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Fig 1.

Biomechanical models.

The DIP/VIP model (left panel) and the corresponding SIP model (right panel).

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Fig 1 Expand

Table 1.

Anthropometric parameters of the DIP model.

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Table 1 Expand

Table 2.

Visco-elastic parameters of the DIP model.

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Table 2 Expand

Fig 2.

Control models.

Upper panel: the hybrid DIP/VIP control model. q1: ankle rotation angle; q2: hip rotation angle; qcom: VIP rotation angle. τ1: total ankle torque; τ2: total hip torque. GRA: Gravity torque model. STI: Stiffness torque model. The DIP/VIP block corresponds of the overall dynamics of the DIP/VIP model. Lower panel: the simplified SIP model.

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Fig 2 Expand

Table 3.

Range of stability of the intermittent controller.

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Table 3 Expand

Fig 3.

Sway movements generated by the simulation of the DIP/VIP hybrid model.

Blue trace: ankle joint rotation; Red trace: hip joint rotation.

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Fig 3 Expand

Fig 4.

Stabilizing ankle torque generated by the simulation of the DIP/VIP hybrid control model.

The DIP/VIP model (red trace) includes the stiffness component (passive, intrinsic, zero-delay feedback) and the intermittent control torque (active, delayed feedback). The counteracting ankle toppling torque due to gravity is displayed by the blue trace.

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Fig 4 Expand

Fig 5.

Sway orbits in the phase plane (qcom vs. ).

Left Panel: oscillations of the SIP model. Right panel: oscillations of the VIP part of the hybrid DIP/VIP model. Both orbits correspond to a 60 s sway. In order to better understand such similarity of VIP-SIP oscillations, we may consider the range of variation (RoV) of different variables during an observation window of 180 s, having defined as “range” the interval containing 90% of the samples stored during the observation time. Table 4 shows the RoVs for angular rotations, angular speeds and angular accelerations of the two models (DIP/VIP vs. SIP).

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Fig 5 Expand

Table 4.

Range of variation.

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Table 4 Expand

Fig 6.

Coordination of Ankle (q1) and Hip (q2) oscillations from the simulation of the DIP/VIP hybrid model.

The quantities showed are the angular rotations (left panel), the angular velocities (central panel) and the angular accelerations (right panel). The plotted traces correspond to a 60 s sway.

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Fig 6 Expand

Table 5.

Influence of the hip stiffness.

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Table 5 Expand