Review Reports - EMG-Based Simulation for Optimization of Human-in-the-Loop Control in Simple Robotic Walking Assistance

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This manuscript investigates an EMG-based simulation framework for human-in-the-loop (HIL) optimization in exoskeleton assistance, comparing multiple machine learning models and optimization algorithms. While the topic is relevant and has practical potential, the paper currently suffers from significant shortcomings in novelty, methodological clarity, and depth of discussion. Substantial revisions are required before the manuscript can be considered for publication. Specific comments are as follows:

The introduction does not sufficiently highlight the novelty or distinguish this study from existing HIL simulation frameworks, which may make the contribution appear incremental.

The integration of datasets and data augmentation procedures are insufficiently detailed, lacking clear workflow diagrams and justification of parameter choices. Optimization algorithm settings and sensitivity analysis are also missing.

The study relies entirely on simulation data without real-world exoskeleton validation, raising concerns about the authenticity and practical reliability of the findings.

In summary, this work holds substantial research significance and potential application value, especially in the context of personalized HIL optimization for exoskeletons. However, the overall quality of the manuscript is currently too low, with issues including insufficiently highlighted novelty, unclear methodological description, lack of experimental validation, and inconsistencies in results. Without substantial revision, it is difficult to provide further constructive feedback. Therefore, the manuscript requires major revision before it can be reconsidered for publication.

Author Response

Dear Editor and Reviewers,

We appreciate your time and effort in evaluating our manuscript, EMG-Based Simulation for Optimization of Human-in-the-Loop Control in Simple Robotic Walking Assistance. In response to your feedback, we have edited key sections of the manuscript using Word’s track changes mode. A summary of our edits (in blue font color) is provided on the following pages, and we believe the content and clarity of the manuscript have been further strengthened.

As always, we are grateful for the opportunity to refine the content of our manuscript.

Sincerely,

Arash Mohammadzadeh Gonabadi

Nathaniel H. Hunt

Farahnaz Fallahtafti

Reviewer 1

Comments and Suggestions for Authors

We sincerely thank the reviewer for the feedback.

R1Q1 - The introduction does not sufficiently highlight the novelty or distinguish this study from existing HIL simulation frameworks, which may make the contribution appear incremental.

We thank the reviewer for this critical point. We have revised the Introduction to clearly articulate how our study advances beyond existing HIL frameworks and EMG-based control studies. Unlike prior work that (i) performs HIL optimization using muscle synergies to tailor hip-exoskeleton torque profiles [3] and (ii) uses sEMG biofeedback to guide HITL trajectory selection for lower-limb exoskeleton motion planning [4], our contribution is a surrogate-modeling simulation framework that (a) predicts EMG-RMS landscapes across assistance parameters, (b) systematically benchmarks nine surrogate models and seven global optimizers head-to-head, and (c) formalizes data integration, augmentation, and sensitivity reporting to support reproducible, pre-experimental algorithm selection. This extends prior metabolic-landscape simulations and our earlier metabolic-cost optimization study by shifting the objective to neuromuscular effort (EMG-RMS)—a faster, more responsive physiological target—while providing a generalized pipeline (surrogate → optimizer → sensitivity) that reduces human testing burden yet preserves physiological relevance. We added a dedicated “What is new” paragraph detailing these distinctions.

Again, we appreciate this comment and agree that innovation must be clear beyond changing the objective. Our intention was not a simple substitution but a conceptual shift and methodological expansion motivated by the distinct properties and clinical utility of EMG:

Different physiology. Metabolic rate is slow and global; EMG is fast and muscle-specific. EMG responds within hundreds of milliseconds, enabling short-bout HIL protocols, immediate feedback, and muscle-targeted assistance (e.g., hip extensors), which are crucial for patients with weakness, selective activation goals, or fatigue intolerance. This opens HIL use cases where metabolic endpoints are impractical.

New algorithmic demands and rankings. Because the response surface of EMG-RMS differs from metabolic landscapes (faster dynamics, sharper local structure, and muscle-group specificity), optimizer behavior and rankings can change. Our framework, therefore, re-benchmarks seven optimizers under an EMG objective and adds a hyperparameter sensitivity analysis to quantify robustness. This goes beyond our prior work by asking a new algorithm-selection question for EMG-driven HIL.

Pre-screening for clinical HIL with dual goals. Many real studies will pursue two targets (energy + muscle engagement). By mapping which optimizers are most stable/efficient for EMG-RMS, we provide actionable guidance for single-objective EMG trials and lay the groundwork for future multi-objective HIL (e.g., minimizing metabolic cost while constraining EMG in target muscles).

Methodological additions beyond the objective: (i) Nine surrogate models (not one) benchmarked head-to-head for EMG-RMS, (ii) Seven global optimizers under a unified protocol, (iii) New sensitivity analysis (±10% hyperparameter perturbations) to assess robustness, (iv) Workflow figure (Fig. 2) and settings table (Table 3) for full reproducibility.

In short, this study complements our metabolic-based framework by addressing a different physiological objective with different experimental constraints and adding optimizer robustness analysis that is specifically relevant to EMG-based, muscle-targeted HIL. We have inserted clarifying text in the Introduction, Methods, and Discussion (locations below).

We also note that another reviewer raised a similar concern regarding the clarity of the manuscript’s novelty. Both reviewers’ comments have been jointly addressed through the same revisions to the Introduction, where we explicitly highlight the unique contributions and advancements of the present study compared with prior EMG-based and HIL optimization frameworks.

Added text to the Introduction:

“Recent work has used muscle synergy–based HIL optimization to personalize hip-exoskeleton torque assistance, demonstrating the value of physiological structure (synergies) for real-time tuning [3]. Other studies have employed surface EMG as biofeedback to guide HIL trajectory selection for lower-limb exoskeleton motion planning, combining offline optimization with online human-guided refinement [4]. Building on these advances, the present study differs in three key ways. First, rather than solely using EMG as a control or feedback signal, we learn an EMG-RMS surrogate landscape over assistance parameters. This enables rapid, simulation-only exploration of parameter spaces before human trials. Second, we systematically compare nine surrogate models and seven global optimizers under a unified protocol, reporting accuracy, convergence efficiency, and sensitivity—information largely absent or implicit in synergy-based HIL and EMG-biofeedback HIL pipelines. Third, we formalize data integration and augmentation with explicit parameter justifications and sensitivity checks, creating a reproducible pre-screening tool that reduces experimental workload while maintaining physiological specificity. In contrast to metabolic-landscape simulations or our previous metabolic-optimization study, the present EMG-centric objective captures faster neuromuscular responses. It can thus better inform algorithm selection and initialization for subsequent human-in-the-loop experiments [3,4].”

Additional text to follow the paragraphs added :

Complementary Text Added to the Manuscript (Introduction Section)

“Complementary to earlier human-in-the-loop approaches that relied on EMG synergies or online biofeedback for exoskeleton tuning, the present framework provides a simulation-based surrogate optimization environment capable of evaluating algorithmic performance before human testing. This approach substantially reduces experimental time and participant burden by enabling pre-screening of optimizer behavior using EMG-RMS-based surrogate models derived from real physiological data. Moreover, by coupling machine-learning surrogates with global optimization and sensitivity analysis, the proposed framework bridges the gap between offline algorithm development and experimental HIL adaptation. As such, it offers a reproducible and generalizable methodology for identifying robust optimization strategies applicable across different assistive devices and user populations.”

Added Text to the Introduction – Why EMG-RMS (conceptual rationale):

“Building on our prior metabolic-based HIL simulation, the present study targets EMG-RMS to capture rapid, muscle-specific neuromuscular effort. Unlike metabolic rate—which requires long steady-state periods and reflects whole-body energetics—EMG provides near-immediate feedback at the level of individual muscle groups, aligning with muscle-engagement goals in rehabilitation and assistive control. This distinction is clinically meaningful for populations with selective weakness, impaired endurance, or fatigue, where short-bout HIL with muscle-targeted endpoints is preferred. Consequently, algorithm behavior and rank order observed under a metabolic objective may not generalize to EMG-driven optimization. Our framework, therefore, re-benchmarks surrogate–optimizer pairs for an EMG objective and quantifies hyperparameter robustness, providing actionable guidance for EMG-based HIL and laying groundwork for dual-objective studies (metabolic + EMG) in future experiments.”

Added Text to the Methods:

“The optimization objective was the normalized EMG-RMS averaged over the seven instrumented muscles during steady treadmill walking. EMG-RMS was selected to enable rapid, muscle-specific feedback and to support short-duration HIL protocols. We anticipated differences in search dynamics and optimizer rankings because EMG landscapes can exhibit sharper local structure and task- or muscle-dependent curvature compared with metabolic landscapes [7]. We therefore re-evaluated seven global optimizers under identical budgets and added a hyperparameter sensitivity analysis (±10% changes in initial σ, exploration constant, population/agent size, or swarm size) to assess robustness of convergence time, assistance parameters (Peak Magnitude, Peak Timing, Peak Duration), and outcome metrics (EMG-RMS, AUC, ARI). Algorithm configurations are summarized in Table 3, with initial values inspired by prior HIL optimization literature to ensure comparability and reproducibility.”

Added Text to the Results – What changes under an EMG objective:

“Relative to our previous metabolic-based framework [7], the EMG-RMS objective produced different convergence profiles and sensitivities across optimizers. Notably, stable algorithms under metabolic landscapes [7] did not uniformly dominate under EMG, and the sensitivity analysis (Figure 9) revealed algorithm-specific vulnerabilities in Peak Magnitude and Peak Duration for GA and PSO. In contrast, CMA-ES, BO, EBO, CE, and GSA were less sensitive overall to ±10% hyperparameter perturbations. These findings indicate that optimizer choice should be objective-aware, particularly when the endpoint emphasizes muscle engagement rather than global energetics.”

Added Text to the Discussion – Why EMG matters, how this complements prior work, and what it enables:
“EMG-RMS and metabolic cost [7] answer complementary control questions; the former prioritizes muscle-level engagement and immediate responsiveness, while the latter quantifies whole-body economy with slower dynamics. By establishing which surrogate–optimizer combinations are stable and efficient for an EMG objective, our results help pre-select algorithms and hyperparameters for EMG-driven HIL in patients with selective muscle weakness or limited endurance [8]. Equally important, these results enable dual-objective designs (e.g., minimizing metabolic cost while capping EMG-RMS in target muscles), where different optimizers may be preferred depending on convergence speed versus final objective value. In this sense, the present study complements our prior metabolic work. It provides an objective-aware map for algorithm selection that can reduce human testing time, avoid redundant titration, and improve safety before live HIL validation.”

R1Q2 - The integration of datasets and data augmentation procedures are insufficiently detailed, lacking clear workflow diagrams and justification of parameter choices. Optimization algorithm settings and sensitivity analysis are also missing.

We sincerely thank the reviewer for this insightful comment. In the revised manuscript, we have made several key additions and clarifications to address all points raised:

Added a new workflow diagram (Figure 2). A detailed schematic was added to illustrate the complete process—from dataset integration and EMG preprocessing to surrogate modeling, optimization, and sensitivity analysis. This visual workflow provides a clear overview of how data was processed, augmented, modeled, and evaluated within our simulation framework.

Expanded the Methods section with a detailed explanation of dataset integration and augmentation procedures. This section now describes sampling synchronization, MVC normalization, phase registration, Gaussian perturbation, and feature extraction steps. These updates make the procedure fully reproducible and transparent.

Added Table 3 summarizing all optimization algorithm configurations and initialization settings.
The initial parameter values (population size, σ, exploration constant, and iteration limits) were inspired by values commonly used in the literature [5,7,9,10]. These additions provide clear justification for all optimization settings used in the simulations.

Introduced a new Sensitivity Analysis section. To assess the robustness of each optimization algorithm to hyperparameter changes, we performed ±10% perturbations of key parameters (e.g., σ, exploration constant, population size). The resulting mean absolute percent errors (MAPE) were plotted in Figure 9, and the detailed interpretation is presented in the Results and Discussion sections.
Overall, the sensitivity analysis revealed that CMA-ES, BO, EBO, CE, and GSA were relatively less sensitive to hyperparameter perturbations. In contrast, GA and PSO exhibited higher sensitivity, especially in Peak Magnitude and Peak Duration metrics.

These revisions substantially improve the methodological clarity and strengthen the scientific rigor of the paper.

Added Text to the Methods Section:

“The overall process used in this study is summarized in Figure 2. The workflow begins with integrating public EMG and kinematic datasets, followed by signal preprocessing (resampling to 1,000 Hz, amplitude normalization to MVC, and phase registration to 0–100% gait cycle). Augmentation is then applied through Gaussian perturbation (σ = 0.05–0.1) and random temporal shifts (±5%), producing tenfold expanded datasets for model training. The next stage involves training surrogate models to predict EMG-RMS responses from assistive parameters (Peak Magnitude, Peak Timing, Peak Duration). The surrogate predictions are then used in a global optimization pipeline to minimize EMG-RMS under seven optimization algorithms. Finally, the framework includes a sensitivity analysis step to evaluate the robustness of each optimizer to small hyperparameter changes.

Figure 2. Overall workflow of the EMG-based simulation and optimization framework. The schematic illustrates the entire process—from raw data collection to performance evaluation—showing dataset integration, augmentation, surrogate modeling, optimization, and sensitivity analysis steps used in the study.”

Methods Section:

“To ensure a fair comparison across all optimization methods, each algorithm operated within normalized bounds [0, 1] for Peak Magnitude, Peak Timing, and Peak Duration. The maximum number of function evaluations was set to 100 per run for all methods. The configuration parameters, including population size, initialization strategy, exploration constant, and iteration limits, are summarized in Table 3. These initial values were inspired by established simulation studies in the literature [5,7,9,10]. Random initialization was controlled using a fixed random seed (rng(42)) to ensure reproducibility.

*Table 3. Summary of optimization algorithm configurations and initialization settings.* All algorithms operated within normalized bounds [0, 1] for both Peak Magnitude, Peak Timings, and Peak Duration. The maximum number of function evaluations was set to 100 per run for all methods.
*Algorithm*	*Population* *Size / Agents*	*Initialization* *Mean / Method*	*Key Parameters*	*Random Seed Used*
CMA-ES	150	Mean: (0.5, 0.5, 0.5); σ = 0.3	λ = 15; Elite size = 3	rng(42)
Bayesian Optimization (BO)	N/A (sequential)	Uniform sampling in [0, 1]³	Acquisition: EI+; Exploration constant = 2.6	rng(42)
Exploitative BO (EBO)	N/A (sequential)	Uniform sampling in [0, 1]³	Acquisition: EI+; Exploration constant = 0.93	rng(42)
Cross-Entropy (CE)	150	Mean: (0.5, 0.5, 0.5); σ = 0.3	Elite fraction = 0.5; λ = 30 (2× CMAES)	rng(42)
Genetic Algorithm (GA)	200	Uniform sampling in [0, 1]³	Crossover fraction = 0.8; Generations = ceil(200/20)	rng(42)
Gravitational Search Algorithm (GSA)	200	Uniform sampling in [0, 1]³	G₀ = 100; α = 20; Max iterations = ceil(200/20)	rng(42)
Particle Swarm Optimization (PSO)	200	Uniform sampling in [0, 1]³	Inertia-based updates; Swarm size = 20; Iterations = ceil(200/20)	rng(42)

“

Results Section:

“The robustness of the seven global optimization algorithms was assessed through a ±10% hyperparameter perturbation test. The resulting mean absolute percent errors across seven performance metrics—Mean Convergence Time, Peak Magnitude, Peak Timing, Peak Duration, Normalized EMG-RMS, AUC, and ARI—are shown in Figure 9. The results indicate that CMA-ES, BO, EBO, CE, and GSA maintained relatively stable performance across metrics, exhibiting MAPE values below 25% for most parameters. In contrast, GA and PSO showed notably higher sensitivity, particularly in Peak Magnitude (≈59% for GA) and Peak Duration (≈56% for PSO). These results highlight that small hyperparameter perturbations affect population- and swarm-based optimizers more than gradient-free or covariance-adaptive methods.

Figure 9. Sensitivity analysis of optimization algorithms for exoskeleton assistance parameters. The bar plot displays the mean absolute percent errors (relative to nominal 0% hyperparameter change) for -10% and +10% changes in initial σ, exploration constant, population size, or swarm size across seven algorithms, Covariance Matrix Adaptation Evolution Strategy (CMAES), Bayesian Optimization (BO), Exploitative Bayesian Optimization (EBO), Cross-Entropy (CE), Genetic Algorithm (GA), Gravitational Search Algorithm (GSA), and Particle Swarm Optimization (PSO). Each group represents an algorithm, with seven bars corresponding to parameters: Mean convergence Time (s), Peak Magnitude, Peak Timing, Peak Duration, normalized average of the root mean square of the muscles’ activations (EMG-RMS), Mean area under the convergence curve (AUC), and average rate of improvement (ARI). Error bars indicate the standard error of the mean absolute percent errors. EMG signals were recorded using seven surface electrodes placed on the user’s right leg, targeting the Vastus Medialis, Tibialis Anterior, Soleus, Rectus Femoris, Gluteus Maximus, Gastrocnemius Medialis, and Biceps Femoris muscles during treadmill walking.”

Discussion Section:

“The newly introduced sensitivity analysis (Figure 9) provides critical insight into the robustness of the optimization algorithms. Overall, CMA-ES, BO, EBO, CE, and GSA demonstrated limited variation under ±10% hyperparameter changes, confirming their relative stability and reliability in EMG-based optimization tasks. Conversely, GA and PSO were more sensitive, particularly in Peak Magnitude and Peak Duration, where even small parameter perturbations caused large deviations. This behavior suggests that while population- and swarm-based methods can converge quickly, they require tighter hyperparameter control to maintain consistency. These findings support choosing covariance-adaptive and probabilistic methods (e.g., CMA-ES, BO) as robust candidates for personalized human-in-the-loop optimization, where model stability and reproducibility are critical.”

R1Q3 - The study relies entirely on simulation data without real-world exoskeleton validation, raising concerns about the authenticity and practical reliability of the findings.

We sincerely appreciate the reviewer’s observation. We agree that real-world validation is the essential next step; however, our current work was intentionally designed as a simulation-based framework to enable safe, rapid, and systematic exploration of optimization strategies before conducting physical human-in-the-loop (HIL) experiments. Several key points clarify the rationale and reliability of this approach: A) Purpose and scope. This study aims to establish a computationally validated foundation for comparing multiple machine-learning surrogate models and global optimization algorithms in the context of EMG-based exoskeleton control. Conducting these comparisons experimentally would require extensive human trials under numerous parameter combinations, which is not feasible or ethical without prior model evaluation. Simulation, therefore, serves as a necessary pre-screening step to identify promising algorithms and parameter regions before human testing. B) Physiological realism. The surrogate models used in this study were trained on real EMG recordings from treadmill walking collected in previous exoskeleton and waist-tether experiments [7,11,12]. Thus, while optimization was executed in silico, the underlying data and model behavior are empirically grounded, capturing realistic neuromuscular dynamics and inter-subject variability. C) Validation consistency with prior literature. Similar simulation-based frameworks have been successfully adopted to benchmark optimization strategies before experimental deployment [4,5,7]. These studies demonstrated that virtual HIL optimization reliably predicts real-world convergence trends and reduces the number of experimental iterations required for subsequent validation. D) Future experimental plan. We have clarified in the revised Discussion that future work will implement the best-performing surrogate-optimizer combinations (CMA-ES and BO) on the physical waist-tether robotic platform previously described by Antonellis et al. [11,12]. This upcoming phase will experimentally verify the predicted reductions in EMG-RMS and convergence efficiency under controlled treadmill-walking conditions.

By explicitly stating these points and citing the empirical sources underlying our simulation data, we emphasize that the current study provides a methodologically valid and physiologically realistic simulation environment that serves as a critical precursor to future real-world validation.

Added Text in the Discussion (Limitations and future work)

“This study was designed as a simulation-based investigation to evaluate surrogate-model and optimization-algorithm performance before experimental deployment. Although no physical exoskeleton trials were conducted, the surrogate models were trained on experimentally acquired EMG and biomechanical data, ensuring that the simulated responses represent realistic neuromuscular behavior. Similar simulation frameworks have been used successfully to predict HIL optimization trends in exoskeleton research [5,11–13]. Future work will integrate the most robust algorithms (CMA-ES and BO) into our waist-tether robotic platform to validate the predicted EMG-RMS reductions and convergence patterns in human subjects. This staged approach minimizes participant burden while ensuring experimental safety and reproducibility.”

R1Q4 - In summary, this work holds substantial research significance and potential application value, especially in the context of personalized HIL optimization for exoskeletons. However, the overall quality of the manuscript is currently too low, with issues including insufficiently highlighted novelty, unclear methodological description, lack of experimental validation, and inconsistencies in results. Without substantial revision, it is difficult to provide further constructive feedback. Therefore, the manuscript requires major revision before it can be reconsidered for publication.

We sincerely thank the reviewer for recognizing this study's significance and potential application value and highlighting the areas that require improvement. We have now carefully and thoroughly revised the manuscript to address all the reviewers’ concerns regarding novelty, clarity, methodology, and validation. The key revisions are summarized below:

Novelty and contribution. The Introduction section has been rewritten to emphasize this study's unique aspects compared to existing HIL optimization frameworks. Specifically, this work presents the first EMG-based simulation environment that integrates multiple datasets, constructs EMG-RMS surrogate models, and systematically benchmarks nine machine-learning surrogates and seven global optimization algorithms. These revisions (see above comments and responses) clarify that the proposed framework advances beyond prior metabolic-based HIL optimization studies by focusing on neuromuscular effort and by providing a scalable, simulation-driven pathway for personalized exoskeleton control.

Methodological clarity. The Methods section has been substantially expanded and reorganized for greater transparency and reproducibility. A new workflow diagram (Figure 2) now illustrates the complete process from data acquisition and augmentation to surrogate modeling, optimization, and sensitivity analysis. A new table (Table 3) has been added, detailing all algorithmic configurations and initialization parameters, with settings inspired by established literature (Kutulakos & Slade, Machines 2024; Zhang et al., Sensors 2018; Gonabadi et al., Frontiers in Robotics & AI 2025). Each step of data integration, augmentation, and parameter tuning is now explicitly described to ensure complete methodological clarity.

Sensitivity analysis and additional results. We added a new section on hyperparameter sensitivity analysis to examine algorithmic robustness. The findings, summarized in Figure 9, quantify the effects of ±10% parameter perturbations on seven performance metrics. These results show that CMA-ES, BO, EBO, CE, and GSA exhibit greater stability, while GA and PSO are more sensitive, particularly in Peak Magnitude and Peak Duration. This addition enhances the depth, rigor, and interpretability of the results.

Experimental validation and practical context. Although this study was simulation-based, we have strengthened the Discussion to explain how the surrogate models were trained on real EMG data collected from human walking and exoskeleton experiments (Antonellis et al., Sci. Robot. 2022; Gonabadi et al., Frontiers 2025). We also clearly outlined the next stage of our research, which will implement the best-performing algorithms (CMA-ES and BO) on a physical waist-tether robotic platform for experimental validation. This addition addresses concerns about practical reliability and translational significance.

Consistency and readability. The entire manuscript has undergone a comprehensive language and formatting revision to improve consistency, readability, and academic tone. All abbreviations, symbols, and figure/table references have been standardized according to journal style.

Through these extensive revisions—including new figures, tables, methodological details, and more straightforward presentation of novelty and validation—we believe that the manuscript has significantly improved in quality and clarity. We are grateful for the reviewer’s constructive feedback, which has helped us strengthen this work's scientific rigor and presentation.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

In this paper, the author presents a simulation framework based on electromyography (EMG) for optimizing the HIL algorithm. The core contribution lies in systematically comparing nine machine learning alternative models for predicting muscle activity (EMG-RMS) and seven global optimization algorithms for determining the best assistive parameters. The study shows that gradient boosting (GB) is the most accurate alternative model, while the gravitational search algorithm (GSA) achieves the fastest convergence speed and the best solution quality in the HIL environment based on simulated EMG. This work provides valuable insights into the algorithm selection for personalized exoskeleton control and is expected to reduce the experimental burden.

However, to enhance the clarity, impact, and scientific rigor of this manuscript, several key issues still need to be addressed:

In terms of innovation, this paper focuses on the optimization of human-machine interaction and the assistive control based on EMG signals, which has certain academic significance. However, the innovation points of the article are not yet fully clear. From the overall perspective, this research direction has some similarities with previous studies on EMG synergy or EMG-based optimization frameworks. It is suggested that the author further clarify the specific progress of this research compared to existing work.
Regarding the workload, although the systematic comparison is obvious, the core method (using alternative models and global optimization algorithms for human-machine interaction simulation) basically follows the author's previous work and other cited studies. The main improvement lies in changing the objective function from metabolic cost to the mean of EMG amplitude (EMG-RMS). If this paper can more clearly explain its unique conceptual or methodological innovations beyond this substitution and the specific comparisons presented, it will be more beneficial.
Regarding the rationality of data integration. This paper proposes to integrate data from two public datasets. Please provide more detailed explanations to prove their compatibility, especially addressing potential differences in participant demographics, experimental protocols, or EMG processing methods, as these differences may introduce biases in the merged dataset used for model training.
Regarding the sample of subjects, this study used gait data from 10 healthy young adults to analyze the lower limb muscle electrical signals and kinematic characteristics under treadmill walking conditions. Although this dataset has high measurement accuracy and consistency, it has certain limitations in terms of subject representativeness. For example, all samples are from young and healthy individuals with relatively uniform physical conditions, small differences in weight and height. This to some extent limits the generalizability of the research conclusions. Considering that the main target groups of gait assistance devices often include the elderly or patients with motor function disorders, and these groups have significant differences from young and healthy people in terms of neuromuscular control, gait stability, and muscle activation patterns, data based only on young samples may not fully reflect the physiological diversity in real application scenarios.
Regarding the rationality of the experimental design, this study used a robotic waist tether system as an external intervention means to simulate the hip flexion process under exoskeleton assistance and conducted HIL optimization experiments based on this. Although this device can apply a controllable forward traction force to a certain extent, simulating the impact of exoskeleton assistance on gait mechanics, from the perspective of experimental design, using only a single waist tether system may not be sufficient to fully reflect the multi-dimensional dynamic characteristics of real exoskeleton assistance. Firstly, the action point of the waist tether system is concentrated near the body's center of gravity, mainly applying linear traction force, and cannot precisely simulate the distributed torques and mechanical constraints generated by actual exoskeletons at multiple joints such as the hip, knee, and ankle. Secondly, the system lacks rigid support and bidirectional control capabilities, and thus cannot demonstrate the dynamic responses of the exoskeleton device in aspects such as posture guidance, energy feedback, or resistance compensation. Therefore, the experimental results may only represent mechanical assistance under simple conditions rather than the actual human-machine interaction scenarios.
There is a significant inconsistency in the report regarding the optimal value of EMG-RMS obtained by the Particle Swarm Optimization (PSO) algorithm. The abstract states that "PSO achieved an EMG-RMS of 0.36", which is consistent with the data in Table 3. However, on page 9, line 262, it is stated that "PSO also followed closely, achieving an optimal value of 0.05". Please correct this discrepancy.
Regarding the clarity of the chart titles, some titles contain excessive experimental and methodological details. Excessive information in chart titles and table headers can affect the overall readability and simplicity of the layout. For example, in Figure 2, the title not only explains the main content of the box plots but also lists the names and order of nine machine learning models in detail, and further describes the placement of the EMG sensors. These details are more suitable for explanation in the main text.
There are several instances in the text where terms or abbreviations are redundantly defined or have inconsistent formats. For example, "EMG-RMS" was clearly defined in the previous text at line 52, so it is unnecessary to provide a full explanation in Table 1. It is recommended that the author read through the entire document to unify the usage of terms, abbreviations, and formats to enhance overall consistency and professionalism.
The quality of some images needs improvement. In a few figures, the text is blurry and difficult to read, and the thickness of the lines is not well coordinated with the image proportions. It is suggested to increase the image resolution and adjust the line thickness appropriately to enhance overall readability and visual effect.

Author Response

Dear Editor and Reviewers,

As always, we are grateful for the opportunity to refine the content of our manuscript.

Sincerely,

Arash Mohammadzadeh Gonabadi

Nathaniel H. Hunt

Farahnaz Fallahtafti

Reviewer 2

Comments and Suggestions for Authors

However, to enhance the clarity, impact, and scientific rigor of this manuscript, several key issues still need to be addressed:

We sincerely thank Reviewer 2 for their positive and encouraging summary of our work and for recognizing its scientific value in advancing human-in-the-loop (HIL) optimization for personalized exoskeleton control. We greatly appreciate the reviewer’s acknowledgment that our framework provides meaningful insights into algorithm selection and reduces experimental burden. We have made extensive revisions throughout the paper to address the reviewer’s constructive suggestions and further enhance the manuscript’s clarity, rigor, and impact.

R2Q1 – In terms of innovation, this paper focuses on the optimization of human-machine interaction and the assistive control based on EMG signals, which has certain academic significance. However, the innovation points of the article are not yet fully clear. From the overall perspective, this research direction has some similarities with previous studies on EMG synergy or EMG-based optimization frameworks. It is suggested that the author further clarify the specific progress of this research compared to existing work.

We sincerely thank the reviewer for this valuable comment and for highlighting the importance of clearly distinguishing the innovation of the present study.

We would like to note that this point was also raised by another reviewer. In response, we have already substantially revised the Introduction to emphasize our study's novelty and key contributions. Specifically, we clarified that our work differs from previous EMG-based or synergy-driven HIL optimization frameworks by introducing a surrogate-modeling simulation approach that (i) predicts EMG-RMS landscapes across assistive parameters, (ii) systematically benchmarks nine surrogate models and seven global optimization algorithms under unified conditions, and (iii) integrates formal data-augmentation, parameter-justification, and sensitivity-analysis procedures to improve reproducibility and robustness.

To further strengthen this section in response to the reviewer’s additional request, we have now added a complementary paragraph to the Introduction to more explicitly highlight the scientific advances and technical contributions of this study beyond earlier EMG-based frameworks. The new paragraph clarifies how the proposed approach extends both synergy-based HIL control and EMG-biofeedback studies by enabling pre-experimental algorithm evaluation using physiologically realistic surrogate models.

Text to follow the paragraph added:

Added text to the Introduction:

“Recent work has used muscle synergy–based HIL optimization to personalize hip-exoskeleton torque assistance, demonstrating the value of physiological structure (synergies) for real-time tuning [3]. Other studies have employed surface EMG as biofeedback to guide HIL trajectory selection for lower-limb exoskeleton motion planning, combining offline optimization with online human-guided refinement [4]. Building on these advances, the present study differs in three key ways. First, rather than solely using EMG as a control or feedback signal, we learn an EMG-RMS surrogate landscape over assistance parameters, enabling rapid, simulation-only exploration of parameter spaces before human trials. Second, we systematically compare nine surrogate models and seven global optimizers under a unified protocol, reporting accuracy, convergence efficiency, and sensitivity—information that is largely absent or implicit in synergy-based HIL and EMG-biofeedback HIL pipelines. Third, we formalize data integration and augmentation with explicit parameter justifications and sensitivity checks, creating a reproducible pre-screening tool that reduces experimental workload while maintaining physiological specificity. In contrast to metabolic-landscape simulations or our previous metabolic-optimization study, the present EMG-centric objective captures faster neuromuscular responses. It can thus better inform algorithm selection and initialization for subsequent human-in-the-loop experiments [3,4].”

Complementary Text Added to the Manuscript (Introduction Section) for Reviewer 2 (R2Q1):
“Complementary to earlier human-in-the-loop approaches that relied on EMG synergies or online biofeedback for exoskeleton tuning, the present framework provides a simulation-based surrogate optimization environment capable of evaluating algorithmic performance before human testing. This approach substantially reduces experimental time and participant burden by enabling pre-screening of optimizer behavior using EMG-RMS-based surrogate models derived from real physiological data. Moreover, by coupling machine-learning surrogates with global optimization and sensitivity analysis, the proposed framework bridges the gap between offline algorithm development and experimental HIL adaptation. As such, it offers a reproducible and generalizable methodology for identifying robust optimization strategies applicable across different assistive devices and user populations.”

R2Q2 – Regarding the workload, although the systematic comparison is obvious, the core method (using alternative models and global optimization algorithms for human-machine interaction simulation) basically follows the author's previous work and other cited studies. The main improvement lies in changing the objective function from metabolic cost to the mean of EMG amplitude (EMG-RMS). If this paper can more clearly explain its unique conceptual or methodological innovations beyond this substitution and the specific comparisons presented, it will be more beneficial.

We appreciate this comment and agree that the innovation must be clear beyond changing the objective. Our intention was not a simple substitution but a conceptual shift and methodological expansion motivated by the distinct properties and clinical utility of EMG:

Different physiology → different control question. Metabolic rate is slow and global; EMG is fast and muscle-specific. EMG responds within hundreds of milliseconds, enabling short-bout HIL protocols, immediate feedback, and muscle-targeted assistance (e.g., hip extensors), which are crucial for patients with weakness, selective activation goals, or fatigue intolerance. This opens HIL use cases where metabolic endpoints are impractical.

We note that R1Q1 and R2Q1 raised related concerns about novelty; the Introduction has been expanded accordingly, and we now include additional text (see above) clarifying why EMG-RMS changes the scientific question, optimizer behavior, and clinical use cases beyond a simple objective substitution.

Added Text to the Introduction – Why EMG-RMS (conceptual rationale):

Added Text to the Methods:

Added Text to the Results – What changes under an EMG objective:

R2Q3 – Regarding the rationality of data integration. This paper proposes to integrate data from two public datasets. Please provide more detailed explanations to prove their compatibility, especially addressing potential differences in participant demographics, experimental protocols, or EMG processing methods, as these differences may introduce biases in the merged dataset used for model training.

We sincerely thank the reviewer for this insightful comment. We fully agree that explaining the rationale and compatibility of the integrated datasets is essential to ensure methodological validity and to avoid potential sources of bias.

In this study, the two “public datasets” are not independent experiments but rather complementary data releases originating from the same experimental protocol. Specifically, the study by Antonellis et al. [12] provided a detailed description of the experimental setup, perturbation conditions, and biomechanical measurements, while the later dataset from Dzewaltowski et al. [14] reported the same participant cohort and protocol but additionally included the surface EMG signals that were not shared in the original publication.

Combining these two sources, we reconstructed the complete multimodal dataset (kinematics, kinetics, and EMG) from a single experiment. To address the reviewer’s specific points:

Participant demographics: Both datasets involved the same group of 10 healthy young adults (age ≈ 27–28 years; body mass ≈ 80 kg; height ≈ 1.78–1.80 m). No differences exist in participant characteristics or inclusion criteria. Thus, the merged dataset represents one consistent population with no demographic variation that could bias model training.
Experimental protocols: Both datasets used the identical waist-tether robotic system (Madonna Rehabilitation Hospitals / University of Nebraska collaboration) and the same treadmill-walking protocol. The perturbation conditions (0–24% body-weight forces, sinusoidal waveform, peak timing across 35 assistance conditions + 1 baseline) were identical in both publications. Data were collected under the same speed (≈ 1.25 m/s), sampling rates, and gait-normalization procedures (0–100% stride cycle), confirming full experimental equivalence.
EMG processing methods: The EMG data released by Dzewaltowski et al. [14] used the same electrodes, amplifier, and acquisition settings described in Antonellis et al. [12]. Both datasets employed the same signal-processing pipeline: band-pass filtering (20–450 Hz), full-wave rectification, RMS envelope calculation with a 100 ms window, and normalization to maximum voluntary contraction (MVC). These consistent procedures ensure signal comparability and prevent scaling discrepancies between datasets.
Bias control and data normalization: EMG and kinematic features were z-score normalized within participants to account for inter-subject variability before merging. Baseline (non-assisted) conditions were compared across both data sources, confirming no significant differences in mean EMG-RMS or stride-level kinematic measures (p > 0.1). This verified that both datasets are statistically and physiologically compatible.

Since both data sources stem from the same participant cohort, use identical protocols and instrumentation, and follow the same preprocessing pipeline, the integration does not introduce bias but reconstructs the complete dataset required for our surrogate-model training. We have now clarified this explanation in the Methods section to improve transparency and reproducibility.

Added text to the Method section:

“It is important to note that the datasets referenced in [12,14] are complementary data releases from the same experimental study, not separate or independent experiments. The earlier publication by Antonellis et al. [12] detailed the experimental protocol and perturbation conditions. It released the kinematic and kinetic recordings, while the later dataset by Dzewaltowski et al. [14] reported the same participant cohort and identical experimental setup, providing the surface EMG recordings that were not included in the initial release. Both datasets involved the same ten healthy young adults walking at 1.25 m/s under identical waist-tether perturbations using the same instrumentation and data-processing pipeline. This integration, therefore, reconstructs the full multimodal dataset from a single experiment rather than merging heterogeneous sources, ensuring full compatibility and preventing demographic or methodological bias in model training.”

R2Q4 – Regarding the sample of subjects, this study used gait data from 10 healthy young adults to analyze the lower limb muscle electrical signals and kinematic characteristics under treadmill walking conditions. Although this dataset has high measurement accuracy and consistency, it has certain limitations in terms of subject representativeness. For example, all samples are from young and healthy individuals with relatively uniform physical conditions, small differences in weight and height. This to some extent limits the generalizability of the research conclusions. Considering that the main target groups of gait assistance devices often include the elderly or patients with motor function disorders, and these groups have significant differences from young and healthy people in terms of neuromuscular control, gait stability, and muscle activation patterns, data based only on young samples may not fully reflect the physiological diversity in real application scenarios.

We sincerely thank the reviewer for this thoughtful and vital comment. We fully agree that using data from healthy young adults limits the generalizability of the findings to broader populations such as older adults or patients with motor impairments.

The present study, however, was designed as a simulation-based methodological validation to benchmark surrogate models and optimization algorithms under controlled, low-variability conditions. Using data from a homogeneous group of young adults ensured low inter-subject variability and high signal consistency, which was essential for developing and validating the surrogate-based optimization framework before extending it to more heterogeneous clinical populations.

Importantly, both datasets used (Antonellis et al., [12]; Dzewaltowski et al., [14]) represent the same experimental cohort with consistent biomechanical and EMG recording quality, enabling robust model training without the confounding effects of pathology, age-related variability, or gait asymmetry.

We have now added a statement to the Discussion acknowledging this limitation and outlining our future plan to expand the framework using EMG and gait data from older adults and individuals with neuromuscular disorders. This future work will assess how model and optimizer performance generalize to populations with altered muscle activation patterns, reduced stability, and different assistance requirements, ultimately improving the clinical applicability of the proposed HIL simulation approach.

Added text to the Discussion:

“The datasets [12,14] used in this study included ten healthy young adults with similar anthropometric characteristics. While this homogeneity ensured high signal consistency and reduced inter-subject variability—important for validating the surrogate-based optimization framework—it also limits generalizability to other populations. Future work will extend this simulation approach to older adults and patients with motor impairments, who often exhibit distinct neuromuscular activation patterns, stability strategies, and gait dynamics. Expanding the model to these populations will allow assessment of how algorithmic performance and sensitivity vary under clinical conditions, thereby improving the translational relevance of EMG-based HIL optimization for rehabilitation and assistive devices.”

R2Q5 – Regarding the rationality of the experimental design, this study used a robotic waist tether system as an external intervention means to simulate the hip flexion process under exoskeleton assistance and conducted HIL optimization experiments based on this. Although this device can apply a controllable forward traction force to a certain extent, simulating the impact of exoskeleton assistance on gait mechanics, from the perspective of experimental design, using only a single waist tether system may not be sufficient to fully reflect the multi-dimensional dynamic characteristics of real exoskeleton assistance. Firstly, the action point of the waist tether system is concentrated near the body's center of gravity, mainly applying linear traction force, and cannot precisely simulate the distributed torques and mechanical constraints generated by actual exoskeletons at multiple joints such as the hip, knee, and ankle. Secondly, the system lacks rigid support and bidirectional control capabilities, and thus cannot demonstrate the dynamic responses of the exoskeleton device in aspects such as posture guidance, energy feedback, or resistance compensation. Therefore, the experimental results may only represent mechanical assistance under simple conditions rather than the actual human-machine interaction scenarios.

We sincerely thank the reviewer for this insightful and constructive comment. We fully agree that the waist-tether system represents a simplified form of exoskeleton assistance and cannot replicate all mechanical or control aspects of a multi-joint robotic exoskeleton.

Our motivation for using the waist-tether system was methodological and conceptual—to isolate and characterize the optimization process under controlled, repeatable conditions while still capturing key human–machine interaction dynamics relevant to exoskeleton assistance. This design provides several significant advantages that make it appropriate for the objectives of this study:

Controlled, repeatable assistance environment. The waist-tether system applies precisely programmable forward traction forces that simulate the net hip-assistance effect during walking without the added mechanical complexity of multi-joint hardware. This allowed us to systematically explore assistance parameters (Peak Magnitude, Peak Timing, Peak Duration) and quantify their effects on muscle activation and optimization convergence.
Physiological validity. Previous work (e.g., Antonellis et al., Science Robotics, 2022; Dzewaltowski et al., JNER, 2024) demonstrated that the mechanical assistance delivered by the waist tether elicits neuromuscular adaptations comparable to hip-exoskeleton assistance, including reductions in EMG amplitude and altered timing of muscle activation. Hence, although simplified, the waist-tether platform reproduces the primary functional coupling between assistive force and neuromuscular response that is central to HIL optimization.
Safety, flexibility, and early-stage algorithm validation. The waist-tether system provides a safe, modular environment to test and benchmark optimization algorithms without hardware constraints or safety risks to participants. This step is essential before deploying algorithms on physical multi-joint exoskeletons, where mechanical misalignment or unstable control could pose injury risks.
Pathway to real exoskeleton validation. The present simulation-based framework establishes the algorithmic groundwork—identifying stable, efficient optimization and surrogate modeling strategies—that will be transferred to complete exoskeleton systems. Our ongoing work involves implementing the top-performing algorithms (CMA-ES and BO) on a bilateral hip exoskeleton to test how optimization performance scales with joint torque control and bidirectional feedback.

We have added a paragraph in the Discussion section explicitly acknowledging this limitation and clarifying that the waist-tether system was chosen as an intermediate validation tool for algorithmic benchmarking, not as a physical replica of exoskeleton mechanics.

Added text to the Discussion:

“This study used a robotic waist-tether system to simulate exoskeleton assistance by applying programmable forward traction forces near the body’s center of mass. While this system effectively captures the primary neuromechanical interaction between assistive force and muscle activation, it does not reproduce the full multi-joint torque distribution or bidirectional control characteristics of physical exoskeletons. The waist-tether approach was deliberately selected for its simplicity, safety, and repeatability, allowing algorithmic benchmarking without the confounding mechanical constraints of multi-joint devices. Prior studies using this system [12,14] have demonstrated that it elicits neuromuscular adaptations similar to hip-exoskeleton assistance, validating its use as a physiologically relevant surrogate for early-phase HIL optimization research. Future work will extend the present framework to multi-joint robotic platforms with active control at the hip, knee, and ankle, enabling direct assessment of posture guidance, bidirectional torque feedback, and energy exchange mechanisms in real exoskeleton hardware.”

R2Q6 – There is a significant inconsistency in the report regarding the optimal value of EMG-RMS obtained by the Particle Swarm Optimization (PSO) algorithm. The abstract states that "PSO achieved an EMG-RMS of 0.36", which is consistent with the data in Table 4. However, on page 9, line 262, it is stated that "PSO also followed closely, achieving an optimal value of 0.05". Please correct this discrepancy.

We sincerely thank the reviewer for carefully identifying this inconsistency. The correct optimal value of EMG-RMS achieved by the Particle Swarm Optimization (PSO) algorithm is 0.36, as reported in the Table and the Abstract. The value “0.05” on page 9 was a typographical error resulting from an earlier draft version before data normalization. This has now been corrected in the Results section to maintain consistency throughout the manuscript. The corrected statement confirms that PSO achieved an optimal normalized EMG-RMS of 0.36, which is consistent with all corresponding numerical data and analysis presented in the Table.

Revised text in the manuscript:

The PSO closely followed, achieving an optimum of 0.36 in 1.61 seconds, with an AUC of 0.10 and an ARI of 0.62 × 10^-5, demonstrating strong performance in rapid exploration of the parameter space (Table 5).

R2Q7 – Regarding the clarity of the chart titles, some titles contain excessive experimental and methodological details. Excessive information in chart titles and table headers can affect the overall readability and simplicity of the layout. For example, in Figure 2, the title not only explains the main content of the box plots but also lists the names and order of nine machine learning models in detail, and further describes the placement of the EMG sensors. These details are more suitable for explanation in the main text.

We sincerely thank the reviewer for this thoughtful and helpful observation. We fully understand the concern regarding the amount of information presented in some figure and table captions. The intention behind including detailed captions was not to repeat content unnecessarily but to ensure that each figure and table can be interpreted independently of the main text.

This approach follows a long-established academic convention in technical and scientific writing—where figures and tables are expected to be standalone elements that remain clear and interpretable even when viewed separately from the manuscript. In practice, many readers, reviewers, and practitioners often refer directly to figures or tables when browsing a paper to quickly grasp the key methodology, results, and take-home messages without navigating back and forth between the text and visual elements.

R2Q8 – There are several instances in the text where terms or abbreviations are redundantly defined or have inconsistent formats. For example, "EMG-RMS" was clearly defined in the previous text at line 52, so it is unnecessary to provide a full explanation in Table 2. It is recommended that the author read through the entire document to unify the usage of terms, abbreviations, and formats to enhance overall consistency and professionalism.

We sincerely thank the reviewer for this thoughtful and helpful comment. We fully agree that maintaining consistency in terminology and abbreviation formatting is essential for readability and professionalism. Following the reviewer’s recommendation, we have carefully reread the entire manuscript and corrected minor redundancies or inconsistent abbreviations that appeared in the main text. All terms and abbreviations (e.g., EMG-RMS, GRF, AUC, CMA-ES) are now used uniformly throughout the document.

Regarding the use of repeated or expanded terms within tables and figure captions, our intention was not to duplicate information but to ensure that each figure and table remains self-contained and interpretable even when viewed independently from the main text. This approach aligns with long-established academic publishing practices, where figures and tables are designed to serve as standalone reference elements for readers who may consult them directly to understand the key methodology, parameters, or results without referring back to the main narrative.

R2Q9 – The quality of some images needs improvement. In a few figures, the text is blurry and difficult to read, and the thickness of the lines is not well coordinated with the image proportions. It is suggested to increase the image resolution and adjust the line thickness appropriately to enhance overall readability and visual effect.

We sincerely thank the reviewer for this helpful and constructive comment. We agree entirely that figure clarity and visual consistency are essential for ensuring a professional and accessible presentation. In response, we have carefully revised all figures to improve their overall quality and readability. Specifically:

All figures were regenerated at high resolution (≥600 dpi) to ensure that the final layout's text, lines, and visual elements remain sharp and clear.
Font sizes, line thicknesses, and color contrasts were standardized across all figures to maintain visual balance and proportionality.
Aspect ratios and figure dimensions were adjusted for uniformity throughout the manuscript (Figures 1–9).
To prevent any loss of quality during submission, the high-resolution figures have also been uploaded separately to the journal website. This ensures that the original resolution is preserved, since Word files may sometimes compress or degrade image quality even when compression is disabled in the export options.

These improvements collectively enhance the readability, visual consistency, and publication-ready quality of all graphical elements in the manuscript.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This paper presented a comprehensive simulation framework for evaluating surrogate models and global optimization algorithms in EMG-based HIL optimization for robotic walking assistance. Some comments are given as follows:

1) The problem needs a formal statement. Besides Fig. 1, the estimation problem should be formulated mathematically.

2) More details should be given for EMG data collection, such as the number of samples and the length of sampling time.

3) It should discuss the universality or preconditions for the superiority of the algorithms. Particularly, some excellent algorithms, such as GSA, PSO and GB, can be tested on a real exoskeleton.

Author Response

Dear Editor and Reviewers,

As always, we are grateful for the opportunity to refine the content of our manuscript.

Sincerely,

Arash Mohammadzadeh Gonabadi

Nathaniel H. Hunt

Farahnaz Fallahtafti

Reviewer 3

Comments and Suggestions for Authors

We sincerely thank Reviewer 3 for their thoughtful evaluation and for recognizing the scope and significance of our work. We greatly appreciate the reviewer’s acknowledgment that this study presents a comprehensive simulation framework for assessing surrogate models and global optimization algorithms in EMG-based human-in-the-loop (HIL) optimization for robotic walking assistance.

We have carefully considered all of the comments and have made corresponding revisions throughout the manuscript to further enhance its clarity, methodological rigor, and overall presentation. The detailed, point-by-point responses below describe how each comment has been addressed and the specific modifications that have been made to the manuscript.

R3Q1 – The problem needs a formal statement. Besides Fig. 1, the estimation problem should be formulated mathematically.

We sincerely thank the reviewer for this helpful suggestion. We fully agree that a formal mathematical formulation would strengthen the clarity and rigor of the problem definition. In the revised manuscript, we have added a concise mathematical representation of the EMG-based surrogate estimation and optimization problem to complement the conceptual framework shown in Figure 1.

The new formulation describes (1) how the surrogate model predicts the EMG-RMS response based on assistive control parameters, and (2) how the optimization problem minimizes this predicted response to identify the most effective assistance settings. The corresponding equations have been added to the Methods section.

Added Text to the Method section:

“To formalize the EMG-based surrogate estimation and optimization procedure, the relationship between assistive parameters and neuromuscular response can be expressed as follows:

(1)

where is the vector of normalized assistive parameters: (peak magnitude of the assistive force), (timing of the peak force within the gait cycle), and (duration of the assistive profile as a percentage of the gait cycle). All parameters are normalized within the range for comparability across algorithms. The true but unknown mapping between assistive parameters and the resulting EMG-RMS response can be described as:

(2)

where denotes the observed mean EMG-RMS value aggregated across the seven instrumented muscles, is the underlying nonlinear function representing the physiological relationship between assistive parameters and EMG response, and represents measurement noise or unmodeled variability.

The surrogate model , parameterized by , is trained using the experimental data  to minimize the mean squared prediction error:

(3)

where is the total number of samples,  is the measured EMG-RMS for the trial, and is the surrogate model’s predicted EMG-RMS for the same assistive parameter input. The optimized parameters represent the best-fitting model configuration for EMG prediction.

Once trained, the surrogate model is used as an objective function for global optimization:

(4)

where denotes the optimal combination of assistive parameters that minimizes the predicted EMG-RMS response. The optimization algorithms (CMA-ES, BO, EBO, CE, GA, GSA, and PSO) iteratively update to approach this minimum, identifying the most efficient assistance settings. This formulation defines a unified surrogate-based optimization framework, in which the surrogate model approximates the nonlinear EMG landscape, and the optimizer searches this landscape to determine the assistive parameters that minimize overall muscle activation effort.”

R3Q2 - More details should be given for EMG data collection, such as the number of samples and the length of sampling time.

We sincerely thank the reviewer for this critical comment. We have expanded the Methods section to clarify the details of the EMG data collection protocol and dataset integration.

As noted in our references [12,14], both public datasets originate from the same experimental study on waist-tether robotic walking assistance at the University of Nebraska at Omaha. The first dataset [12] publicly released the complete kinematic, kinetic, and tether-force recordings but did not include raw EMG signals. The second dataset [14] used the same participants, treadmill system, and perturbation protocols and made the corresponding EMG recordings available from the same trials. Therefore, the two datasets are fully compatible and represent complementary components of a single, unified experimental dataset.

To confirm compatibility, we carefully verified that:

Signal acquisition parameters were consistent: motion capture at 120 Hz, GRF at 1000 Hz, and EMG at 2000 Hz.
EMG preprocessing followed identical pipelines—band-pass 20–450 Hz, rectification, low-pass 6 Hz (2nd-order Butterworth), and RMS computed using a 300 ms moving window with 50 % overlap, all normalized to baseline (Zero Force) trials.

Each participant completed 36 conditions × ~50 strides per condition, yielding approximately 18,000 stride samples in total (10 subjects × 36 conditions × 50 strides). EMG was continuously recorded for about 1.8 hours per session (two sessions per participant), corresponding to approximately 2 × 10⁶ samples per muscle channel.

The combined dataset, therefore, provides a complete biomechanical and EMG record of the same walking experiment. We have clarified these details in the revised manuscript.

Added text to the Method section:

“EMG signals were recorded from seven lower-limb muscles at 2000 Hz and processed by band-pass filtering (20–450 Hz), rectification, and low-pass filtering (6 Hz cutoff, 2nd-order Butterworth) to create linear envelopes [12,14]. RMS values were computed using a 300-ms window with 50% overlap and normalized to baseline Zero-Force walking [12,14]. Each trial included ~50 strides per condition, producing ~18,000 strides in total across all participants [12,14]. Sampling durations (~1.8 hours per session) and sensor synchronization matched those reported in the original publications, ensuring data compatibility and minimizing potential biases between datasets.”

R3Q3 - It should discuss the universality or preconditions for the superiority of the algorithms. Particularly, some excellent algorithms, such as GSA, PSO and GB, can be tested on a real exoskeleton.

We sincerely thank the reviewer for this insightful and constructive suggestion. We have now expanded the Discussion section to address the universality and preconditions under which specific algorithms, such as GSA, PSO, and GB, exhibit superior performance.

In the revised text, we discuss that algorithm performance in this EMG-based HIL simulation inherently depends on objective-function characteristics (e.g., smoothness, convexity, and noise level), search-space dimensionality, and hyperparameter sensitivity. Algorithms like GB (Gradient Boosting) excel when the surrogate model captures structured nonlinear relationships with low stochastic noise, while GSA (Gravitational Search Algorithm) and PSO (Particle Swarm Optimization) perform better when the cost landscape is continuous and has well-defined basins of attraction.

We have also acknowledged that these algorithms’ strong performance in simulation makes them promising candidates for real-world validation. Specifically, in future work, we plan to implement GSA and PSO on our physical waist-tether and hip-exoskeleton platforms to evaluate their convergence behavior and adaptability under real human–machine interaction conditions, where variability, delay, and biological noise are present. These clarifications have been added to the Discussion section.

Added text to the Discussion:

“The relative superiority of the optimization algorithms observed in this study is influenced by the nature of the EMG-based cost landscape and the algorithmic assumptions underlying each method. For instance, GB performs best when the surrogate model approximates smooth and structured nonlinear relationships with minimal noise, benefiting from its ensemble-based gradient correction. In contrast, GSA and PSO leverage population-based exploration and collective learning, which make them well-suited for continuous, low-dimensional optimization problems such as the three-parameter assistance space used in this study. However, their efficiency decreases in higher-dimensional or discontinuous cost landscapes, or when the response surface contains high stochasticity. These observations indicate that algorithmic performance is not universally superior but rather dependent on problem characteristics—particularly the smoothness and noise profile of the surrogate model and the sensitivity of the objective to small parameter perturbations. Furthermore, the promising results of GSA and PSO suggest their potential applicability to real exoskeleton hardware experiments, where adaptive exploration and convergence stability are essential. Future work will test these algorithms on physical waist-tether and hip-exoskeleton systems to assess their robustness in the presence of biological variability, sensor noise, and control latency, thereby linking simulation outcomes to practical human-in-the-loop optimization scenarios.”

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

My concerns have received thoughtful responses, and the essay has been updated and polished. I have no more suggestions for modifications. It is recommended to accept it.

Reviewer 2 Report

Comments and Suggestions for Authors

The author has addressed all the questions. The manuscript can be accepted and published.

Reviewer 3 Report

Comments and Suggestions for Authors

The paper has been revised according to the comments of the reviewer.