Purpose Exoskeleton-assisted walking for individuals with paraplegia presents unique biomechanical challenges due to minimal lower-limb actuation and substantial reliance on upper-body support via crutches. However, quantitative models rarely elucidate the dynamic interplay between exoskeleton actuation and crutch assistance. Methods We introduce a double-inverted pendulum model that captures the essential dynamics of crutch-supported exoskeleton gait. The model extends the canonical inverted pendulum framework by directly encoding gravitationally induced hip torques and ground reaction forces (GRFs) from the crutches. Then it reformulates the equations of motion into the canonical single-inverted pendulum form. Analytic predictions are validated against experimental gait data from a participant using an exoskeleton and crutches. Results The model reconstructed internal mechanical energetics, with <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\textrm{RMSE} = 9\%\)</EquationSource> </InlineEquation> of a detailed skeletal model’s total mechanical energy cycle range and Pearson’s correlation <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(r = 0.94\)</EquationSource> </InlineEquation>. It also faithfully reproduced the external-force dynamics from foot and crutch GRFs, and the offset between the center of mass (CoM) and the pelvis on the mediolateral, anteroposterior, and axial movements of the pelvis, with low <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\textrm{RMSE}\)</EquationSource> </InlineEquation> (<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(4-6\%\)</EquationSource> </InlineEquation>) and high <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(R^2\)</EquationSource> </InlineEquation> (<InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(0.88-0.94\)</EquationSource> </InlineEquation>). Building on these results, the model clarified the respective contributions of CoM-pelvis offset and crutch GRFs in restoring energy lost at heel strike, and identified how exoskeleton and user maneuvers influence them. Conclusions The analytically tractable double-inverted pendulum model provides a validated framework for quantifying the division of functional roles between user and device in crutch-supported exoskeleton gait. This approach explicitly addresses key biomechanical features that were previously overlooked by prior models, enabling future work on user control strategies.

Modeling and validation of crutch-supported exoskeleton gait using a double-inverted pendulum approach

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2026年4月15日

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Reza Norouzzadeh,
Saeed Behzadipour,
Abolfazl Mohebbi,
Matteo Lancini

摘要

Purpose

Exoskeleton-assisted walking for individuals with paraplegia presents unique biomechanical challenges due to minimal lower-limb actuation and substantial reliance on upper-body support via crutches. However, quantitative models rarely elucidate the dynamic interplay between exoskeleton actuation and crutch assistance.

Methods

We introduce a double-inverted pendulum model that captures the essential dynamics of crutch-supported exoskeleton gait. The model extends the canonical inverted pendulum framework by directly encoding gravitationally induced hip torques and ground reaction forces (GRFs) from the crutches. Then it reformulates the equations of motion into the canonical single-inverted pendulum form. Analytic predictions are validated against experimental gait data from a participant using an exoskeleton and crutches.

Results

The model reconstructed internal mechanical energetics, with \(\textrm{RMSE} = 9\%\) of a detailed skeletal model’s total mechanical energy cycle range and Pearson’s correlation \(r = 0.94\) . It also faithfully reproduced the external-force dynamics from foot and crutch GRFs, and the offset between the center of mass (CoM) and the pelvis on the mediolateral, anteroposterior, and axial movements of the pelvis, with low \(\textrm{RMSE}\) ( \(4-6\%\) ) and high \(R^2\) ( \(0.88-0.94\) ). Building on these results, the model clarified the respective contributions of CoM-pelvis offset and crutch GRFs in restoring energy lost at heel strike, and identified how exoskeleton and user maneuvers influence them.

Conclusions

The analytically tractable double-inverted pendulum model provides a validated framework for quantifying the division of functional roles between user and device in crutch-supported exoskeleton gait. This approach explicitly addresses key biomechanical features that were previously overlooked by prior models, enabling future work on user control strategies.