Phase-Based Repetitive Control for Rehabilitation Systems: A Case Study on Ankle Assistance

Abstract

Active ankle foot orthoses (AAFOs) are widely used in gait rehabilitation to assist patients with impaired dorsiflexion and plantarflexion control. Due to the cyclic and quasi-periodic nature of human walking, repetitive disturbances and tracking errors frequently arise from actuator dynamics, transmission nonlinearities, and human device interaction forces. This article presents a phase based repetitive control (RC) framework specifically tailored for AAFO systems and integrated with a baseline impedance like controller to ensure safe and compliant assistance. By embedding an internal model of gait periodicity through phase synchronized learning, the proposed controller progressively reduces cycle to cycle tracking errors while remaining robust to cadence variations. A simulation case study demonstrates that the AAFO can learn a phase dependent assistive torque profile, resulting in improved tracking accuracy and smooth assistance under variable gait conditions. The results highlight the suitability of repetitive control as an interpretable and performance enhancing strategy for rehabilitation oriented biomechatronic devices.

Keywords

• Repetitive
• control
• rehabilitation
• ankle

Rehabilitasyon Sistemleri için Faz Tabanlı Tekrarlayan Kontrol: Ayak Bileği Destek Sistemi Üzerine Bir Vaka Çalışması

Abstract

Aktif ayak bileği-ayak ortezleri (AAFO'lar), ayak bileği dorsifleksiyon ve plantarfleksiyon kontrolünde bozukluk yaşayan hastalara yardımcı olmak için yürüyüş rehabilitasyonunda yaygın olarak kullanılmaktadır. İnsan yürüyüşünün döngüsel ve yarı periyodik doğası nedeniyle, aktüatör dinamikleri, iletim doğrusal olmayanlıkları ve insan-cihaz etkileşim kuvvetlerinden kaynaklanan tekrarlayan bozulmalar ve izleme hataları sıklıkla ortaya çıkar. Bu makale, AAFO sistemleri için özel olarak tasarlanmış ve güvenli ve uyumlu destek sağlamak için temel empedans benzeri bir kontrolörle entegre edilmiş faz tabanlı tekrarlayan kontrol (RC) çerçevesini sunmaktadır. Faz senkronize öğrenme yoluyla yürüyüş periyodikliğinin içsel bir modelini yerleştirerek, önerilen kontrolör, kadans varyasyonlarına karşı sağlam kalırken döngüden döngüye izleme hatalarını kademeli olarak azaltır. Bir simülasyon vaka çalışması, AAFO'nun faza bağlı bir yardımcı tork profili öğrenebileceğini ve bunun da değişken yürüyüş koşulları altında izleme doğruluğunu ve düzgün desteği iyileştirdiğini göstermektedir. Sonuçlar, tekrarlayan kontrolün rehabilitasyon odaklı biyomekatronik cihazlar için yorumlanabilir ve performansı artırıcı bir strateji olarak uygunluğunu vurgulamaktadır.

Keywords

• Tekrarlayan
• kontrol
• rehabilitasyon
• ayak bileği

References

1. Basu, A., Jujjavarapu, S. S., & Esfahani, E. T. (2020, August). Design of a novel variable stiffness active ankle foot orthosis using permanent magnets for drop foot assistance. In International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (Vol. 83990, p. V010T10A049). American Society of Mechanical Engineers.
2. Basu, A., Jujjavarapu, S. S., & Esfahani, E. T. (2020, August). Design of a novel variable stiffness active ankle foot orthosis using permanent magnets for drop foot assistance. In International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (Vol. 83990, p. V010T10A049). American Society of Mechanical Engineers.
3. Baud, R., Manzoori, A. R., Ijspeert, A., & Bouri, M. (2021). Review of control strategies for lower-limb exoskeletons to assist gait. Journal of neuroengineering and rehabilitation, 18(1), 119.
4. Bristow, D. A., Tharayil, M., & Alleyne, A. G. (2006). A survey of iterative learning control. IEEE control systems magazine, 26(3), 96-114.
5. DeBoer, B., Hosseini, A., & Rossa, C. (2021, October). An extended parameter estimation disturbance observer for an active ankle foot orthosis. In 2021 IEEE International Conference on Systems, Man, and Cybernetics (SMC) (pp. 1105-1110). IEEE.
6. DeBoer, B., Hosseini, A., & Rossa, C. (2022). A discrete non-linear series elastic actuator for active ankle-foot orthoses. IEEE Robotics and Automation Letters, 7(3), 6211-6217.
7. DeBoer, B., Hosseini, A., & Rossa, C. (2023). Model predictive control of an active ankle-foot orthosis with non-linear actuation constraints. Control Engineering Practice, 136, 105538.
8. DeBoer, B., Hosseini, A., & Rossa, C. (2023). Model predictive control of an active ankle-foot orthosis with non-linear actuation constraints. Control Engineering Practice, 136, 105538.

9. Francis, B. A., & Wonham, W. M. (1976). The internal model principle of control theory. Automatica, 12(5), 457-465.
10. Giannattasio, R., Boccardo, N., Vaccaro, R., Bhatt, H., Maludrottu, S., De Momi, E., & Laffranchi, M. (2025). Design, development, and validation of a non-backdrivable active ankle-foot orthosis for the TWIN lower-limb exoskeleton. Frontiers in Robotics and AI, 12, 1647989.
11. Hara, S., Yamamoto, Y., Omata, T., & Nakano, M. (1988). Repetitive control system: A new type servo system for periodic exogenous signals. IEEE Transactions on automatic control, 33(7), 659-668.
12. Hogan, N. (1985). Impedance control: An approach to manipulation: Part II—Implementation. Journal of dynamic systems, measurement, and control, 107(1), 8-16.
13. Jradi, R., Rifaï, H., & Mohammed, S. (2023). Adaptive active disturbance rejection control of an actuated ankle foot orthosis for ankle movement assistance. IEEE Robotics and Automation Letters, 9(1), 367-374.
14. Jradi, R., Rifaï, H., & Mohammed, S. (2023). Adaptive active disturbance rejection control of an actuated ankle foot orthosis for ankle movement assistance. IEEE Robotics and Automation Letters, 9(1), 367-374.
15. Kirtas, O., Savas, Y., Bayraker, M., Baskaya, F., Basturk, H., & Samur, E. (2021). Design, implementation, and evaluation of a backstepping control algorithm for an active ankle–foot orthosis. Control Engineering Practice, 106, 104667.
16. Lara-Velazquez, C. A., Ramirez-Paredes, J. P., & González-Sandoval, B. V. (2024). Active Ankle–Foot Orthosis Design and Computer Simulation with Multi-Objective Parameter Optimization. Applied Sciences, 14(7),2726.
17. Giannattasio, R., Boccardo, N., Vaccaro, R., Bhatt, H., Maludrottu, S., De Momi, E., & Laffranchi, M. (2025). Design, development, and validation of a non-backdrivable active ankle-foot orthosis for the TWIN lower-limb exoskeleton. Frontiers in Robotics and AI, 12, 1647989.
18. Utomo, B. P., Wulansari, P., Parahita, A. N., Smaradhana, D. F., & Son, L. (2023). Development of Ankle-Foot Orthosis Using Servo Motor with On-Off Control System for Drop-Foot. International Journal of Automotive and Mechanical Engineering, 20(4), 10931-10942.