Cross-step detection using center-of-pressure based algorithm for real-time applications

Abstract

Background

Gait event detection is crucial for assessment, evaluation and provision of biofeedback during rehabilitation of walking. Existing online gait event detection algorithms mostly rely on add-on sensors, limiting their practicality. Instrumented treadmills offer a promising alternative by utilizing the Center of Pressure (CoP) signal for real-time gait event detection. However, current methods have limitations, particularly in detecting cross-step events during perturbed walking conditions.

Methods

We present and validate a CoP-based algorithm to detect gait events and cross-steps in real-time, which combines thresholding and logic techniques. The algorithm was evaluated on CoP datasets from healthy participants (age range 21–61 years), stroke survivors (age range 20–67 years), and people with unilateral transtibial amputation (age range 28–63 years) that underwent perturbation-based balance assessments, encompassing different walking speeds. Detected gait events from a simulated real-time processing operation were compared to offline identified counterparts in order to present related temporal absolute mean errors (AME) and success rate.

Results

The proposed algorithm demonstrated high accuracy in detecting gait events during native gait, as well as cross-step events during perturbed walking conditions. It successfully recognized the majority of cross-steps, with a detection success rate of 94%. However, some misclassifications or missed events occurred, mainly due to the complexity of cross-step events. AME for heel strikes (HS) during native gait and cross-step events averaged at 78 ms and 64 ms respectively, while toe off (TO) AME were 126 ms and 111 ms respectively. A statistically significant difference in the algorithm's success rate score in detecting gait events during cross-step intervals was observed across various walking speeds in a sample of 12 healthy participants, while there was no significant difference among groups.

Conclusion

The proposed algorithm represents an advancement in gait event detection on instrumented treadmills. By leveraging the CoP signal, it successfully identifies gait events and cross-steps in the simulated real-time processing operation, providing valuable insights into human locomotion. The algorithm's ability to accommodate diverse CoP patterns enhance its applicability to a wide range of individuals and gait characteristics. The algorithm's performance was consistent across different populations, suggesting its potential for diverse clinical and research settings, particularly in the domains of gait analysis and rehabilitation practices.

Introduction

Gait analysis plays a crucial role in understanding human locomotion and assessing the effectiveness of rehabilitation therapies [1,2,3]. Accurate and reliable real-time detection of gait events, such as heel strikes (HS) and toe offs (TO), is essential for monitoring various gait parameters as well as for providing real-time biofeedback during gait training. Such immediate feedback allows researchers and clinicians to evaluate data in real-time, as well as to make on-the-fly adjustments and interventions. In rehabilitation, it is crucial to tailor exercises to an individual's gait pattern and abilities to maximize the effectiveness of the training. This ensures that the exercises are both appropriate and beneficial for the individual's specific needs. Real-time gait event detection also plays a key role in prosthetics, enabling responsive control for artificial limbs and resulting in a more natural walking experience. Additionally, it is essential for fall detection systems for the elderly, triggering timely preventive measures. Overall, real-time gait event detection enhances customization and optimization in rehabilitation programs, ensuring effective and personalized treatment. Conventionally, online gait event detection algorithms rely on various sensors (Inertial Measurement Units – IMU, pressure insoles, angular sensors or optical tracking systems) attached to the lower limbs or body to capture the kinematics of movement [4,5,6,7]. Particularly, IMU systems, whether using a single or multiple units, have the capability to detect gait events, though their success depends on several factors such as the quality of the IMU units, signal processing techniques, individual's gait behaviour or suitable sensor positioning [8, 9]. However, these methods can be often burdensome for participants, have potential issues with synchronization and often limit the practicality of the procedure setup, especially for everyday use in a clinical environment [10].

In recent years, instrumented treadmills equipped with force transducers to measure Center of Pressure (CoP) during walking, including single or split-belt treadmill variations, have gained popularity as a valuable tool for gait analysis and training [11,12,13,14]. Here, the CoP represents the point where the vertical ground reaction force is applied and can provide valuable insights into gait dynamics [15,16,17,18]. Leveraging the CoP signal, researchers have developed real-time algorithms for detecting gait events and gait subphases without the need for additional human add-on sensors [16, 19,20,21]. Additionally, force signals from the instrumented split-belt treadmills have been used by the researchers to employ a thresholding method based on force data for detecting gait events [22, 23]. However, it's important to note that this technique is applicable solely during native (unperturbed) gait, where each leg makes contact with each belt of the treadmill. Conversely, in the case of a cross-step, both feet are in contact with only one belt, rendering the conventional method ineffective.

Two related studies have examined the CoP-based algorithm, one involving healthy participants and the other focusing on subjects with amputations [16, 20]. In the both studies, participants performed their native gait, revealing asymmetrical butterfly-shaped CoP signals assessed in people with amputations [20] as opposed to the unimpaired gait in healthy subjects [16]. The acquired signals were analyzed to assess specific gait characteristics such as step length, width, time, and durations of double and single support. However, these studies did not include analysis and evaluation of perturbed walking conditions.

One particular challenge for real-time gait event detection algorithms is accurate identification of stepping responses during perturbation-based balance training (PBT). PBT has emerged as a valuable approach for improving balance control and reducing the risk of falls in the elderly and neurologically impaired [24,25,26]. During PBT, individuals experience controlled perturbations that challenge their stability, leading to different reactive balance strategies. These strategies involve adjustments in step length and width to regain dynamic stability. Among these adjustments, cross-steps have been identified as reactive balance responses following outward perturbations, where individuals cross their legs during the gait cycle to stabilize the body and restore equilibrium [27,28,29]. Therefore, accurately detecting cross-steps poses a significant challenge to traditional algorithms, as cross-steps disrupt the expected "butterfly-shaped" pattern of CoP movement following externally or internally elicited perturbation [27, 28]. While these studies have explored gait abnormalities caused by pathology or varying step widths and lengths, the specific scenario of crossing legs during walking has not been thoroughly investigated. Consequently, there is a gap in contemporary methods that can reliably examine cross-step events. Currently, the lack of real-time algorithms capable of detecting and quantifying cross-steps without the need for wearable sensors is a notable limitation hindering the use of real-time biofeedback during gait training.

The aim of this study was to develop a real-time algorithm that utilizes the CoP signal from a single-belt instrumented treadmill to accurately detect HS and TO events during both native and perturbed gait, specifically addressing cross-step events. We conducted extensive experiments to evaluate the algorithm's reliability and accuracy on diverse populations, including healthy participants, subjects with unilateral transtibial amputations, and individuals after stroke, across different walking speeds.

Methods

Algorithm description

The operational overview of the algorithm is shown in Fig. 1. The algorithm that was designed to detect gait events in real-time relies exclusively on the CoP signal and comprises two main components: adaptive relay-like functions and logic for determining gait events. Two adaptive relay-like functions, one for CoP_ML and the other for CoP_AP axis, monitor the limits of the CoP signal during each gait phase (LeftSingleSupport, DoubleSupportToRight, RightSingleSupport and DoubleSupportToLeft) and ensure the CoP signal pushes the limits, denoted as UpperLimit_ML,AP and LowerLimit_ML,AP, in anteroposterior (AP) and mediolateral (ML) direction. Thereafter, relay-like functions dynamically adjust the upper T_U and lower T_L thresholds for either the ML or AP axis, according to the rules outlined in equations (1) and (2). The parameter Ratio_ML,AP defines the position of thresholds T_U and T_L between UpperLimit_ML,AP and LowerLimit_ML,AP. Both thresholds T_U and T_L are also limited between minimal T_min and maximal value T_max as shown in equation (3), to ensure they are neither too close nor too far from the UpperLimit_ML,AP or LowerLimit_ML,AP boundaries. By utilizing equation (4), the threshold Threshold_ML,AP then selects the appropriate threshold (T_U or T_L) based on the ongoing function state. In the ML direction, the algorithm indicates if the CoP is on the left or right “wing” of the butterfly shape (RightSide or LeftSide). In the AP direction, it indicates whether the CoP is positioned at the front or back of the butterfly shape (FrontSide or RearSide).

Fig. 1.

The algorithm for real-time gait event and cross-step detection operates by employing a thresholding technique applied to the Center of Pressure (CoP) signal

$${T}_{U}={UpperLimit}_{ML, AP}-{Ratio}_{ML,AP} \left({UpperLimit}_{ML,AP} -{LowerLimit}_{ML,AP}\right)$$

(1)

$${T}_{L}={LowerLimit}_{ML, AP}+{Ratio}_{ML, AP} \left({UpperLimit}_{ML, AP} -{LowerLimit}_{ML, AP}\right)$$

(2)

$${T}_{U,L}=\left\{\begin{array}{ccc}{T}_{min}& if& {T}_{U,L}\le {T}_{min}\\ {T}_{U,L}& if& {T}_{min}<{T}_{U,L}< {T}_{max}\\ {T}_{max}& if& {T}_{U,L}\ge {T}_{max}\end{array}\right.$$

(3)

$${Threshold}_{ML, AP}=\left\{\begin{array}{ccc}{T}_{U}& if& RightSide\ or\ FrontSide\\ {T}_{L}& if& LeftSide\ or\ RearSide\end{array}\right.$$

(4)

Upon the CoP crossing either Threshold_ML or Threshold_AP, the adaptive relay-like functions switch sides and provide output to identify potential operational sides: Side_ML (RightSide or LeftSide) and Side_AP (FrontSide or RearSide). An example of adaptive relay-like function is shown in Fig. 2. The logic component of the algorithm then monitors the crossings of the thresholds and provide gait events at the corresponding instances of threshold crossings. Essentially, if both the CoP_ML and CoP_AP cross their respective thresholds (Threshold_ML and Threshold_AP) during the same gait phase, the algorithm recognizes it as a normal gait and outputs the occurrence of the corresponding gait event (LHS, RTO, RHS or LTO), allowing for asymmetric CoP patterns resembling a “butterfly” shape. However, if CoP crosses the threshold in AP axis twice consecutively, without any threshold crossing in the ML axis, the algorithm identifies it as a cross-step event. In such cases, the gait events are determined based on the crossings of the Threshold_AP. The algorithm terminates the cross-step state when the CoP_ML crosses Threshold_ML again. The parameters of the algorithm were configured as follows: Ratio_ML and Ratio_AP were both assigned a value of 0.2. For the AP direction, T_min and T_max were both set to 0.04 m, while for the ML direction, T_min and T_max were set to 0.05 m and $\infty$ m (infinity), respectively. The algorithm parameters were chosen based on our prior experience from previous experiments where the algorithm was utilized, acquired through the iterative experimentation and refinement to ensure optimal performance of the algorithm. These parameters were consistent across all simulations conducted on CoP datasets in the present study.

Fig. 2.

Adaptive relay-like function used in the algorithm, where the threshold adapts based on the upper and lower limits of the CoP. The function alters its state (sides) whenever CoP crosses the threshold, which is seen at the switch points

Participants

This study utilized data from our previous measurements, involving a total of forty-four participants [3, 18, 28, 30]. These participants represent three groups: thirteen stroke survivors (2 females, 5 with left-sided hemiparesis in subacute phase, age range 20–67 years, mean 48 ± 8.7; height 178 ± 8 cm; body mass 79 ± 11 kg), ten subjects with transtibial amputation (2 females, 5 with left-sided amputation, age range 28–63 years, mean 50 ± 10; height 176 ± 11 cm; body mass 87 ± 18 kg) and twenty-one healthy adults (3 females, age range 21-61 years, mean 36 ± 11; height 179 ± 6 cm; body mass 77 ± 9 kg) without any known neurological, muscular or orthopaedic problems. The inclusion criteria for the stroke survivors and subjects with transtibial amputation required them to be independent in ambulation (with a functional ambulation category FAC of at least 5 on a scale from 1 to 6 [31]), capable to walk independently or under supervision without the use of walking aids, and able to follow instructions. There were no specific inclusion criteria for healthy adults. The study received approval from The National Medical Ethics Committee of the Republic of Slovenia and all participants provided written informed consent.

Procedures and measurements

The CoP data was obtained during our previous studies, which assessed dynamic balancing responses using a Balance Assessment Robot for Treadmill Walking (BART). BART utilizes a custom-designed, wide instrumented treadmill and an actuated pelvic link with a pelvis brace. In these studies, participants experienced perturbing force impulses applied to the pelvis while walking on the instrumented treadmill [3, 18, 28, 30]. Each participant started gait balance assessment with an introductory session in order to familiarize with treadmill walking as well as with the perturbation amplitudes that were normalized to 5%, 10% or 15% of the participant’s body weight. To establish their natural gait pattern (native gait), each participant walked for 2–3 minutes without any perturbations (unperturbed walking), followed by an approximately 7–10 minutes assessment during which force impulses were randomly applied to either the left or right side of the pelvis every 8 seconds on average. The variation in trial lengths for gathering native and perturbed gait data was due to differences in the protocols used in our previous studies, where varying walking speeds, as well as differing types and amounts of perturbations, were applied. The experimental protocol is shown in Fig. 3. The perturbing force impulses, directed mediolaterally, provoked reactive balance responses that often led to cross-stepping behaviour following the onset of the perturbation. CoP signals were obtained through four precise force transducers (K3D120, ME Systeme GmbH) placed underneath the treadmill and equipped with measuring amplifiers (measuring amplifiers GSV-1A4, ME Systeme GmbH). The perturbing force impulses were triggered when the participant entered left or right stance phase (i.e. at left or right HS). Our database consisted of three datasets, each associated with a different walking speed: (1) sessions with healthy participants walking at speeds of 0.4 m/s, 0.6 m/s, and 0.8 m/s consecutively; (2) sessions with stroke participants walking at a speed of 0.4 m/s; and (3) sessions with subjects with transtibial amputation walking at a speed of 0.5 m/s.

Fig. 3.

Experimental protocol consists of introductory session followed by unperturbed walking to capture participants' native gait and perturbed walking to induce cross-step reactions

Data processing and evaluation

The algorithm script was written and evaluated in the post hoc simulated real-time processing operation using Matlab R2021a (The MathWorks, Inc.). CoP signals from both the native gait and perturbed gait of each participant were sampled at a frequency of 200 Hz. Subsequently, CoP signals from both walking conditions were processed using the algorithm simulation. The simulation outputs consisted of the identification of gait events including left and right HS, left and right TO and cross-step events. The native gait contained approximately 20 to 60 gait cycles, depending on duration of the unperturbed walking and walking speed. During perturbed gait we specifically focused on collecting cross-step performances, which encompassed eight consecutive gait events starting from the HS event. Moreover, the CoP_AP signal was subjected to offline manual analysis to precisely determine the locations of each gait event. Detecting gait events from the CoP pattern offline is straightforward when the CoP forms a butterfly shape. However, during cross-step movements, the butterfly shape is lost in the CoP_ML signal while retained in the CoP_AP signal, maintaining its saw-shaped appearance from unperturbed gait. In such cases, gait events remain identifiable when analyzed offline. Specifically, the peaks of the CoP_AP signal were identified, with positive peaks indicating TO events (aligned with the walking direction), while negative peaks represented HS [20]. This approach served as the gold standard in the validation experiment process, similar to the methodology employed in [7]. Conversely, if the CoP is disrupted by undefined oscillations due to unconventional alternative stepping such as foot pivoting, cross-uncrossing, rear foot crossing as described in [27], such alternative stepping responses (not recognized as cross-steps) were excluded from the analysis. Consequently, we calculated the absolute mean errors (AME, in ms) to assess the algorithm's temporal accuracy in detecting gait events by subtracting offline identified gait event times from the counterparts obtained from the algorithm's output (error is positive for a delayed algorithm’s estimation). Histograms were generated to illustrate the AME of the gait events for each walking speed and participant group individually, with the average and standard deviation of the calculated AME provided. The primary outcome of this study was the algorithm’s success rate (%) of detecting cross-step events. The success rate (%) for each participant was defined as the ratio between successfully recognized cross-steps and the total number of cross-steps performed at each walking speed. In the case of the natural gait, the success rate (%) was determined based on both successfully and unsuccessfully detected gait events.

Statistical analysis

A repeated measures analysis of variance (ANOVA) was employed to assess the potential relationship between the success rate of cross-step detection by the algorithm and various walking speeds. This analysis incorporated data from a group of 12 healthy participants, examining walking speeds of 0.4 m/s, 0.6 m/s, and 0.8 m/s. To investigate the impact of pathology on the algorithm's cross-step detection success rate, a one-way ANOVA was utilized. Specifically, the analysis compared the cross-step detection success rates of the algorithm for three groups: a healthy group walking at 0.4 m/s, a stroke group walking at 0.4 m/s, and an amputee group walking at 0.5 m/s. The statistical significance level was set at 5%.

Results

Figure 4 illustrates the typical CoP pattern of cross-step performance together with the consecutive steps following the perturbation (Fig. 4b) when compared to the native gait pattern (Fig. 4a). In the native gait, the CoP exhibits a distinctive butterfly-like shape, conversely, in the cross-step gait the CoP deviates from the butterfly shape, either deflecting to the left (as depicted in Fig. 4b) or to the right side of the butterfly. We show that accurate HS detection (indicated by solid circle markers) occurs at the two bottom extremes of the CoP butterfly and TO occurs at the two top extremes (indicated by solid square markers). On the other hand, gait events detected in the simulated real-time processing operation using the algorithm (blank circle and square markers) exhibit a temporal AME in relation to the actual occurrences of gait events, particularly evident in the time-dependent graphs of CoP in Fig. 4c.

Fig. 4.

An illustration of the a) native gait and b) cross-step gait by showing consecutive steps and CoP pattern, and the c) time-dependent graphs of CoP, where markers represent gait events (toe offs, heel strikes) gathered manually offline (solid markers) and by the proposed algorithm (blank markers)

In the datasets comprising the CoP data from all 44 participants, we manually examined 2253 instances of cross-steps. In a simulated real-time processing operation, the proposed algorithm demonstrated successful recognition of 2120 cross-steps by identifying the correct order of all gait events within each cross-step interval (for example shown in Fig. 4c: LHS-RTO-RHS-LTO-LHS-RTO-RHS-LTO), where it neither omitted nor misattributed any gait events during these intervals. However, there were 133 cross-steps classified as failures, where at least one gait event within the cross-step period was recognized incorrectly (e.g. left HS instead of right HS) or missed entirely, even if the other gait events were recognized correctly.

Table 1 represents the simulation results of walking for three different speeds (0.4, 0.6, and 0.8 m/s) in the healthy group, walking at 0.4 m/s in the stroke group, and walking at 0.5 m/s in the amputee group. Simulation results contain calculated AME between true and detected gait events of native gait and cross-step gait, along with the corresponding success rates for native and cross-step gait. These results are also visualized as histograms in Figs. 5 and 6, showing the normalized frequency distributions of specific gait event AME. The first row of the histograms represents the combined AME of HS (combined left and right), while the subsequent row displays histograms for TO AME (combined left and right). Each participant's group is presented separately in these histograms.

Table 1. Detection temporal absolute mean errors (AME) and the algorithm’s success rate across groups

Fig. 5.

Normalized frequency distribution of heel strike and toe off detection absolute mean errors across participant groups and walking speeds during native gait. The mean values accompanied by the corresponding standard deviation are denoted as M (STD)

Fig. 6.

Normalized frequency distribution of heel strike and toe off detection absolute mean errors across participant groups and walking speeds during cross-step events. The mean values accompanied by the corresponding standard deviation are denoted as M (STD)

Figure 5 illustrates the AME of gait events under native walking conditions for all three groups, while Fig. 6 demonstrates the AME of gait events during cross-step periods. Each histogram includes the mean value and standard deviation of the corresponding gait event AME. On average, the AME for HS during native gait was 78 ms (standard deviation 32 ms), while during cross-step events, it decreased to 64 ms (standard deviation 28 ms). In contrast, TO AME exhibited higher average values of 126 ms (standard deviation 47 ms) during native gait and 111 ms (standard deviation 47 ms) during cross-step events. The simulation of the algorithm conducted on native gait data successfully detected all gait events, which show 100% success rate. The success rate of identifying cross-step events and therefore all gait events in their proper sequence, reached 94% (standard deviation 11%).

A repeated measures ANOVA conducted on a sample of 12 healthy participants show statistically significant difference in the algorithm’s cross-step detection success rate score across different walking speeds (F(2, 11) = 5.95, p = 0.0086). A one-way ANOVA revealed that there was no statistically significant difference in the algorithm’s cross-step detection success rate among different pathologies—stroke, amputee and a healthy group (F(2, 41) = 2.08, p = 0.1374).

Discussion

In this study we presented and validated a real-time gait event detection algorithm that utilizes the CoP signal from the single-belt instrumented treadmill. By focusing on the CoP signal, the proposed algorithm eliminates the need for additional sensors attached to the participant's lower extremities or body, simplifying the setup process for everyday rehabilitation therapy. The algorithm was designed to overcome the limitations of current CoP-based gait event detection methods, which may not identify cross-step events. The results of the study demonstrated the effectiveness and reliability of the proposed algorithm in accurately detecting cross-step events, as well as other gait events during native gait. Validation was performed on different datasets assessed during native and perturbed walking requiring cross-steps in healthy and impaired populations.

The distinctive pattern of cross-step performance, characterized by a deviation from the butterfly-shaped CoP movement observed in native gait, formed the basis for developing the algorithm. The algorithm was successful when recognizing gait events during native walking patterns of all participants. Furthermore, it successfully recognized the majority of cross-steps, with a high average accuracy rate of 94%. However, there were some cases where gait events within the cross-step period were misclassified or missed entirely, resulting in a failure rate of approximately 6%. These misclassifications could be attributed to the complexity of individual cross-step events, which disrupted the CoP pattern and posed a challenge to the algorithm. It is important to note that in instances of misclassifications, the algorithm continues its operation without interruption. Rather, it simply overlooks the occurrence of a gait event and awaits the subsequent one, thereby demonstrating high level of robustness, which is particularly needed for providing real-time biofeedback during gait training.

The AME in detecting gait events were analyzed for both native gait and cross-step events. The algorithm exhibited a temporal AME in detecting gait events compared to their actual occurrences, which is a common characteristic of real-time gait event detection algorithms [6, 7, 20, 32]. In a comparison of studies, TO gait event detection AME was found to be 31 ms on average, while HS AME was around -3 ms, indicating early estimation [20]. Similarly, another study reported average AME of 11 ms for HS and 29 ms for TO across various locomotion tasks, including walking, running, and directional changes [32]. Multiple studies utilizing either single or multiple IMUs have reported gait event detection times during normal walking to be within 100 ms [5]. Notably, none of the mentioned studies, including those reviewed, conducted perturbation-based gait event detection, especially during cross-step movements. However, when comparing our results of AME, it was seen that the AME of the proposed algorithm are slightly higher on average. Such increased AME can be attributed not only to the nature of the threshold-based algorithm but may also be influenced by the lower walking speed in our experiments compared to the substantially higher walking speeds in comparative studies.

In the presented study, two key features characterize AME in gait event detection: (1) TO AME are consistently higher compared to HS AME across all subsets—this was also observed in comparable studies [20, 32]; and (2) AME (both TO and HS) decreased with higher walking speed. These characteristics are influenced by both the algorithm's design and the CoP behaviour. The AME are directly related to the algorithm's parameters, including the Ratio (ML or AP) and T_min, T_max, which introduce AME in gait event detection. However, despite similar parameter choices for both axes, higher TO AME are mainly influenced by the CoP pattern. TO events are detected in the early single support period, where the CoP velocity is significantly lower than in the double support period, where HS is detected. Consequently, CoP velocity dictates the speed at which the CoP reaches the threshold line, resulting in faster HS detection compared to TO. Therefore, with increasing walking speed, TO and HS are detected more rapidly. Additionally, a larger subset of healthy participants and stroke patients exhibit higher AME and lower success rates at a walking speed of 0.4 m/s, with stroke patients showing slightly higher success rates at this speed compared to healthy participants. The lower success rate in healthy subjects may be attributed to higher CoP oscillations during single support, as our previous research suggests that participants often attempt to counteract perturbations on the stance leg, leading to increased CoP oscillations [28]. These high CoP oscillations can result in the algorithm failing to detect one or more gait events. Considering the inclusion of three distinct groups (healthy, stroke, and amputee) and the variation in walking speeds, we conclude that the results from all sub-groups are representative and do not compromise the method's reliability when applied to other subjects.

The algorithm has variety of parameters that implicitly define the accuracy and reliability of detecting gait events and cross-steps. The CoP might be very fluctuant due to various possible reasons such as: variable pathological gait as also reported in [12] or the aforementioned the initial attempt to counteract perturbations in healthy population [28], precision and resolution of the force plates, and the CoP filtering [33]. In these cases, the parameters in the proposed algorithm such as threshold ratio need to be appropriate not to false detect local extrema of the CoP. There are also low-pass filters embedded in the measuring amplifiers or additionally added in the data acquisition software in order to cut away higher degree of oscillations of the CoP. However, real-time filtering introduces time AME into the system by itself. Similar issue was reported in [20], where more conservative CoP peak detection sensitivity introduces temporal AME of 0.1 s between true CoP peak occurrence and the online detected one.

The algorithm's performance was evaluated on different populations, including healthy participants, subjects with unilateral transtibial amputation, and individuals after stroke. The results demonstrated that the algorithm was effective across these populations, with no significant difference in the cross-step detection success rate among different pathologies. This finding suggests that the algorithm can be applied in diverse clinical and research settings, making it a potentially valuable tool for gait analysis and training in clinical rehabilitation.

Limitations

The present study on the proposed real-time CoP-based algorithm that detects gait events and cross-steps has several limitations. To ensure successful operation of the algorithm, at least one of the CoP (ML or AP) signals must exhibit deterministic behaviour, clearly displaying signal peaks. In cases where the CoP signals are non-deterministic and the CoP oscillates unpredictably during stepping, the algorithm's functioning may be compromised. However, once a predictable CoP pattern is established, the algorithm is designed to persistently operate. Additionally, if the CoP signal lacks clear expression, causing the algorithm to fail in detecting gait events, those events will be skipped until the CoP pattern becomes sufficiently evident. This limitation highlights the dependency of the algorithm's performance on the clarity of the CoP signal, indicating that it may not accurately capture all gait events in situations where the CoP expression is indistinct. Another two limitations of this study are related to the dataset used for algorithm evaluation. The first stems from the inclusion of patients and healthy individuals without considering gender or age, hindering the establishment of a balanced representation. Despite potential age-related differences, our primary focus was not on analysing postural response disparities but rather on evaluating the algorithm's success rate and time AME in online gait event detection across diverse datasets, especially those involving subjects performing cross-steps. Second, we included a variety of gait measurements from our database, where participants performed cross-steps during studies on dynamic balance responses following perturbations. Here, the datasets across different groups included varying walking speeds and perturbation amplitudes ranging from 5% to 15% of body weight. This variability in the dataset made it challenging to conduct direct statistical analyses. However, the diversity in the datasets proves beneficial for the analysis of the algorithm itself, as it exposes the algorithm to a wider range of CoP behaviours and allows for a comprehensive evaluation.

Conclusion

In conclusion, the proposed algorithm for detecting gait events and cross-steps demonstrates great potential for various applications in the field of biofeedback training and virtual reality. By effectively identifying gait events and cross-steps, the algorithm enables perturbation triggering and ensures the safety of individuals by detecting also cross-steps. Moreover, the algorithm's adaptive relay-like function opens up possibilities for triggering or monitoring other biomechanical signals, extending its utility beyond gait analysis. An additional strength of the algorithm is its resilience to signal drifting, allowing for accurate and reliable detection over extended periods. Additionally, its ability to accommodate diverse CoP patterns enhances its applicability to a wide range of individuals and their gait characteristics.

Overall, the proposed algorithm represents a significant advancement in gait event detection during walking on instrumented treadmills. By leveraging the CoP signal, this real-time algorithm provides a valuable tool for accurately identifying cross-step events, offering valuable insights into human locomotion. These findings have far-reaching implications for gait analysis and rehabilitation techniques, promising to enhance patient care and treatment outcomes without the need of add-on sensors. Further research can focus on refining the algorithm and validating its performance in real-world scenarios to facilitate its widespread utilization.