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Ortiz et al. Intell Robot 2021;1(2):131-50 I http://dx.doi.org/10.20517/ir.2021.09 Page 143

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SLAM
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unknow
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Figure 5. Sliding mode simultaneous localization and mapping and genetic algorithm in complete unknown environment.
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Figure 6. Polar histogram method in complete unknown environments.
until the target point was reached the results obtained are shown in Figure 5. When we used the polar
histogram method for path planning [50] , only the local solutions could be found [Figure 6].
Now, we compare the path lengths with the polar histogram method. The following density of the obstacles
give the navigation complexity. The environment is free of obstacles when = 0. The whole environment
is occupied by the obstacles when = 1. The index for the trajectory error is
ℎ − ℎ
= (43)
100
We use the averages of the path length. The obstacles density is defined as
Í
( )
∈
= (44)
k k
The path length is defined as
ℎ
= (45)
ℎ
The averages of the path lengths of our RA and the polar histogram are shown in Figure 7. When the density