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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 147

8

6 14
15
27 16
31 28
26
4
30 23
5
25 18
y (m) 2 2 21 19 11 17
24
3 20
4
0 22 1
7 13 12
29
-2 9 10
6
8
-4
-5 0 5 10 15 20
x (m)
Figure 13. Results of extended Kalman filter simultaneous localization and mapping with noises.

8

6 10
11
12
4 22
24 21
y (m) 2 23 18 2 13
15 6
7
0 1 20
16
14
9
17 19
-2 8
5
3 4
-4
-5 0 5 10 15 20
x (m)
Figure 14. Results of sliding mode simultaneous localization and mapping with noise.

Figure 14 shows the results with SM-SLAM. Under the same bounded noises, SM-SLAM works very well,
because of the sliding mode technique.

To compare the errors, we define the average of the Euclidean errors as

q
1 Õ 1 Õ
∗ 2
∗ 2
= ( − ) + ( − ) , = − ∗ (46)

=1 =1
where is the data number; , , and are real values for robot position and orientation; and , , and
∗
∗
∗

are estimations of them. Figure 15 shows the errors of EKF-SLAM and sliding mode SLAM. Obviously,
the errors of EKF-SLAM increase quickly. Robots have better estimation in long distances with sliding mode
SLAM.