Fuzzy Super-twisting Second Order Sliding Mode Trajectory Tracking Control for Robotic Manipulator

doi:10.16182/j.issn1004731x.joss.21-0066

Abstract

Abstract:

A fuzzy super-twisting second order sliding mode control method is proposed for the uncertainties of the model error and external disturbance on the trajectory tracking accuracy of robotic manipulator. Based on the dynamic model of the robotic, a new non-singular terminal sliding mode manifold is designed, and an improved super-twisting algorithm is used to design the second order sliding mode controller. In order to solve the problem that the matching disturbance can only be compensated under the condition of the known disturbance boundary in the sliding mode control, the fuzzy logic algorithm is used to carryout the online compensation for uncertainty of the system. The stability of the closed-loop control system is guaranteed by Lyapunov theory. The simulation and experiment results show that the proposed controller can track the trajectory accurately under the uncertainty of the robotic and can effectively suppress the chattering phenomenon of the system.

Key words: second order sliding mode control, fuzzy reasoning algorithm, uncertain robotic manipulator, trajectory tracking

CLC Number:

TP273

Baolin Du, Dachang Zhu, Yihua Pan. Fuzzy Super-twisting Second Order Sliding Mode Trajectory Tracking Control for Robotic Manipulator[J]. Journal of System Simulation, 2022, 34(6): 1343-1352.

Figures/Tables 13

Table 1

Fuzzy control rules

$s$	$s ˙$
$s$	NB	NM	ZO	PM	PB
NB	PB	PB	PB	PM	ZO
NM	PB	PM	PM	ZO	NM
ZO	PM	PM	ZO	NM	NM
PM	PM	ZO	NM	NM	NM
PB	ZO	NM	NB	NB	NB

Table 1

Fig. 1

Fig. 2

Table 2

Model parameters of 3 DoF Robotic manipulator

连杆	质量 $m i$ /kg	长度 $L i$ /m	质心距离 $r i$ /m	惯量 $I i$ /(kg·m²)
1	1.50	0	0	0.35
2	1.50	0.20	0.10	0.30
3	1.00	0.20	0.10	0.30

Table 2

Fig. 3

Fig. 4

Fig. 5

Table 3

Performance parameters for each controller

性能指标	PID	NTSMC	本文方法
关节1跟踪误差 $\| \| e 1 \| \| R M S$ /rad	0.021 7	0.018 4	0.008 8
关节2跟踪误差 $\| \| e 2 \| \| R M S$ /rad	0.035 2	0.021 0	0.013 0
关节3跟踪误差 $\| \| e 3 \| \| R M S$ /rad	0.029 6	0.023 8	0.014 4
关节1输出力矩 $\| \| τ 1 \| \| R M S$ /(N·m)	0.617 9	4.268 3	1.258 7
关节2输出力矩 $\| \| τ 2 \| \| R M S$ /(N·m)	4.655 8	5.923 9	3.400 7
关节3输出力矩 $\| \| τ 3 \| \| R M S$ /(N·m)	1.710 3	2.743 5	1.290 8

Table 3

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Table 4

Performance parameters for each controller (under experimental conditions)

控制器	PID	NTSMC	本文方法
关节1跟踪误差 $\| \| e 1 \| \| R M S$ /rad	0.022 8	0.020 3	0.009 1
关节2跟踪误差 $\| \| e 1 \| \| R M S$ /rad	0.035 9	0.025 7	0.013 2
关节1输出力矩 $\| \| τ 1 \| \| R M S$ /(N·m)	1.163 8	1.802 5	1.169 6
关节2输出力矩 $\| \| τ 2 \| \| R M S$ /(N·m)	4.211 0	4.828 3	4.321 9

Table 4

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