Composite Error-Based Intelligent Adaptive Sliding Mode Control for Uncertain Bilaterally Symmetrical Hybrid Robot with Variational Desired Trajectories
Abstract
:Featured Application
Abstract
1. Introduction
2. Dynamic Modeling and Problem Formulation
2.1. Robot Description
2.2. Dynamic Modeling
2.3. Problem Formulation
- A.
- The tracking errors of UBSHR’s active joints are defined as follows:
- B.
- The tracking errors of UBSHR’s end-effector are defined as follows:
3. Controller Design
3.1. The Design of CE-SOSMC
3.2. The Design of SC-AFNN
3.2.1. Fuzzy Rules Generation
3.2.2. SC-AFNN Construction
- (1)
- ;
- (2)
- , when ;
- (3)
- , when .
4. Simulations
4.1. Case 1
4.2. Case 2
5. System Experiments
5.1. Control System Construction
5.2. Experimental Results
6. Conclusions
- (1)
- A novel composite error considering the synchronization errors and tracking errors of a UBSHR’s end-effector was defined. The CE-SOSMC was realized combined with the SOSMC method to solve the uncertainty problem and the synchronization problem simultaneously. The relationship of asymptotic convergence among the novel composite error, tracking errors, and synchronization errors was stated. Strict theoretical proof of the stability of CE-SOSMC was presented.
- (2)
- AFNN was introduced, and subtractive clustering in conjunction with evolutionary algorithm was applied for constructing fuzzy rule base with fewer rules automatically. Based on the fuzzy rule base, the SC-AFNN was further constructed to realize self-learning and self-adjusting of control rules and control parameters to conquer the flexible control problem of active adaption to different technological requirements without artificially adjusting the control parameters or switching the hardware system. The asymptotic stability of SC-AFNN was analyzed.
- (3)
- Compared with the existing synchronization error, the defined composite error could ensure the synchronization performance not only of active joints but also of the end-effector. Compared with the existing SMC method based on linear sliding mode surface, the presented SOSMC method possesses superiorities such as small chattering, non-singularity, and fast convergence rate. Compared with the existing control methods for systems with definite desired trajectories, the proposed SC-AFNN can track variational desired trajectories for hybrid robots.
- (4)
- Simulation and experimental researches were carried out to further validate the validity of the developed SC-AFNN method.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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CE-SMC | SC-AFNN | ||
---|---|---|---|
Steady-state reaching time | z (s) | 1.24 | 0.38 |
(s) | 1.26 | 1.04 | |
Maximum tracking error | z ( m) | 5.18 | 2.20 |
( rad) | 6.55 | 3.08 |
CE-SOSMC | SC-AFNN | ||
---|---|---|---|
Steady-state reaching time | z (s) | 2.08 | 0.26 |
(s) | 1.36 | 0.72 | |
Maximum tracking error | z ( m) | 72.05 | 14.45 |
( rad) | 14.01 | 7.88 | |
RMSE | - | 0.54 | 0.30 |
Maximum Tracking Error | RMSE | |||
---|---|---|---|---|
z ( m) | ( rad) | () | ||
Desired trajectory 1 | CE-SOSMC | 28.64 | 63.15 | 2.60 |
SC-AFNN | 3.05 | 8.65 | 0.47 | |
Desired trajectory 2 | CE-SOSMC | 79.04 | 214.68 | 9.62 |
SC-AFNN | 22.95 | 21.05 | 1.44 |
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Qin, Q.; Gao, G. Composite Error-Based Intelligent Adaptive Sliding Mode Control for Uncertain Bilaterally Symmetrical Hybrid Robot with Variational Desired Trajectories. Appl. Sci. 2021, 11, 2613. https://doi.org/10.3390/app11062613
Qin Q, Gao G. Composite Error-Based Intelligent Adaptive Sliding Mode Control for Uncertain Bilaterally Symmetrical Hybrid Robot with Variational Desired Trajectories. Applied Sciences. 2021; 11(6):2613. https://doi.org/10.3390/app11062613
Chicago/Turabian StyleQin, Qiuyue, and Guoqin Gao. 2021. "Composite Error-Based Intelligent Adaptive Sliding Mode Control for Uncertain Bilaterally Symmetrical Hybrid Robot with Variational Desired Trajectories" Applied Sciences 11, no. 6: 2613. https://doi.org/10.3390/app11062613
APA StyleQin, Q., & Gao, G. (2021). Composite Error-Based Intelligent Adaptive Sliding Mode Control for Uncertain Bilaterally Symmetrical Hybrid Robot with Variational Desired Trajectories. Applied Sciences, 11(6), 2613. https://doi.org/10.3390/app11062613