by a sequence of rods that
twisted in such a way that first one half of the robot would rotate forward, then the other. Some
examples of successful machines are shown in Figure 4.6c and their physical instantiations are
shown in Figure 4.6d.
A comparison of robots evolved using the developmental encoding to robots whose construction
sequence was evolved directly revealed that robots evolved with the generative representation not
only had higher average fitness, but also tended to move in a more continuous manner. In general,
robots evolved using the generative representation increased their speed by repeating rolling
segments to smoothen out their gaits, and increasing the size of these segments or appendages to
increase the distance moved in each oscillation.
One of the fundamental questions is whether the actual grammar evolved in the successful
L-systems has captured some of the intrinsic properties of the design space. A way to quantify this
is to measure the correlation between fitness change and a random mutation of various sizes, and
compare this with the correlation observed in random mutations on the nongenerative represen-
tation as a control experiment. If the observed correlation is distinguishable and better for the
generative system than it is for the blind system, then the generative system must have captured
some useful properties.
The plot in Figure 4.6e is a comparison of the fitness-mutation correlation between a generative
representation and a random control experiment on the same substrate and on the same set of
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