part of the snake robot and the
‘x’
axis. RMS denotes
the roots mean square error between the robot part’s position and the
‘x’
axis.
X
L1
stands
for the forward distance towards the
‘x’
axis.
DIST
AVG
RMS
Fitness
1
7
1
2
i
i
L
AVG
RMS
7
7
1
i
i
L
AVG
1
L
X
DIST
106
In the lateral undulation locomotion, this term of the fitness-function must be close to zero.
This fitness-
function defines the “snake robot” behavior for lateral undulation locomotion
tasks. The first term
(RMS)
in the fitness function shows that the robot must keep itself in-
line by moving parallel to the
‘x’
axis. The second term
(AVG)
shows that the robot must
escape from the
‘x’
axis and the 3rd term
(DIST)
in the fitness function shows that the
robot usually don’t move in the frontal direction.
(9-3)
Figure
9-7: Wave generated for lateral undulation
locomotion
Figure
9-6: Snake robot lateral undulation locomotion
X
Y
29
.
3
,
06
.
3
27
.
4
6
.
0
09
.
1
45
.
0
51
.
0
07
.
1
39
.
2
46
.
3
,
17
.
4
18
.
2
33
.
4
89
.
4
85
.
2
44
.
3
79
.
1
01
.
0
8
.
0
I
Tb
Ta
107
After a first generation of 100 chromosomes, the robot learns to move in the lateral
undulation with a corresponding set of CNN templates, which are obtained by the
evolution method. These templates are shown in Equation 9-3. A task manager in the high
level can select a best template for performing a specific task by the robot. On the other
hand, each set of templates corresponds to a specific robot movement/locomotion. In
another evaluation we define a fitness function according to Equation 9-4. This function is
defined for robot rectilinear locomotion with a minimum sidle. According to this equation,
each term must be close to zero. The first term
(RMS)
shows that the robot must have a
minimum deviance to the
‘x’
axis. The second term
(AVG)
shows that the robot should not
be away from this axis. The last term
(DIST)
shows that the robot must crawl on the
‘x’
axis.
After each breed, a new chromosome is added to the chromosome population. After
checking of new chromosomes by the fitness function, they will be sorted in a population
list ordered by the best fitness. According to the evolution theory, after many generations,
some chromosomes (“children”) can inherit good properties from others (“parents”) which
are best and fit chromosomes.
After nearly 790 chromosome generations the robot would have learned to move with
the highest speed. With Equation 9-5, the CNN processor can generate a hinge wave
according to Figure 9-8. This wave is optimum for the robot rectilinear locomotion using
an evolution algorithm. Figure 9-9 shows the robot during the simulation in rectilinear
locomotion. Figure 9-10 is the plot of the time evolution of the fitness function obtained
after 790 generation of chromosomes; the robot has learned the best movement and
locomotion. The extension of this architecture or learning method to another kind of robot
is possible. By connecting the CNN outputs to unknown/arbitrary robot actuators, the
robot can learn any locomotion. Due to the high capacity of CNN, we can connect the CNN
output to the robot hinges actuators by any arrangement and structure. The results are
same although both learning and optimization times might change.
(9-4)
DIST
AVG
RMS
Fitness
1
|
