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arxiv: 2110.00062 · v1 · pith:UVHVDKHTnew · submitted 2021-09-30 · 💻 cs.RO · cs.SY· eess.SY

Simulation-based multi-criteria comparison of mono-articular and bi-articular exoskeletons during walking with and without load

Ali KhalilianMotamed Bonab , Volkan Patoglu This is my paper

Pith reviewed 2026-05-24 13:11 UTC · model grok-4.3

classification 💻 cs.RO cs.SYeess.SY
keywords exoskeleton designmono-articularbi-articularmetabolic costPareto optimizationmusculoskeletal modelingwalking assistancejoint reaction forces
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The pith

Simulations show mono-articular exoskeletons reduce peak joint reaction forces better than bi-articular designs during loaded walking, while bi-articular power use is less sensitive to load and inertia.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper uses musculoskeletal simulations to compare mono-articular and bi-articular exoskeletons for walking assistance under different loads. It applies Pareto optimization to find torque profiles that balance lower human metabolic cost against lower device power consumption, while accounting for actuator limits, device inertia, and energy regeneration. Results indicate that both device types provide similar levels of metabolic assistance, yet mono-articular versions lower peak joint forces more effectively. Bi-articular versions show power consumption that changes less with added load, and their metabolic cost is less harmed by added device inertia without losing optimal trade-off solutions. The work supplies concrete guidelines for selecting device kinematics and assistance profiles based on these criteria.

Core claim

A simulation-based multi-criteria comparison under actuator saturation finds that mono-articular and bi-articular exoskeletons deliver comparable metabolic assistance during walking with and without loads, yet mono-articular devices reduce peak reaction forces more, bi-articular power consumption is less sensitive to loading, and bi-articular device inertia produces smaller increases in metabolic cost while leaving Pareto-optimal solutions unchanged. The study derives optimal assistance torque profiles for each kinematics type, superposes inertia and regeneration effects, and explains how heavy loads alter the preferred torque shapes.

What carries the argument

Pareto optimization of exoskeleton power consumption versus human metabolic rate reduction, applied to musculoskeletal model simulations of mono- versus bi-articular kinematics under actuator saturation, inertia, and regeneration.

If this is right

  • Heavy loads shift the optimal assistance torque profiles for both device types.
  • Design guidelines emerge for choosing mono- or bi-articular kinematics under torque limits, inertia, and regeneration.
  • Mono-articular devices outperform on peak reaction force reduction despite similar metabolic assistance.
  • Bi-articular power consumption varies less with changes in load.
  • Bi-articular inertia affects metabolic cost less severely and preserves Pareto optimality of solutions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Bi-articular designs may suit applications where device mass or load varies frequently.
  • The simulation framework could be extended to test hybrid kinematics that combine mono- and bi-articular elements.
  • These load-dependent guidelines could be checked against other locomotion tasks such as stair ascent.
  • Real hardware prototypes built from the optimized profiles would allow direct comparison of measured versus simulated metabolic savings.

Load-bearing premise

The musculoskeletal model correctly predicts real human metabolic cost, muscle activation, and joint reaction forces when exoskeleton dynamics and torque profiles are added.

What would settle it

Direct measurements of metabolic cost, muscle activity, and joint forces on human subjects wearing the simulated mono-articular and bi-articular exoskeletons while walking with loads, compared against the model's predicted advantages.

Figures

Figures reproduced from arXiv: 2110.00062 by Ali KhalilianMotamed Bonab, Volkan Patoglu.

Figure 1
Figure 1. Figure 1: Kinematics of assistive devices. A parallelogram is used to implement the kinematics of the bi-articular exoskeleton, while the mono-articular exoskeleton is modeled as a two-link serial manipulator. Symbols qA to qD represent the hip and knee joint angles, respectively. Bodies T orso, A, D represent the torso (depicted as grounded for simplicity of analysis), the upper leg, and the lower leg of the user. … view at source ↗
Figure 2
Figure 2. Figure 2: Assistive actuator model of assistive devices. The blue and red arrows represent the action and reaction torques of the assistive actuators on the assistive devices, respectively. October 4, 2021 7/72 [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: presents an overview of the musculoskeletal simulation workflow using OpenSim. The first step of conducting the simulations for each subject is scaling the generic dynamic model to acquire a musculoskeletal model that matches with the anthropometry of each subject. This scaling is performed using OpenSim Scale Tool. Similarly, the maximum isometric forces of the muscles are scaled according to the mass and… view at source ↗
Figure 4
Figure 4. Figure 4: Schematic representation of multi-criteria comparison of bi-articular and mono-articular exoskeletons October 4, 2021 11/72 [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The average absolute power consumption of exoskeletons, maximum positive power of exoskeletons and metabolic rate of subjects. The average absolute and the positive peak power consumption of assistive actuators at each joint and their effect on whole-body metabolic rate of the subjects while walking under noload and loaded conditions. Superscripts indicate statistically significant differences over 7 subje… view at source ↗
Figure 6
Figure 6. Figure 6: Assistance torque profiles and muscle generated moment at each joint under noload and loaded walking conditions. The assistive torques for subjects walking under noload (blue) and loaded (dark blue) conditions, the net joint moments generated by unassisted muscles for walking under noload (green) and loaded (black) conditions, and the moment generated by assisted muscles under noload (rose red) and loaded … view at source ↗
Figure 7
Figure 7. Figure 7: Power profiles of exoskeletons and corresponding net power at the joint. The power profiles of exoskeletons for subjects under noload (blue) and loaded(dark blue) walking conditions, and the net joint power profiles for noload (green) and loaded (black) conditions are shown for each actuator of the exoskeletons. The curves are averaged over simulations of 7 subjects with 3 trials and normalized by the subj… view at source ↗
Figure 8
Figure 8. Figure 8: Representative of bi-articular and mono-articular lower extremity muscles devices, since the ideal assistance torques applied to the joints are practically identical, they result in an identical effect on the muscular activation of the subjects. Note that this result is valid only for ideal devices, assuming that there are no constraints on the actuator torques and the devices lack mass and inertial effect… view at source ↗
Figure 9
Figure 9. Figure 9: Activation of representative lower limb muscles of assisted and unassisted subjects. The activation of unassisted subjects under noload (green) and loaded (black) walking conditions, and assisted subjects under noload (pink) and loaded (dark violet) walking conditions are shown for nine important muscles. The curves are averaged over 7 subjects with 3 trials. is important to note that, while the assistance… view at source ↗
Figure 10
Figure 10. Figure 10: Reaction forces of knee joint of assisted and unassisted subjects. The knee joint reaction forces of unassisted subjects under noload (green) and loaded (black) walking conditions, and assisted subjects by bi-articular/mono-articular exoskeleton during noload (rose red/blue) and loaded (dark rose red/dark blue) walking conditions are shown in anterior/posterior, proximal/distal, and medial/lateral directi… view at source ↗
Figure 11
Figure 11. Figure 11: Reaction forces of patellofemoral joint of assisted and unassisted subjects. The patellofemoral joint reaction forces of unassisted subjects under noload (green) and loaded (black) walking conditions, and assisted subjects by bi-articular/mono-articular exoskeleton during noload (rose red/blue) and loaded (dark rose red/dark blue) walking conditions are shown in anterior/posterior, proximal/distal, and me… view at source ↗
Figure 12
Figure 12. Figure 12: Pareto-front curves characterizing the trade-off between metabolic cost reduction and absolute power consumption. The data points on the Pareto-front curves represent the average and standard deviations over 7 subjects and 3 trials per subjects. The label on each marker denotes results from different peak torque constraints. The hip peak torque constraints are labeled with capital letters from A to E to r… view at source ↗
Figure 13
Figure 13. Figure 13: Power consumption of actuators of optimal exoskeletons lying on the Pareto-front curves. The horizontal axes refer to the non-dominated exoskeletons on the Pareto-front curve. The vertical error bars represent the standard deviation of devices over 7 subjects and 3 trials per subject. October 4, 2021 29/72 [PITH_FULL_IMAGE:figures/full_fig_p029_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Torque profiles of the non-dominated exoskeletons together with the joint moments. Each line represents the torque profile of a non-dominated exoskeleton as defined in the color bar. The data points represent the average over 7 subjects with 3 trials and are normalized by subject mass. The label on each marker denotes results from different peak torque constraints, as defined in [PITH_FULL_IMAGE:figures/… view at source ↗
Figure 15
Figure 15. Figure 15: Power profiles of the non-dominated exoskeletons together with the joint power. Each line represents the power profile of a non-dominated exoskeleton as defined in the color bar. The data points represent the average over 7 subjects with 3 trials and are normalized by subject mass. The label on each marker denotes results from different peak torque constraints, as defined in [PITH_FULL_IMAGE:figures/full… view at source ↗
Figure 16
Figure 16. Figure 16: Inclusion of regeneration effect with different efficiencies on the Pareto solutions. The label on each marker denotes different peak torque constraints, as defined in [PITH_FULL_IMAGE:figures/full_fig_p035_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Pareto fronts under regeneration with 65% efficiency. The label on each marker is denoted to results from different peak torque constraints, as defined in [PITH_FULL_IMAGE:figures/full_fig_p036_17.png] view at source ↗
Figure 17
Figure 17. Figure 17: Inclusion of inertial effects on the Pareto solutions One of the main challenges in the design of mobile exoskeletons is keeping their mass and inertia low, as inertial effects detrimentally impact the metabolic rate of assisted subjects. The effect of inertial properties on the metabolic cost of walking has been studied in the literature, and strong evidence has been provided to show that the metabolic p… view at source ↗
Figure 18
Figure 18. Figure 18: Inclusion of inertial and/or regeneration effects on the Pareto solutions. The label on each marker denotes different peak torque constraints, as defined in [PITH_FULL_IMAGE:figures/full_fig_p038_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Comparison of Pareto-fronts of the mono-articular exoskeletons with various knee actuator placements to bi-articular exoskeletons. Comparison of Pareto-front curves of various exoskeletons: a mono-articular exoskeleton with knee actuation unit placed at the knee, a mono-articular exoskeleton with the knee actuation unit placed on the upper-leg, a mono-articular exoskeleton with the knee actuation unit pla… view at source ↗
Figure 20
Figure 20. Figure 20: Comparison of non-dominated solutions. The mono-articular and bi-articular exoskeleton configurations are compared under (a) ideal conditions, (b) considering the mass/inertia effects on metabolic power consumption, (c) considering power regeneration effects on power consumption, and (d) under both mass/inertia and regeneration effects. The data points on the Pareto-front curves are computed by averaging … view at source ↗
Figure 21
Figure 21. Figure 21: Comparison of Pareto-fronts of the mono-articular exoskeletons with knee actuator near waist to bi-articular exoskeletons. Pareto-front curves of the mono-articular and bi-articular exoskeletons during noload walking condition under ideal conditions and comparison of the Pareto-front curves of the mono-articular exoskeleton with knee actuator near the waist and bi-articular exoskeletons during noload walk… view at source ↗
Figure 22
Figure 22. Figure 22: Torque and power profiles of mono-articular Cb and bi-articular Ec exoskeletons. The torque and power profiles of assistive devices for subjects walking without an additional load (blue), and net joint power and torque profile for noload (green) condition are shown for each actuator of the devices. The torque profile of moment generated by muscles (rose pink) is shown for each joint for both devices. The … view at source ↗
Figure 23
Figure 23. Figure 23: Torque, power, and muscles generated moment profiles of assistive devices. The root mean square error between actuators of bi-articular and mono-articular devices and the muscles generated moment of subjects assisted by these devices. The RMSE was calculated during a total gait cycle (A), loading response (B), mid stance (C), terminal stance (D), pre swing (E), initial swing (F), mid swing (G), and termin… view at source ↗
read the original abstract

Developing exoskeletons that can reduce the metabolic cost of assisted subjects is challenging since a systematic design approach is required to capture the effects of device dynamics and the assistance torques on human performance. Design studies that rely on musculoskeletal models hold high promise in providing effective design guidelines, as the effect of various devices and different assistance torque profiles on metabolic cost can be studied systematically. In this paper, we present a simulation-based multi-criteria design approach to systematically study the effect of different device kinematics and corresponding optimal assistive torque profiles under actuator saturation on the metabolic cost, muscle activation, and joint reaction forces of subjects walking under different loading conditions. For the multi-criteria comparison of exoskeletons, we introduce a Pareto optimization approach to simultaneously optimize the exoskeleton power consumption and the human metabolic rate reduction during walking, under different loading conditions. We further superpose the effects of device inertia and electrical regeneration on the metabolic rate and power consumption, respectively. Our results explain the effects of heavy loads on the optimal assistance profiles of the exoskeletons and provide guidelines on choosing optimal device configurations under actuator torque limitations, device inertia, and regeneration effects. The multi-criteria comparison of devices indicates that despite the similar assistance levels of both devices, mono-articular exoskeletons show better performance on reducing the peak reaction forces, while the power consumption of bi-articular devices is less sensitive to the loading. Furthermore, for the bi-articular exoskeletons, the device inertia has lower detrimental effects on the metabolic cost of subjects and does not affect the Pareto-optimality of solutions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The paper presents a simulation-based multi-criteria design approach using musculoskeletal models to compare mono-articular and bi-articular exoskeletons during walking with and without load. It employs Pareto optimization to simultaneously minimize exoskeleton power consumption and human metabolic rate reduction under actuator saturation, while superposing effects of device inertia and electrical regeneration. Results indicate that mono-articular devices better reduce peak reaction forces despite similar assistance levels, bi-articular device power consumption is less sensitive to loading, and bi-articular inertia has lower detrimental effects on metabolic cost without affecting Pareto-optimality.

Significance. If the underlying musculoskeletal model predictions hold, the work offers systematic design guidelines for exoskeleton kinematics and torque profiles across loading conditions, with the Pareto-front approach providing a clear multi-objective framework that accounts for actuator limits, inertia, and regeneration. The simulation methodology enables exploration of parameter spaces not easily accessible experimentally.

major comments (2)
  1. [Abstract] Abstract and results sections: All comparative claims (mono- vs. bi-articular performance on peak reaction forces, loading sensitivity of power consumption, and inertia effects on metabolic cost) rest on forward simulation outputs from a single musculoskeletal model taken as ground truth for metabolic rate, muscle activation, and joint forces. No cross-validation against human subject data under the same torque profiles, actuator saturation, or added inertia is referenced, making the reported differences sensitive to any systematic model bias in device-human interaction.
  2. [Methods] Methods (model description): The central assumption that the model accurately predicts metabolic cost and reaction forces under exoskeleton assistance and varying loads is load-bearing for the multi-criteria comparison and design guidelines, yet the manuscript provides no experimental validation or sensitivity analysis to alternative model parameters for these assisted conditions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive feedback on our simulation-based study. We address the major comments below regarding the reliance on the musculoskeletal model.

read point-by-point responses

  1. Referee: [Abstract] Abstract and results sections: All comparative claims (mono- vs. bi-articular performance on peak reaction forces, loading sensitivity of power consumption, and inertia effects on metabolic cost) rest on forward simulation outputs from a single musculoskeletal model taken as ground truth for metabolic rate, muscle activation, and joint forces. No cross-validation against human subject data under the same torque profiles, actuator saturation, or added inertia is referenced, making the reported differences sensitive to any systematic model bias in device-human interaction.

    Authors: The study is designed as a simulation investigation to systematically explore exoskeleton designs using established musculoskeletal modeling techniques. While we acknowledge that the results depend on the model's accuracy and that direct experimental validation under assisted conditions is not included, the comparative claims are made relative to the same model for both device types, allowing for consistent comparison. We will revise the abstract, results, and discussion sections to explicitly note the simulation nature of the work and the potential for model bias, and to suggest future experimental studies for validation. This will ensure the claims are appropriately qualified. revision: yes

  2. Referee: [Methods] Methods (model description): The central assumption that the model accurately predicts metabolic cost and reaction forces under exoskeleton assistance and varying loads is load-bearing for the multi-criteria comparison and design guidelines, yet the manuscript provides no experimental validation or sensitivity analysis to alternative model parameters for these assisted conditions.

    Authors: We agree that experimental validation for assisted conditions would be ideal. The model is based on standard OpenSim implementations with metabolic cost models validated in literature for unassisted walking. To strengthen the manuscript, we will add a dedicated subsection in the discussion on model assumptions, limitations, and the need for sensitivity analyses. We will also perform and include a basic sensitivity analysis on key parameters affecting metabolic cost and joint forces if feasible within the revision timeline. revision: partial

Circularity Check

0 steps flagged

No circularity: results derive from forward simulation on standard musculoskeletal models

full rationale

The paper performs Pareto optimization of exoskeleton power consumption versus metabolic rate reduction by running forward dynamics simulations on established musculoskeletal models under varying loads and actuator constraints. All reported comparisons (mono- vs. bi-articular performance on peak forces, inertia sensitivity, Pareto fronts) are direct outputs of these simulations rather than quantities fitted to data within the paper and then re-labeled as predictions. No self-citation chains, uniqueness theorems, or ansatzes imported from prior author work are used to justify the central claims; the model itself is treated as an external, independently developed benchmark. This is the normal case of a self-contained simulation study.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The paper relies on standard musculoskeletal simulation frameworks and optimization routines drawn from prior literature; no new free parameters, ad-hoc axioms, or invented physical entities are introduced in the abstract.

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Reference graph

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