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Nonlinear observer-based optimal control of an active transfemoral prosthesis

基于非线性观察者的主动股骨假体的最优控制

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Abstract

This paper designs a joint controller/observer framework using a state dependent Riccati equation (SDRE) approach for an active transfemoral prosthesis system. An integral state control technique is utilized to design a tracking controller for a robot/prosthesis system. This framework promises a systematic flexible design using which multiple design specifications such as robustness, state estimation, and control optimality are achieved without the need for model linearization. Performance of the proposed approach is demonstrated through simulation studies, which show improvements versus a robust adaptive impedance controller and an extended Kalman filter-based state estimation method. Numerical results confirm the benefits of our method over the above-mentioned approaches with regard to control optimality and state estimation.

摘要

摘要本文使用状态依赖的Riccati 方程(SDRE)方法为主动经股假体系统设计联合控制器/观察器框架。 利用积分状态控制技术来设计机器人/假体系统的跟踪控制器。该框架保证了系统灵活设计, 通过该设 计, 可以实现多种设计参数优化, 例如鲁棒性、状态估计和控制最佳性, 而无需模型线性化。仿真研 究证明了该方法的性能, 较鲁棒的自适应阻抗控制器和基于扩展卡尔曼滤波器的状态估计方法有所改 进。数值结果证实了本方法在控制最优性和状态估计方面优于上述方法。

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References

  1. AZIMI V, SIMON D, RICHTER H. Stable robust adaptive impedance control of a prosthetic leg [C]//ASME 2015 Dynamic Systems and Control Conference. 2015: 1–10. DOI: https://doi.org/10.1115/DSCC2015-9794.

  2. POPOVIĆ D, OĞUZTÖRELI M N, STEIN R B. Optimal control for an above-knee prosthesis with two degrees of freedom [J]. Journal of Biomechanics, 1995, 28(1): 89–98. DOI: https://doi.org/10.1016/0021-9290(95)80010-7.

    Article  Google Scholar 

  3. SUP F, BOHARA A, GOLDFARB M. Design and control of a powered transfemoral prosthesis [J]. The International Journal of Robotics Research, 2008, 27(2): 263–73. DOI: https://doi.org/10.1177/0278364907084588.

    Article  Google Scholar 

  4. RICHTER H, SIMON D. Robust tracking control of a prosthesis test robot [J]. Journal of Dynamic Systems, Measurement, and Control, 2014, 136(3): 031011. DOI: https://doi.org/10.1115/1.4026342.

    Article  Google Scholar 

  5. ZHAO H, HORN J, REHER J, PAREDES V, AMES A D. First steps toward translating robotic walking to prostheses: A nonlinear optimization based control approach [J]. Autonomous Robots, 2017, 41(3): 725–742. DOI: https://doi.org/10.1007/s10514-016-9565-1.

    Article  Google Scholar 

  6. AZIMI V, ABOLFAZL FAKOORIAN S, TIEN N T, SIMON D. Robust adaptive impedance control with application to a transfemoral prosthesis and test robot [J]. Journal of Dynamic Systems, Measurement, and Control, 2018, 140(12): 121002. DOI: https://doi.org/10.1115/1.4040463.

    Article  Google Scholar 

  7. AZIMI V, SHU T, ZHAO H, GEHLHAR R, SIMON D, AMES A D. Model-based adaptive control of transfemoral prostheses: Theory, simulation, and experiments [J]. IEEE Transaction on Systems, Man, and Cybernetics: Systems. 2019, 15: 1–18. DOI: https://doi.org/10.1109/TSMC.2019.2896193.

    Google Scholar 

  8. BAVARSAD A, FAKHARIAN A, MENHAJ M B. Nonlinear optimal control of an active transfemoral prosthesis using state dependent Riccati equation (SDRE) approach [J]. Amirkabir Journal of Mechanical Engineering, 2020, Online. DOI: https://doi.org/10.22060/MEJ.2020.17815.6668.

  9. BAVARSAD A, FAKHARIAN A, MENHAJ M B. Optimal sliding mode controller for an active transfemoral prosthesis using state-dependent Riccati equation approach [J]. Arabian Journal for Science and Engineering, 2020, 45: 6559–6572. DOI: https://doi.org/10.1007/s13369-020-04563-x.

    Article  Google Scholar 

  10. SLOTINE J J, LI W. Applied nonlinear control [M]. Englewood Cliffs, NJ: Prentice Hall, 1991.

    MATH  Google Scholar 

  11. ÇIMEN T. State-dependent Riccati equation (SDRE) control: A survey [C]//IFAC Proceedings Volumes. Seoul, 2008: 3761–3775. DOI: https://doi.org/10.3182/20080706-5-KR-1001.00635.

  12. CLOUTIER J R. State-dependent Riccati equation techniques: An overview [C]//In Proceedings of the 1997 American Control Conference (Cat.No.97CH36041) IEEE. 1997, 2: 932–936. DOI: https://doi.org/10.1109/ACC.1997.609663.

    Article  Google Scholar 

  13. KORAYEM M H, NEKOO S R. State-dependent differential Riccati equation to track control of time-varying systems with state and control nonlinearities [J]. ISA Transactions, 2015, 57: 117–135. DOI: https://doi.org/10.1016/j.isatra.2015.02.008.

    Article  Google Scholar 

  14. KORAYEM M H, NEKOO S R. Finite-time state-dependent Riccati equation for time-varying nonaffine systems: Rigid and flexible joint manipulator control [J]. ISA Transaction 2015, 54: 125–44. DOI: https://doi.org/10.1016/j.isatra.2014.06.006.

    Article  Google Scholar 

  15. BEIKZADEH H, TAGHIRAD H D. Stability analysis of the discrete-time difference SDRE state estimator in a noisy environment [C]//2009 IEEE International Conference on Control and Automation. 2009: 1751–1756. IEEE. DOI: https://doi.org/10.1109/ICCA.2009.5410145.

  16. ÇIMEN T, MCCAFFREY D, HARRISON R F, BANKS S P. Asymptotically optimal nonlinear filtering [C]//IFAC Proceedings Volumes, 2007, 40(7): 756–761. DOI: https://doi.org/10.3182/20070625-5-FR-2916.00129.

    Article  Google Scholar 

  17. KORAYEM M H, LADEMAKHI N Y, NEKOO S R. Application of the state-dependent Riccati equation for flexible-joint arms: Controller and estimator design [J]. Optimal Control Applications and Methods, 2018, 39(2): 792–808. DOI: https://doi.org/10.1002/oca.2377.

    Article  MathSciNet  Google Scholar 

  18. NEKOO R S. Tutorial and review on the state-dependent Riccati equation [J]. Journal of Applied Nonlinear Dynamics, 2019, 8(2): 109–66. DOI: https://doi.org/10.5890/JAND.2019.06.001.

    Article  MathSciNet  Google Scholar 

  19. FAKOORIAN S A, SIMON D, RICHTER H, AZIMI V. Ground reaction force estimation in prosthetic legs with an extended Kalman filter [C]//2016 Annual IEEE Systems Conference (SysCon). Orlando, 2016: 1–6. IEEE. DOI: https://doi.org/10.1109/SYSCON.2016.7490563.

  20. FAKOORIAN S, AZIMI V, MOOSAVI M, RICHTER H, SIMON D. Ground reaction force estimation in prosthetic legs with nonlinear Kalman filtering methods [J]. Journal of Dynamic Systems, Measurement, and Control, 2017, 139(11): 111004. DOI: https://doi.org/10.1115/1.4036546.

    Article  Google Scholar 

  21. MOOSAVI S M, FAKOORIAN S A, AZIMI V, RICHTER H, SIMON D. Derivative-free Kalman filtering-based control of prosthetic legs [C]//In 2017 American Control Conference (ACC). Seattle, 2017: 5205–5210. DOI: https://doi.org/10.23919/ACC.2017.7963763.

  22. AZIMI V, NGUYEN T T, SHARIFI M, FAKOORIAN S A, SIMON D. Robust ground reaction force estimation and control of lower-limb prostheses: Theory and simulation [J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2018, 50(8): 1–12. DOI: https://doi.org/10.1109/TSMC.2018.2836913.

    Google Scholar 

  23. NEKOO S R. Digital implementation of a continues-time nonlinear optimal controller: An experimental study with real-time computations [J]. ISA Transaction, 2020, 101: 346–357. DOI: https://doi.org/10.1016/j.isatra.2020.01.020.

    Article  Google Scholar 

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Authors and Affiliations

  1. Faculty of Electrical, Biomedical and Mechatronics Engineering, Qazvin Branch, Islamic Azad University, Qazvin, 34185-1416, Iran

    Anna Bavarsad & Ahmad Fakharian

  2. Department of Electrical Engineering, Amirkabir University of Technology, Tehran, 15875-4413, Iran

    Mohammad Bagher Menhaj

Authors
  1. Anna Bavarsad
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  2. Ahmad Fakharian
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  3. Mohammad Bagher Menhaj
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Contributions

The initial idea generation was by Ahmad FAKHARIAN. The design of the control system and estimator, simulations, data analysis, and the initial draft of manuscript was done by Anna BAVARSAD. Review of designs and simulation results and editing of the article by Ahmad FAKHARIAN and Mohammad Bagher MENHAJ.

Corresponding author

Correspondence to Ahmad Fakharian.

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Conflict of interest

Anna BAVARSAD, Ahmad FAKHARIAN, and Mohammad Bagher MENHAJ declare that they have no conflict of interest.

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Bavarsad, A., Fakharian, A. & Menhaj, M.B. Nonlinear observer-based optimal control of an active transfemoral prosthesis. J. Cent. South Univ. 28, 140–152 (2021). https://doi.org/10.1007/s11771-021-4592-2

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  • DOI: https://doi.org/10.1007/s11771-021-4592-2

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