Page 48 - Read Online

Ortiz et al. Intell Robot 2021;1(2):131-50 I http://dx.doi.org/10.20517/ir.2021.09 Page 141

Using Equation (42), we have

∗
( +1 ) ≤ ( ≠ ∀0 < ≤ )(1 − )
∗ 2
≤ ( ≠ ∀0 < ≤ ( − 1) )(1 − )
∗ ∗
≤ ( ≠ ∀0 < ≤ 0) ( ≠ ∀0 < ≤ )(1 − )
1
= (1 − )
where ( ≠ ∀0 < ≤ 0) = 1, then
∗

1
lim ( +1 ) ≤ lim (1 − )
→∞ →∞

= 1 lim (1 − ) = 0

→∞
Since 0 < ≤ 1, the algorithm converges exponentially to in: population size and iteration number .
∗
The algorithm of the SLAM-based roadmap GA for the path planning is as follows.

SLAM based roadmap GA. (1) Initiate population randomly ( ) of size that belong in set . (2) The
fitness value is with Euclidean distance for each chromosome . (3) The population is from lower to
higher fitness: ( 1 ) ≥ ( 2 ) ≥ · · · ≥ ( ). (4) Crossing set in the chromosomes, ∩ → , .
(5) Next population ( + 1) is replaced by the chromosomes with poor skills. (6) Random mutation with
poor skills. (7) Go to Step (2)

4. AUTONOMOUS NAVIGATION
Our AN uses both sliding mode SLAM (Algorithm 1) and the roadmap GA method (Algorithm 2). The
autonomous navigation algorithm is:

Autonomous navigation. The initial state , the target = ( 1 ), = ( 2 ) =
+
−
gain sliding mode, = search radius =search_obstacles( , ) = Path_Planning( , , ) 0 =
Controller( , ) while ≠
− +
ˆ
, = _ , , , , , ,

ˆ
= (end state) ( : ℎ( )) = [
] =Path_Planning( , , ) if > = ( , , , )
ˆ
end if; +1 = Controller( , ) end while return ,
The PP needs the map, robot position, and target. This information is given by the sliding mode SLAM algo-
rithm. When the algorithm falls into a local solution, we use the function to provide
another which is outside the local zone.

5. COMPARISONS

Inthis section, we use several examples to compare our method with the three other recent methods: the polar
histogram method for path planning [50] , the grid method for path planning [51] , and SLAM with extended
Kalman filter [52] .