# Gait Phase Estimation Based on User-Walker Interaction Force  
[PERSON]  
1 Department of Mechanical System Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan; [EMAIL_ADDRESS] (Y.A. ); [EMAIL_ADDRESS] (Y.X) 1  
[PERSON]  
2 School of Automation and Electrical Engineering, University of Science and Technology Beijing, 30 Xueyuan Road, Haifa District, Beijing 100083, China; [EMAIL_ADDRESS] 2  
[PERSON]  
2 School of Automation and Electrical Engineering, University of Science and Technology Beijing, 30 Xueyuan Road, Haifa District, Beijing 100083, China; [EMAIL_ADDRESS] 2  
[PERSON]  
3 Business Innovation Division, Panasonic Corp., Oza Kadoma-shi, Osaka 571-8501, Japan; [EMAIL_ADDRESS] (K.Y. ); [EMAIL_ADDRESS] (M.Y.) May 19, 202  
phase estimation, which is crucial for developing control methods for rehabilitation. In fact, obtaining and analyzing gait phase information can help develop rehabilitation strategies. For example, function-related muscles can be strengthened at the precise timing as when the corresponding muscle groups are activated, as demonstrated in a previous study, in which we proposed gait-phase-dependent control for rehabilitation [11]. To provide proper assistance and maximize the rehabilitation outcomes, various assistive robots and rehabilitation robots extract information of the user's gait phases during walking [12]. Such information is essential for wearable robots because if they cannot provide the proper assistance in the correct gait phases; they would be a burden rather than a support. [PERSON] [13] used the instants of HS detected from foot switches and the average duration of the last several gait cycles to estimate the current gait phase. Hence, gait phase of a walker user can be estimated by leveraging [PERSON]'s method, where the gait phase can be considered as the accumulation of the estimated frequency that starts from an HS. Researchers have applied the cycles of kinetic or kinematic data of ground reaction force or joint angle for estimating the gait phase by using adaptive oscillators (AOs) [14; 15]. An AO is a mathematical tool proposed by [PERSON] [16; 17] that synchronizes its phase and frequency with any quasi-periodic signal to extract these parameters from the signal. Despite its accurate gait events estimation, the [PERSON]'s method presents some limitations. (1) When it is directly applied to estimate the gait phase, the estimation accuracy depends on the correct detection of gait events and predicted duration of the gait cycle, which is in turn based on previous gait cycle durations [18]. (2) The estimation performance deteriorates when gait event detection fails because an incorrect duration degrades the estimation accuracy of the gait phase in the subsequent cycles, and the estimated phase is the integral of the estimated frequency. If a considerable phase estimation error occurs, it can only diminish when the next gait cycle starts, leading to discontinuity in phase estimation during the transition period. The AO can provide a zero-delay accurate frequency and phase estimation provided that the input signal has slow dynamics. However, a drastic change in the frequency or amplitude of the target signal substantially degrades the estimation accuracy due to slow convergence. Although the estimation convergence can be accelerated by increasing the gains in the estimation loop, fluctuations in the estimates may occur [19; 20]. As for the case of interaction force based gait phase estimation, the amplitude of the interaction force is not constant but can change drastically because it depends on the bodyweight transmitted to the handle. In addition, although the frequency of walking does not change rapidly, many people exhibit asymmetric gait patterns [21], which may vary the signal frequency over consecutive gait cycles. Therefore, it is crucial to mitigate the influence of the transient changes to reach an accurate and stable gait phase estimation.