Research on Lower Limb Exoskeleton Trajectory Tracking Control Based on the Dung Beetle Optimizer and Feedforward Proportional–Integral–Derivative Controller
Abstract
:1. Introduction
2. LLE Mathematical Model
3. Control Strategy
3.1. FPID Controller
3.2. DBO Optimizer
3.3. DBO–FPID Control Strategy
4. Simulation Experiment
4.1. Gait Data Collection
4.2. Simulation Settings and Results
5. Joint Module Experiments
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
- Dewi, N.S.; Komatsuzaki, M. On-body personal assist suit for commercial farming: Effect on heart rate, EMG, trunk movements, and user acceptance during digging. Int. J. Ind. Ergon. 2018, 68, 290–296. [Google Scholar] [CrossRef]
- Golabchi, A.; Riahi, N.; Fix, M.; Miller, L.; Rouhani, H.; Tavakoli, M. A framework for evaluation and adoption of industrial exoskeletons. Appl. Ergon. 2023, 113, 104103. [Google Scholar] [CrossRef] [PubMed]
- Kim, H.J.; Noh, J.; Yang, W. Knee-Assistive Robotic Exoskeleton (KARE-1) Using a Conditionally Singular Mechanism for Industrial Field Applications. Appl. Sci. 2020, 10, 5141. [Google Scholar] [CrossRef]
- Su, Q.; Pei, Z.; Tang, Z. Tracking Control for a Lower Extremity Exoskeleton Based on Adaptive Dynamic Programing. Biomimetics 2023, 8, 353. [Google Scholar] [CrossRef]
- Tu, Y.; Zhu, A.; Song, J.; Zhang, X.; Cao, G. Design and Experimental Evaluation of a Lower-Limb Exoskeleton for Assisting Workers with Motorized Tuning of Squat Heights. IEEE Trans. Neural Syst. Rehabil. Eng. 2022, 30, 184–193. [Google Scholar] [CrossRef] [PubMed]
- Wang, B.; Liang, Y.; Xu, D.; Wang, Z.; Ji, J. Design on electrohydraulic servo driving system with walking assisting control for lower limb exoskeleton robot. Int. J. Adv. Robot. Syst. 2021, 18, 1729881421992286. [Google Scholar] [CrossRef]
- Xiao, F. Proportional myoelectric and compensating control of a cable-conduit mechanism-driven upper limb exoskeleton. ISA Trans. 2019, 89, 245–255. [Google Scholar] [CrossRef]
- Abdul-Ameer, H.K. Quantitative analysis and control of the torque profile of the upper limb using a kinetic model and motion measurements. Int. J. Artif. Organs 2022, 45, 631–641. [Google Scholar] [CrossRef]
- Dong, R.; Pedrycz, W. Approximation grid evaluation-based PID control in cascade with nonlinear gain. J. Frankl. Inst. 2015, 352, 4279–4296. [Google Scholar] [CrossRef]
- Kunyou, H.; Lumin, C. Research of Fuzzy PID Control for Lower Limb Wearable Exoskeleton Robot. In Proceedings of the 4th International Conference on Intelligent Autonomous Systems, ICoIAS 2021, Wuhan, China, 14–16 May 2021; pp. 385–389. [Google Scholar]
- Kilic, E.; Sekerci, B.; Kizilhan, H.; Baser, O. Evaluation of position tracking control performance of a variable stiffness ankle exoskeleton robot with various controller types. J. Fac. Eng. Archit. Gazi Univ. 2020, 35, 1551–1563. [Google Scholar]
- Liu, J.; Fang, H.; Xu, J. Online Adaptive PID Control for a Multi-Joint Lower Extremity Exoskeleton System Using Improved Particle Swarm Optimization. Machines 2022, 10, 21. [Google Scholar] [CrossRef]
- Belkadi, A.; Oulhadj, H.; Touati, Y.; Khan, S.A.; Daachi, B. On the robust PID adaptive controller for exoskeletons: A particle swarm optimization based approach. Appl. Soft Comput. 2017, 60, 87–100. [Google Scholar] [CrossRef]
- Yuan, T.; Zhang, C.; Yi, F.; Lv, P.; Zhang, M.; Li, S. RBFNN-Based Adaptive Integral Sliding Mode Feedback and Feedforward Control for a Lower Limb Exoskeleton Robot. Electronics 2024, 13, 1043. [Google Scholar] [CrossRef]
- Merola, A.; Colacino, D.; Cosentino, C.; Amato, F. Model-based tracking control design, implementation of embedded digital controller and testing of a biomechatronic device for robotic rehabilitation. Mechatronics 2018, 52, 70–77. [Google Scholar] [CrossRef]
- Figueiredo, J.; Fernandes, P.N.; Moreno, J.C.; Santos, C.P. Feedback-Error Learning for time-effective gait trajectory tracking in wearable exoskeletons. Anat. Rec. 2023, 306, 728–740. [Google Scholar] [CrossRef] [PubMed]
- Lin, C.-J.; Sie, T.-Y. Design and Experimental Characterization of Artificial Neural Network Controller for a Lower Limb Robotic Exoskeleton. Actuators 2023, 12, 55. [Google Scholar] [CrossRef]
- Resquin, F.; Gonzalez-Vargas, J.; Ibanez, J.; Brunetti, F.; Pons, J.L. Feedback Error Learning Controller for Functional Electrical Stimulation Assistance in a Hybrid Robotic System for Reaching Rehabilitation. Eur. J. Transl. Myol. 2016, 26, 6164. [Google Scholar] [CrossRef]
- Joyo, M.K.; Raza, Y.; Ahmed, S.F.; Billah, M.M.; Kadir, K.; Naidu, K.; Ali, A.; Yusof, Z.M. Optimized Proportional-Integral-Derivative Controller for Upper Limb Rehabilitation Robot. Electronics 2019, 8, 826. [Google Scholar] [CrossRef]
- Sharma, R.; Gaur, P.; Bhatt, S.; Joshi, D. Optimal fuzzy logic-based control strategy for lower limb rehabilitation exoskeleton. Appl. Soft Comput. 2021, 105, 107226. [Google Scholar] [CrossRef]
- Soleimani Amiri, M.; Ramli, R.; Ibrahim, M.F.; Abd Wahab, D.; Aliman, N. Adaptive Particle Swarm Optimization of PID Gain Tuning for Lower-Limb Human Exoskeleton in Virtual Environment. Mathematics 2020, 8, 2040. [Google Scholar] [CrossRef]
- Zhao, C.; Liu, Z.; Zhu, L.; Wang, Y. Design and Research of Series Actuator Structure and Control System Based on Lower Limb Exoskeleton Rehabilitation Robot. Actuators 2024, 13, 20. [Google Scholar] [CrossRef]
- Amiri, M.S.; Ramli, R.; Aliman, N. Adaptive Swarm Fuzzy Logic Controller of Multi-Joint Lower Limb Assistive Robot. Machines 2022, 10, 425. [Google Scholar] [CrossRef]
- Li, J.; Tai, Y.; Meng, F. Rehabilitation exoskeleton torque control based on PSO-RBFNN optimization. PLoS ONE 2023, 18, e0285453. [Google Scholar] [CrossRef] [PubMed]
- Al-dujaili, A.Q.; Hasan, A.F.; Humaidi, A.J.; Al-Jodah, A. Anti-disturbance control design of Exoskeleton Knee robotic system for rehabilitative care. Heliyon 2024, 10, e28911. [Google Scholar] [CrossRef]
- Aliman, N.; Ramli, R.; Haris, S.M.; Amiri, M.S.; Van, M. A robust adaptive-fuzzy-proportional-derivative controller for a rehabilitation lower limb exoskeleton. Eng. Sci. Technol. Int. J. 2022, 35, 101097. [Google Scholar] [CrossRef]
- Xue, J.; Shen, B. Dung beetle optimizer: A new meta-heuristic algorithm for global optimization. J. Supercomput. 2023, 79, 7305–7336. [Google Scholar] [CrossRef]
- Shen, Q.; Zhang, D.; Xie, M.; He, Q. Multi-Strategy Enhanced Dung Beetle Optimizer and Its Application in Three-Dimensional UAV Path Planning. Symmetry 2023, 15, 1432. [Google Scholar] [CrossRef]
- Jin, H.; Ji, H.; Yan, F. An Effective Obstacle Avoidance and Motion Planning Design for Underwater Telescopic Arm Robots Based on a Tent Chaotic Dung Beetle Algorithm. Electronics 2023, 12, 4128. [Google Scholar] [CrossRef]
- Amiri, M.S.; Ramli, R.; Ibrahim, M.F. Initialized Model Reference Adaptive Control for Lower Limb Exoskeleton. IEEE Access 2019, 7, 167210–167220. [Google Scholar] [CrossRef]
Parameters | Hip | Knee | ||||||
---|---|---|---|---|---|---|---|---|
DBO–FPID | DBO–PID | PSO–FPID | PSO–PID | DBO–FPID | DBO–PID | PSO–FPID | PSO–PID | |
kp | 8.0381 | 8.0381 | 8.23722 | 8.23722 | 2.3221 | 2.3221 | 9.814255 | 9.814255 |
ki | 1.07255 | 1.07255 | 1.68581 | 1.68581 | 0.024061 | 0.024061 | 0.105555 | 0.105555 |
kd | 50.112 | 50.112 | 83.4124 | 83.4124 | 6.0659 | 6.0659 | 137.1816 | 137.1816 |
k1 | 125.022 | −85.62981 | 54.2868 | −26.6664 | ||||
k2 | 69.40883 | 156.3278 | 20.7605 | 64.5435 | ||||
k3 | 5.815122 | 5.226777 | 2.30838 | 32.838 | ||||
k4 | 0.108704 | 0.2433991 | 0.0476948 | 0.0533645 |
Indexes | Hip | Knee | ||||||
---|---|---|---|---|---|---|---|---|
DBO–FPID | DBO–PID | PSO–FPID | PSO–PID | DBO–FPID | DBO–PID | PSO–FPID | PSO–PID | |
IAE (°) | 58.2124 | 222.5931 | 461.1682 | 547.1105 | 131.5939 | 801.2457 | 2225.4 | 2472.6 |
MEAE (°) | 0.0582 | 0.2224 | 0.4607 | 0.5466 | 0.1315 | 0.8004 | 2.2232 | 2.4701 |
MAE (°) | 0.3766 | 1.4608 | 1.5968 | 2.5298 | 0.9952 | 5.7764 | 6.2693 | 9.2723 |
RMSE (°) | 0.0820 | 0.3378 | 0.5374 | 0.6971 | 0.1943 | 1.1497 | 2.6133 | 3.0370 |
Indexes | Hip | Knee | ||||||
---|---|---|---|---|---|---|---|---|
DBO–FPID | DBO–PID | PSO–FPID | PSO–PID | DBO–FPID | DBO–PID | PSO–FPID | PSO–PID | |
IAE (°) | ||||||||
Scene 2 | 384.1358 | 814.3416 | 1170.4 | 1534.7 | 207.0941 | 1070.6 | 2837.1 | 3430.5 |
Scene 3 | 123.7093 | 404.9149 | 626.8465 | 892.2566 | 204.3195 | 1118.9 | 2715.9 | 3594.4 |
Scene 4 | 338.5276 | 887.4463 | 993.4773 | 1681.7 | 389.4159 | 1762.6 | 2800.8 | 3735.8 |
MEAE (°) | ||||||||
Scene 2 | 0.3838 | 0.8135 | 1.1692 | 1.5332 | 0.2069 | 1.0695 | 2.8343 | 3.4271 |
Scene 3 | 0.1236 | 0.4045 | 0.6262 | 0.8914 | 0.2041 | 1.1178 | 2.7132 | 3.5908 |
Scene 4 | 0.3382 | 0.8866 | 0.9925 | 1.6800 | 0.3890 | 1.7608 | 2.7980 | 3.7320 |
MAE (°) | ||||||||
Scene 2 | 5.3048 | 9.7206 | 9.2546 | 13.7469 | 1.4831 | 8.1599 | 10.4331 | 13.9228 |
Scene 3 | 1.0152 | 3.1406 | 3.7607 | 7.0526 | 1.7605 | 10.8578 | 12.4174 | 15.6317 |
Scene 4 | 6.8780 | 10.1990 | 8.8998 | 12.5339 | 3.2037 | 10.2793 | 12.5177 | 15.7884 |
RMSE (°) | ||||||||
Scene 2 | 0.8560 | 1.7227 | 2.0339 | 2.7306 | 0.3023 | 1.7040 | 3.5310 | 4.3846 |
Scene 3 | 0.1895 | 0.6838 | 0.8614 | 1.3557 | 0.3187 | 1.8387 | 3.3156 | 4.6806 |
Scene 4 | 0.8312 | 1.7722 | 1.6249 | 2.7269 | 0.6384 | 2.6138 | 3.6101 | 4.8806 |
Indexes | Unloaded Motor | Hip | ||||||
---|---|---|---|---|---|---|---|---|
DBO–FPID | DBO–PID | PSO–FPID | PSO–PID | DBO–FPID | DBO–PID | PSO–FPID | PSO–PID | |
IAE (°) | ||||||||
Scene 1 | 861.7772 | 1007.1 | 1015.9 | 1192.1 | 2341.2 | 2570.5 | 2789.3 | 2933.8 |
Scene 2 | 1291.2 | 1485.1 | 1465.8 | 1742.0 | 3278.3 | 3608.2 | 3813.1 | 3992.3 |
Scene 3 | 964.5609 | 1181.8 | 1135.3 | 1400.4 | 2750.4 | 3119.3 | 3256.7 | 3493.3 |
Scene 4 | 1462.0 | 1821.5 | 1728.0 | 2155.2 | 3556.2 | 3867.2 | 3996.5 | 4289.5 |
MEAE (°) | ||||||||
Scene 1 | 0.8609 | 1.0061 | 1.0149 | 1.1909 | 2.3388 | 2.5679 | 2.7865 | 2.9308 |
Scene 2 | 1.2899 | 1.4837 | 1.4644 | 1.7402 | 3.2750 | 3.6046 | 3.8093 | 3.9883 |
Scene 3 | 0.9636 | 1.1806 | 1.1342 | 1.3990 | 2.7476 | 3.1162 | 3.2535 | 3.4898 |
Scene 4 | 1.4605 | 1.8196 | 1.7262 | 2.1530 | 3.5527 | 3.8634 | 3.9925 | 4.2852 |
MAE (°) | ||||||||
Scene 1 | 3.8383 | 4.1705 | 4.7346 | 5.1705 | 9.0412 | 9.5008 | 10.3127 | 10.8686 |
Scene 2 | 6.1421 | 7.0115 | 7.1811 | 7.9666 | 19.5760 | 20.0768 | 20.0768 | 20.0768 |
Scene 3 | 5.0142 | 5.8058 | 6.2402 | 7.3933 | 12.8158 | 13.6784 | 14.8158 | 14.9534 |
Scene 4 | 6.1624 | 7.4472 | 6.7636 | 8.5789 | 18.6408 | 20.2123 | 20.2123 | 20.6408 |
RMSE (°) | ||||||||
Scene 1 | 1.1586 | 1.2822 | 1.3652 | 1.5201 | 2.9430 | 3.2003 | 3.4895 | 3.6510 |
Scene 2 | 1.7620 | 2.0222 | 2.0898 | 2.3668 | 5.0957 | 5.3124 | 5.5868 | 5.6105 |
Scene 3 | 1.3570 | 1.5926 | 1.6456 | 1.9210 | 3.8778 | 4.1414 | 4.4274 | 4.5987 |
Scene 4 | 1.9461 | 2.2895 | 2.2507 | 2.7342 | 4.9633 | 5.3544 | 5.5185 | 5.8429 |
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Li, C.; Di, H.; Liu, Y.; Liu, K. Research on Lower Limb Exoskeleton Trajectory Tracking Control Based on the Dung Beetle Optimizer and Feedforward Proportional–Integral–Derivative Controller. Actuators 2024, 13, 344. https://doi.org/10.3390/act13090344
Li C, Di H, Liu Y, Liu K. Research on Lower Limb Exoskeleton Trajectory Tracking Control Based on the Dung Beetle Optimizer and Feedforward Proportional–Integral–Derivative Controller. Actuators. 2024; 13(9):344. https://doi.org/10.3390/act13090344
Chicago/Turabian StyleLi, Changming, Haiting Di, Yongwang Liu, and Ke Liu. 2024. "Research on Lower Limb Exoskeleton Trajectory Tracking Control Based on the Dung Beetle Optimizer and Feedforward Proportional–Integral–Derivative Controller" Actuators 13, no. 9: 344. https://doi.org/10.3390/act13090344