Fig 1.
Overview of simulation approach.
Left: We used a two-step approach to simulate the effect of ankle plantarflexion and inversion-eversion exoskeleton torques during walking. In the first step, we used OpenSim Moco to create muscle-driven simulations of walking that tracked experimental motion capture data. In the second step, we applied different ankle plantarflexion and inversion-eversion torques at times between 20% (foot-flat) and 60% (toe-off) of the gait cycle and simulated the effects using forward integration. We simulated five different exoskeleton torques: plantarflexion, eversion, inversion, plantarflexion plus eversion, and plantarflexion plus inversion. The initial state of each exoskeleton simulation was set using the tracking simulation state at the beginning of the applied torque. In the muscle-driven simulations, the excitations from the tracking simulation were prescribed to the muscles and torque actuators in the model. In the torque-driven simulations, the torques generated by muscles in the tracking simulation were applied to the model. Right: The exoskeleton torques had a magnitude of 0.1 N-m/kg and rise and fall times equal to 10% and 5% of the gait cycle, respectively. We computed center of mass acceleration and center of pressure changes at the time of peak exoskeleton torque, and center of mass velocity and position changes were computed at the time that exoskeleton torque ended. The curves illustrate when each quantity was calculated, but do not represent actual trajectories for each quantity.
Fig 2.
Transverse-plane changes in center of mass velocity.
The change in center of mass velocity, calculated at exoskeleton torque end time, projected onto the transverse plane. Velocity changes are normalized to the dimensionless Froude number. Columns represent velocity changes for each exoskeleton torque condition: eversion (light orange), plantarflexion plus eversion (dark orange), plantarflexion (black), plantarflexion plus inversion (dark blue), and inversion (light blue). Thick arrows with filled heads represent changes using the muscle-driven model; thin arrows with open heads represent results using the torque-driven model. Each column includes velocity changes at different exoskeleton torque end times, ranging from 25% (bottom) to 65% (top) of the gait cycle. The horizontal arrow directions are medio-lateral changes in velocity, and the vertical arrow directions are fore-aft changes in velocity. The horizontal axes provide scales for medio-lateral velocity changes, and the fore-aft changes represented by each arrow are scaled to match the horizontal axes. The maximum transverse velocity change observed across both muscle-driven and torque-driven conditions was 0.056 m s-1.
Fig 3.
Sagittal-plane changes in center of mass velocity.
The change in center of mass velocity, calculated at exoskeleton torque end time, projected onto the sagittal plane. Velocity changes are normalized to the dimensionless Froude number. The arrows represent the velocity changes averaged across subjects. Rows represent velocity changes for each exoskeleton torque condition: eversion (light orange), plantarflexion plus eversion (dark orange), plantarflexion (black), plantarflexion plus inversion (dark blue), and inversion (light blue). Thick arrows with filled heads represent changes using the muscle-driven model; thin arrows with open heads represent results using the torque-driven model. Each row includes velocity changes at different exoskeleton torque end times, ranging from 25% (left) to 65% (right) of the gait cycle. The horizontal arrow directions are fore-aft changes in velocity, and the vertical arrow directions are vertical changes in velocity. The vertical axes provide scales for vertical velocity changes, and the fore-aft changes represented by each arrow are scaled to match the vertical axis. The maximum transverse velocity change observed across both muscle-driven and torque-driven conditions was 0.072 m s-1.
Fig 4.
Changes in right foot center of pressure position.
The change in right foot center of pressure position, calculated at exoskeleton peak time, in the sagittal plane. The arrows represent the position changes normalized by foot width and averaged across subjects. Rows represent position changes for each exoskeleton torque condition: eversion (light orange), plantarflexion plus eversion (dark orange), plantarflexion (black), plantarflexion plus inversion (dark blue), and inversion (light blue). Thick arrows with filled heads represent changes using the muscle-driven model; thin arrows with open heads represent results using the torque-driven model. Each row includes position changes at different exoskeleton timings, ranging from 20% (bottom) to 60% (top) of the gait cycle. The horizontal arrow directions are medio-lateral changes in position, and the vertical arrow directions are fore-aft changes in position. The horizontal axes provide scales for medio-lateral position changes, and the fore-aft changes represented by each arrow are scaled to match the horizontal axes. The maximum center of pressure position change observed across both muscle-driven and torque-driven conditions was 0.024 m.