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Page 12 of 14 Ma et al. Complex Eng Syst 2023;3:10 I http://dx.doi.org/10.20517/ces.2023.14

0.3 25
-3 5
10
2 20 0
0.15 0 -5
-2 15 30 31 32
30 31 32
0 10
5
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30 31 32 20
0
10
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0 20 40 60 80 100 0 20 40 60 80 100
Figure 4. Comparative results of sliding mode surfaces in the experi- Figure 5. Comparative results of control torques in the experiment.
ment.

0.8 0.4
0.04
0
0.4 -0.04
30 31 32 0
0
0.06
-0.4 -0.4 0
0 20 40 60 80 100 -0.06
30 31 32
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0
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-0.02
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0.06
0 0
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30 31 32
0 -0.05
-0.2
0 20 40 60 80 100 -0.1
0 20 40 60 80 100
Figure 6. Comparative results of tracking errors , , in the experi- Figure 7. Disturbance estimation ˆ 1 and ˆ 2 in the experiment.
ment.
a trajectory tracking mission for the WMR, and guarantee the tracking error converges within a fixed time.
Finally, the proposed control approach has been verified by a mobile robotic platform, and the experimental
results show fine control performances. Our future work will focus on how to realize the formation tracking
control of multi-wheeled mobile robots in both theory and experiment.

DECLARATIONS
Acknowledgments
The authors would like to thank the editors and reviewers for their valuable comments dedicated to this article.

Authors’ contributions
Made significant contributions in writing, methodology, review: Li B
Executed writing-original draft, experiment verification: Ma L
Methodology validation: Wang C