Early gait phase recognition methods for wearable exoskeletons mainly relied on event detection, such as heel-strike and toe-off, using foot switches, pressure insoles, or kinematic thresholds. These approaches are computationally efficient and easy to implement, making them suitable for real-time control.

However, event-based methods inherently provide discrete gait state transitions, which may lead to abrupt changes in control commands. This limitation can reduce control smoothness and negatively affect human-exoskeleton interaction, especially during speed transitions or irregular gait patterns. Moreover, these methods are sensitive to sensor noise and may suffer from reduced robustness in pathological gait conditions.

With advances in machine learning, various data-driven approaches have been proposed for gait phase estimation and trajectory prediction. Neural networks such as artificial neural networks (ANNs), support vector machines (SVMs), and especially long short-term memory (LSTM) networks [18] have been widely adopted due to their ability to model temporal dependencies in gait signals.

Learning-based methods have demonstrated high prediction accuracy and adaptability across different walking speeds and subjects. Some studies have extended these approaches to continuous gait phase estimation and short-term trajectory forecasting for exoskeleton control. Nevertheless, these methods typically require large training datasets and involve considerable computational complexity. Their real-time performance on embedded systems commonly used in wearable exoskeletons remains a challenge, and model generalization to unseen gait patterns or impaired users is still an open issue.

Bio-inspired control strategies based on central pattern generators (CPGs) [19] have also been extensively studied for gait planning [20] and lower-limb exoskeleton control. CPG-based approaches generate rhythmic joint trajectories using coupled nonlinear oscillators [21], enabling smooth and continuous motion patterns.

These methods offer advantages in terms of biological plausibility and motion continuity. However, CPG-based gait generation often relies on predefined oscillatory structures and parameter tuning. Adapting such models to irregular, asymmetric, or pathological gait—common in rehabilitation scenarios—can be challenging and may require additional adaptive or supervisory mechanisms.

More recently, research has shifted toward multimodal human-exoskeleton cooperative control frameworks [22], which integrate multiple wearable sensors such as inertial measurement units (IMUs) [23], force sensors [24], plantar pressure sensors, and electromyography (EMG). These systems typically adopt a hierarchical or multi-level control architecture, where high-level intent or gait state estimation informs low-level joint control.

While multimodal approaches enhance robustness and adaptability, they also increase system complexity, sensor requirements, and computational burden. In practical wearable exoskeleton applications, especially ankle exoskeletons, minimizing sensor dependency and computational cost remains an important consideration.

Different from system-level cooperative control strategies or learning-intensive prediction models, this paper focuses on a lightweight and real-time gait phase recognition and trajectory prediction framework for ankle exoskeletons. By employing a dual-stage approach based on DTW and short-term trajectory prediction, the proposed method achieves continuous gait phase estimation without requiring extensive training or multimodal sensing.

The proposed approach is complementary to existing multimodal or hierarchical control frameworks and can serve as a reliable perception and prediction module for practical ankle exoskeleton systems, particularly under real-time and embedded hardware constraints.

The DTW and KM template selection method, as depicted in Fig. 2, combines the temporal alignment capability of DTW with the clustering strength of K-Means to extract representative gait cycle templates from gait data. This method is sensitive to disparities in walking conditions, such as changes in walking speed and terrain, and is able to accommodate the variability of individual gait patterns. By merging these two techniques, DTW-KM effectively captures the dynamic nature of human gait while providing a robust mechanism to identify key gait patterns in diverse walking scenarios.

The process begins by segmenting the raw gait data into discrete gait cycles, resulting in a gait database denoted 𝒯={T1,T2,…,Tn}, where each Ti represents an individual gait cycle sample. These gait cycles are the fundamental units for further analysis, as they form the raw input for the DTW distance computation.

Next, DTW is employed to compute the distance d(Ti,Tj) between each pair of gait cycles. The DTW distance measures the similarity between two gait cycles while accounting for temporal misalignments, such as variations in duration or speed. This step produces a DTW distance matrix W=[wij]n×n, where each element wij represents the DTW distance between gait cycles Ti and Tj: (1)wij=DTW(Ti,Tj)

Importantly, this distance is normalized to ensure that differences in duration and speed across gait cycles do not distort the measurement.

Each row of this distance matrix, wi∗, can be viewed as a vector Vi, representing the gait cycle Ti in a high-dimensional feature space. Specifically, the vector Vi=[wi1,wi2,…,win] encapsulates the similarity profile of gait cycle Ti in relation to all other gait cycles in the dataset. This vector effectively serves as a fingerprint of the gait cycle in the context of the entire gait database.

To identify key gait patterns within this high-dimensional space, K-means clustering is applied to the set of vectors {V1,…,Vn}. The K-Means algorithm partitions the data into k clusters {C1,C2,…,Ck}, with the objective of minimizing the sum of squared distances from each vector Vi to the centroid of its assigned cluster. This clustering process groups gait cycles with similar temporal profiles together, allowing for the identification of central gait patterns that represent typical walking behaviors.

The K-Means clustering objective is mathematically expressed as (2)minimizeC1,C2,…,Ck∑i=1n∑j=1kI(Vi∈Cj)‖Vi−cj‖2where I(Vi∈Cj) is an indicator function that assigns each gait cycle vector Vi to its nearest centroid cj.

For each cluster Ci, a representative gait template Mi is selected as the medoid time series, defined as (3)Mi=arg⁡minv∈Ci∑u∈CiDTW(v,u),where DTW(⋅,⋅) denotes the DTW distance between two time series.

Although cluster centroids are used internally during the DTW-KMeans clustering process, DTW distances are computed only between time series. Therefore, the final gait template for each cluster is selected as a medoid rather than the centroid, ensuring that all DTW distance computations are mathematically well-defined.

In this equation, vij refers to the j-th gait cycle vector within cluster Ci, and ci is the centroid of cluster Ci. The function argmin identifies the gait cycle vij that minimizes the DTW distance to the centroid, thus ensuring that Mi is the most representative gait cycle for cluster Ci. This template Mi effectively captures the central gait pattern of its cluster, providing a generalized representation of the gait behavior for that group.

The final set of representative templates is denoted as ℳ={M1,M2,…,Mk}, which serves as a benchmark for several tasks, including gait phase recognition, anomaly detection, and gait trajectory prediction. These templates reflect the core gait patterns of the user population, and they are flexible enough to accommodate variability in walking conditions.

The pseudocode for the DTW-KM template selection method is outlined in Algorithm 1. The algorithm describes the step-by-step procedure for segmenting the gait data, computing the DTW distances, performing the K-Means clustering, and selecting the representative gait templates. This method effectively handles the temporal dynamics of gait data, providing a set of templates that are not only temporally aligned but also clustered in a meaningful way.

In summary, the DTW-KM method offers an effective solution for extracting representative gait templates from diverse gait data. By combining the temporal alignment of DTW with the data clustering of K-Means, the method addresses the complexities of gait variability across different walking conditions and individual users. The resulting templates provide a valuable foundation for real-time gait analysis and prediction, supporting the development of more adaptive and accurate wearable exoskeletons and other assistive technologies.

Let n denote the number of gait sequences and L the average length of each sequence. The dominant computational cost of the proposed template selection method arises from the construction of the DTW-based similarity matrix. Computing the DTW distance between two sequences requires 𝒪(L2) time, resulting in an overall complexity of 𝒪(n2L2) for all pairwise comparisons.

The subsequent clustering step operates on the n×n similarity matrix. Assuming k clusters and I iterations, the clustering complexity is 𝒪(Ikn2), which is negligible compared to the DTW computation since k≪n and I is typically small.

Template selection within each cluster is performed using a medoid-based strategy, requiring pairwise DTW computations within each cluster. The total complexity of this step is approximately 𝒪(n2kL2).

Overall, the proposed offline template construction method has a time complexity of 𝒪(n2L2) and a space complexity of 𝒪(n2). Since this process is performed offline, it does not affect the real-time performance of the online gait phase estimation and trajectory prediction.

Human walking patterns exhibit a high degree of regularity and repetitiveness, which allows for relatively straightforward estimation with minimal complexity. Using the DTW-KM method to capture motion patterns and match them with real-time sensor data, we can identify local gait changes and predict gait phases with high precision. To further enhance the accuracy of these predictions, we have developed an integrated local-global template matching algorithm. This approach is designed to combine both local adjustments, reflecting immediate changes in the user’s gait, and global template matching, which maintains consistency with the overall walking pattern. The flow of this method is illustrated in Fig. 3.

The final step involves updating the time window with the latest sensor data and repeating the template matching and fitting process. This iterative refinement allows the system to continuously adjust to dynamic changes in the user’s gait, ensuring that predictions remain accurate and responsive to real-time walking conditions.

In summary, the SCW template matching method provides an effective approach to real-time gait phase identification and prediction. By combining local adjustments with global template matching, it offers a flexible and adaptive solution for wearable devices to synchronize with the user’s natural gait. Iterative refinement of the model ensures that the system remains accurate over time, making it a valuable tool to improve the functionality and responsiveness of wearable exoskeletons and other assistive devices.

Real-time gait prediction presents significant challenges, particularly in terms of noise resilience and parameter stability. These factors are crucial for ensuring the smooth operation of assistive devices such as exoskeletons, which rely on accurate, real-time synchronization with the user’s natural movements. To address these challenges, we propose the Soft Constraint Weight (SCW) template matching algorithm. This method is specifically designed to enhance both the precision and stability of the prediction of the gait phase while optimizing computational resources. By incorporating soft constraints and a weighted loss function, the SCW algorithm can better adapt to dynamic walking conditions, ensuring that predictions remain accurate even as walking speed, terrain, or user fatigue fluctuate.

The experimental dataset was collected in-house to evaluate gait phase estimation and short-term trajectory prediction under diverse walking conditions. Fourteen healthy male adults (mean age: 24.3 years; mean body mass: 72.9 kg; mean height: 177.8 cm), with no reported musculoskeletal or neurological impairments, participated in the study.

During data acquisition, each participant wore a single IMU (Xsens DOT, Enschede, The Netherlands) mounted on the anterior tibial surface. The sensor was secured using an adjustable strap to minimize relative motion. The IMU coordinate frame was aligned with the tibial longitudinal axis and calibrated prior to collection. Kinematic data were streamed wirelessly at 60 Hz, including tri-axial angular velocity and acceleration. In this study, sagittal-plane tibial angular velocity was used as the primary input for gait phase estimation.

To ensure coverage of diverse gait dynamics, multiple walking conditions were recorded, including continuous level-ground walking, intermittent walking with frequent start–stop transitions, turning maneuvers, and static standing. Participants additionally performed simulated irregular gait patterns with increased variability in cadence and amplitude to approximate pathological features such as tremor-dominated motion.

The dataset comprises approximately 1500 segmented gait instances, including normal walking, rapid transitions, turning, standing, shuffling, and simulated pathological patterns. Transitions between locomotion and rest were explicitly included to evaluate robustness under non-steady-state conditions. For model development and evaluation, the dataset was partitioned into training (70%) and testing (30%) sets. All offline templates used in the proposed method were constructed exclusively from the training data, while the testing set was reserved strictly for performance evaluation.

Gait events, including heel strike, toe-off, and intermediate weight-transfer phases, were annotated offline using synchronized video recordings and non-real-time signal inspection. All experiments were conducted in a controlled indoor environment. For online evaluation, sequences with different motion modes were concatenated to emulate realistic daily walking scenarios involving alternating movement and rest.

To evaluate the real-time feasibility of the proposed framework, we measured its computational performance on a desktop platform equipped with an Intel Core i5-10400 CPU (2.90 GHz, up to 3.97 GHz) and 16 GB RAM. All algorithms were implemented in MATLAB/Python and executed in a single-threaded configuration.

The average execution time per prediction cycle, including gait phase estimation and trajectory prediction, was 4.2 ms, which is significantly lower than the sensor sampling interval (16.7 ms at 60 Hz). This confirms that the proposed method can operate in real time without introducing perceptible latency. For context, this is 3× faster than the typical single-threaded execution time of lightweight deep learning baselines (e.g., 12–15 ms for a TCN-based trajectory predictor) [25] and 2× faster than traditional model-based approaches (e.g., 8–10 ms for an extended Kalman filter with gait phase coupling) [26].

Unlike deep learning-based methods, the proposed framework does not require offline training, parameter tuning, or model updates during deployment. Memory consumption is limited to storing a small number of representative gait templates, making the method particularly suitable for embedded wearable systems with constrained computational resources.

To clearly distinguish the computational burden of different stages, the proposed framework separates processing into an offline template construction phase and an online gait estimation and prediction phase, as summarized in Table 1.

The offline stage involves DTW-based similarity computation and clustering, resulting in a higher computational cost. However, this stage is executed only once and does not affect real-time system performance.

In contrast, the online stage operates with linear complexity with respect to the window length and the number of gait templates. No iterative optimization or global DTW computation is performed online, ensuring low latency and stable real-time execution suitable for wearable exoskeleton systems.

In this phase, which involves the offline clustering and template generation process using the DTW-KM algorithm, and compare it to a traditional Euclidean distance-based clustering method. The primary objective of this phase is to evaluate the performance of the DTW-KM algorithm for gait cycle clustering and template generation, and to compare it against a traditional Euclidean distance-based clustering algorithm. To do this, we performed clustering on a specific gait dataset and computed the Within-Cluster Sum of Squares (WCSS) for varying numbers of clusters. The WCSS is a measure of the compactness of the clusters, and it is calculated as follows:(10)J=∑i=1k∑x∈Ci‖x−μi‖2where k is the number of clusters, Ci denotes the i-th cluster, x represents a data point in the cluster, and μi is the centroid of the i-th cluster.

The experiments were conducted by clustering the gait data into a range of cluster numbers, from k=2 to k=15. This range of clusters was chosen to observe how both clustering algorithms perform at different levels of granularity. The WCSS values were calculated for each clustering configuration, and the results are presented in the subsequent figures.

In this section, we present the evaluation of the SCW algorithm for real-time trajectory prediction and gait phase estimation. The evaluation focuses on assessing the algorithm’s prediction accuracy for up to 10 frames ahead, using metrics such as Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and the coefficient of determination (R2). Additionally, we compare the SCW performance with two ablation studies: one without the quadratic weighting (QW) and one without the soft constraint (SC), as summarized in Table 2.

The results in Table 2 show that the SCW method demonstrated strong performance across all prediction frames, consistently achieving low RMSE, MAE, and high R2 values. Notably, even for predictions as far ahead as 10 frames, the SCW algorithm maintained high accuracy. For example, when predicting a single frame, the SCW method achieved an RMSE of 5.81, an MAE of 4.57, and an R2 value of 0.93. As the prediction horizon increased to 10 frames, the performance remained stable, with the RMSE reaching 5.97, the MAE increasing slightly to 4.55, and the R2 value dropping marginally to 0.93. This demonstrates the SCW method’s capability for long-term prediction without significant loss in accuracy.

In contrast, the removal of soft constraints (Ablation SC) and quadratic weighting (Ablation QW) resulted in noticeable declines in performance, especially for longer-term predictions. For example, without the soft constraints, the RMSE increased by 0.26 for 1-frame predictions and continued to rise for longer prediction horizons, while the R2 value dropped significantly by the 10-frame prediction (from 0.93 with SCW to 0.90 without SC). This highlights the importance of incorporating soft constraints in maintaining prediction stability and reducing overfitting.

The inclusion of quadratic weighting also showed an improvement in prediction accuracy, especially for the first few frames, as seen in the improvement of the RMSE values in the first few predictions with quadratic weighting. These findings confirm the effectiveness of both soft constraints and quadratic weighting in improving the SCW algorithm’s prediction precision.

The DTW-KM algorithm effectively addresses the challenge of generating diverse, representative gait templates for various walking scenarios. By incorporating DTW and K-Means clustering, the method captures complex, time-varying gait dynamics and groups them into meaningful clusters that reflect different walking speeds and patterns. The clustering results show clear distinctions between gait cycles of different speeds, with consistent cluster separation observed in the DTW distance matrix. For instance, slower gaits were distinctly categorized into one cluster, while normal and irregular gait patterns were represented in separate clusters. These templates, once extracted, provide a solid foundation for real-time matching and prediction tasks.

The versatility of the DTW-KM algorithm is particularly important in addressing the inherent variability in human gait, both across different users and in varying environmental conditions. By adapting to the specific characteristics of each gait cycle, the DTW-KM method offers a more accurate and personalized approach to gait phase recognition.

The SCW algorithm is a key component in this study, enabling real-time trajectory prediction and continuous phase estimation. By integrating soft constraints and a quadratic weighted loss function, SCW stabilizes the prediction model and reduces oscillations, ensuring smooth and accurate adjustments to the gait trajectory over time. The results of the ablation study reveal the significant impact of soft constraints and quadratic weighting in improving prediction accuracy. Without these features, the model showed notable performance degradation, especially for longer prediction horizons. This emphasizes the importance of incorporating stability mechanisms such as soft constraints to maintain accuracy over time.

The SCW method’s ability to predict up to 10 frames ahead, with minimal loss in accuracy, is particularly promising for practical applications in exoskeletons. Even as the prediction horizon extends, SCW maintains high prediction performance, as evidenced by its consistently low RMSE and MAE values. These results suggest that SCW can effectively assist in real-time control of wearable devices, where continuous prediction of gait phases is required for smooth and responsive operation.

Our evaluation of SCW’s phase estimation performance against established methods demonstrated its strong alignment with existing literature. SCW’s accuracy in identifying key gait phases such as HS, FF, HO, and TO is comparable to or even better than other methods, particularly in real-time scenarios. The timing discrepancies for these phases were within an acceptable range when compared with previous studies, indicating that SCW can reliably estimate phase transitions with high precision. To further clarify the advantages of the proposed approach, a qualitative comparison with representative gait prediction and phase estimation methods is summarized in Table 4.

Continuous phase estimation refers to the ability to provide smooth and continuous gait phase information rather than discrete event detection. Real-time performance indicates whether the method can be executed with low latency on embedded or wearable systems. Computational complexity reflects the relative computational burden of the method. Comfort potential refers to the capability of the control-related gait prediction method to reduce abrupt assistance changes and improve human–exoskeleton interaction smoothness.

While SCW performs well in detecting gait phases, there are some areas for improvement. For instance, the variability observed in the estimation of the FF and HO phases indicates that more fine-tuning may be needed for these specific transitions, especially when dealing with highly variable or irregular gaits. Future work could focus on refining the SCW method to improve phase detection in these instances, possibly through more advanced feature extraction techniques or multi-modal sensor fusion.

Real-time performance is a critical requirement for ankle exoskeleton control systems. Unlike learning-based gait prediction methods that require computationally intensive model inference, the proposed method is based on online DTW and template-based trajectory prediction, which involve only distance calculation and simple mapping operations.

The computational complexity of the DTW-based phase recognition is bounded due to the use of short sliding windows, and the trajectory prediction stage introduces negligible computational overhead. As a result, the proposed method is suitable for real-time implementation on embedded systems commonly used in wearable exoskeletons.

Compared with deep learning and optimization-based methods, the proposed approach provides a favorable trade-off between prediction accuracy and real-time feasibility.

Compared with healthy users, individuals with partial hemiparesis typically exhibit asymmetric gait patterns, increased stride-to-stride variability, and reduced voluntary control of the ankle joint. These characteristics make hemiparetic users more sensitive to control latency, phase misalignment, and abrupt assistance changes when wearing ankle exoskeletons.

In such cases, inappropriate timing or unstable control outputs may trigger strong resistance responses, including discomfort, altered muscle activation, or gait instability. Therefore, control strategies validated on healthy subjects may not directly translate to impaired populations without additional robustness mechanisms.

The proposed method incorporates DTW-based temporal alignment and soft-constrained online parameter adaptation to mitigate these issues. By suppressing abrupt parameter changes and enabling continuous gait phase estimation with short-term prediction, the framework aims to reduce the likelihood of strong adverse responses when applied to hemiparetic gait assistance.

Although the experimental evaluation in this study is conducted on healthy subjects, the algorithmic design explicitly accounts for gait irregularities and temporal distortions commonly observed in hemiparetic gait. Future work will include clinical experiments with hemiparetic users to quantitatively evaluate user comfort, resistance response, and human–exoskeleton interaction safety.