Fractional-order SMC controller for mobile robot trajectory tracking under actuator fault

Figures & data

Figure 1. Wheeled mobile robot with two independent driving wheels.

Figure 2. Overall control block diagram.

Figure 3. Robot posture error coordinates scheme.

Table 1. Controller parameters.

	parameters
Kinematics controller	$k_1=5,k_2=5,k_3=5$
Dynamic controller	$\lambda \text{ = diag(10,10), }{K}_1\text{ = diag(4,4)},K_2=diag(2,0.5),\alpha =0.5,\epsilon =1$

Figure 4. Robot following circle shape trajectory.

Figure 5. Fault observation performance.

Table 2. X-axis tracking performance indicators.

	$x_e$
Performance index	ISMC	ISMC + ERA	ISMC + STA	FOSMC + STA
ISE	0.1453	0.03325	0.06123	0.02961
IAE	1.001	0.1989	0.3859	0.2034
ITAE	12.28	1.075	3.298	1.225

Table 3. Y-axis tracking performance indicators.

	$y_e$
Performance index	ISMC	ISMC + ERA	ISMC + STA	FOSMC + STA
ISE	0.2633	0.09748	0.1475	0.08904
IAE	1.217	0.3892	0.6211	0.3356
ITAE	13.03	1.588	4.036	1.13

Table 4. Reference velocities $v_r$ and ${\omega }_r$ in tracking eight path.

Range	$v_r(m/s)$	${\omega }_r(rad/s)$
$t\ge 0\text{ and }t<9$	0.2	−0.4
$t\ge 9\text{ and }t<22.5$	0.15	0
$t\ge 22.5\text{ and }t<32.65$	0.2	0.4
$t>32.65\text{ and }t<46.15$	0.15	0
$t\ge 46.15$	0.2	−0.4

Figure 6. Robot following the eight-shape trajectory.

Figure 7. Fault observation performance.

Table 5. X-axis tracking performance indicators.

	$x_e$
Performance index	ISMC	ISMC + ERA	ISMC + STA	FOSMC + STA
ISE	0.8772	0.3124	0.3683	0.3353
IAE	5.928	1.66	1.76	1.684
ITAE	159.5	11.78	9.563	8.492

Table 6. Y-axis tracking performance indicators.

	$y_e$
Performance index	ISMC	ISMC + ERA	ISMC + STA	FOSMC + STA
ISE	0.6883	0.3392	0.3614	0.3531
IAE	4.668	1.537	1.562	1.483
ITAE	126.8	10.09	7.484	6.45

Data availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.