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Applied Sciences
Volume 16
Issue 1
10.3390/app16010402
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

A Novel Stability Criterion Based on the Swing Projection Polygon for Gait Rehabilitation Exoskeletons

by
Moyao Gao
1,
Wei Yang
1,
Yuexi Zhong
1,
Yingxue Ni
1,
Huimin Jiang
2,
Guokai Zhu
1,
Jing Li
3,
Zhanli Wang
3,
Jiaqi Bu
1 and
Bo Wu
1,*
1
School of Mechatronic Engineering, Changchun Institute of Technology, Changchun 130012, China
2
Institute of Electromechanical Technology, Jilin Academy of Agricultural Machinery, Changchun 130021, China
3
School of Mechatronic Engineering, Changchun University of Technology, Changchun 130012, China
*
Author to whom correspondence should be addressed.
Appl. Sci. 2026, 16(1), 402; https://doi.org/10.3390/app16010402 (registering DOI)
Submission received: 24 October 2025 / Revised: 23 November 2025 / Accepted: 29 December 2025 / Published: 30 December 2025
(This article belongs to the Section Mechanical Engineering)
Versions Notes

Abstract

Intelligent lower-limb exoskeleton rehabilitation robots are increasingly superseding traditional rehabilitation equipment, making them a focus of research in this field. However, existing systems remain challenged by dynamic instability resulting from various disturbances during actual walking. To address this limitation, this study proposes a novel dynamic stability criterion. Through an analysis of the principles and limitations of the traditional zero-moment point (ZMP) stability criterion, particularly during the late single-leg support phase, a new stability criterion is introduced, which is founded on the swing projection polygon during single-leg support. This approach elucidates the variation patterns of the stability polygon during a single-step motion and facilitates a qualitative analysis of the stability characteristics of the human–robot system in multiple postures. To further enhance the stability and smoothness of gait trajectories in lower-limb exoskeleton rehabilitation robots, the shortcomings of conventional gait planning approaches, namely their non-intuitive nature and discontinuity, are addressed. A recurrent gait planning method leveraging Long Short-Term Memory (LSTM) neural networks is proposed. The integration of the periodic motion characteristics of human gait serves to validate the feasibility and correctness of the proposed method. Finally, based on the recurrent gait planning method, the dynamic stability of walking postures is verified through theoretical analysis and experimental comparisons, accompanied by an in-depth analysis of key factors influencing dynamic stability.
Keywords: lower limb rehabilitation robot; dynamic stability; ZMP theory; LSTM neural network; test analysis lower limb rehabilitation robot; dynamic stability; ZMP theory; LSTM neural network; test analysis

Share and Cite

MDPI and ACS Style

Gao, M.; Yang, W.; Zhong, Y.; Ni, Y.; Jiang, H.; Zhu, G.; Li, J.; Wang, Z.; Bu, J.; Wu, B. A Novel Stability Criterion Based on the Swing Projection Polygon for Gait Rehabilitation Exoskeletons. Appl. Sci. 2026, 16, 402. https://doi.org/10.3390/app16010402

AMA Style

Gao M, Yang W, Zhong Y, Ni Y, Jiang H, Zhu G, Li J, Wang Z, Bu J, Wu B. A Novel Stability Criterion Based on the Swing Projection Polygon for Gait Rehabilitation Exoskeletons. Applied Sciences. 2026; 16(1):402. https://doi.org/10.3390/app16010402

Chicago/Turabian Style

Gao, Moyao, Wei Yang, Yuexi Zhong, Yingxue Ni, Huimin Jiang, Guokai Zhu, Jing Li, Zhanli Wang, Jiaqi Bu, and Bo Wu. 2026. "A Novel Stability Criterion Based on the Swing Projection Polygon for Gait Rehabilitation Exoskeletons" Applied Sciences 16, no. 1: 402. https://doi.org/10.3390/app16010402

APA Style

Gao, M., Yang, W., Zhong, Y., Ni, Y., Jiang, H., Zhu, G., Li, J., Wang, Z., Bu, J., & Wu, B. (2026). A Novel Stability Criterion Based on the Swing Projection Polygon for Gait Rehabilitation Exoskeletons. Applied Sciences, 16(1), 402. https://doi.org/10.3390/app16010402

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