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Ma et al. Complex Eng Syst 2023;3:10 I http://dx.doi.org/10.20517/ces.2023.14 Page 11 of 14

Figure 2. The Quanser QBot 2e Mobile Robot Platform.

1.5

1

0.5
0.54

0
0.5
0.8 0.85 0.9
-0.5

-1

-1.5
-1.5 -1 -0.5 0 0.5 1 1.5

Figure 3. The comparative trajectory tracking experiment results of the WMR. WMR: wheeled mobile robot.

It is obvious that the WMR trajectory tracking mission can be achieved by the designed control method as
plotted in the red track in Figure 3. The time response curves of the sliding mode surfaces, 1 and 2, are
shown in Figure 4, which converge very quickly. To illustrate the excellence of the proposed control method, a
comparative experiment on the trajectory tracking of WMRs is conducted between this work and reference [26] .
The control inputs of the designed control scheme and reference are shown in Figure 5, which are nonsingular
and continuous. Figure 6 illustrates the tracking errors in this experiment, which have a big fluctuation due to
the influence of external disturbances. In the experiment, the external disturbance is from the experimental
environment, such as uneven ground. The observed disturbance values are shown in Figure 7, which indicates
the effectiveness of the proposed disturbance observer in this work. From the experimental results, it can
be concluded that the designed control scheme has the robustness against the external disturbance and high
tracking accuracy.

5. DISCUSSION
In this paper, a universal control scheme for fixed-time trajectory tracking based on ISMC is put forward.
The dynamic model of the WMR has been transformed into two error subsystems. Then utilizing the fixed-
time technology and ISMC, a new fixed-time disturbance observer has been proposed and applied on the two
error subsystems. Furthermore, an observer-based tracking control method has been proposed to achieve