Fig 1.
The DIP/VIP model (left panel) and the corresponding SIP model (right panel).
Table 1.
Anthropometric parameters of the DIP model.
Table 2.
Visco-elastic parameters of the DIP model.
Fig 2.
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.
Table 3.
Range of stability of the intermittent controller.
Fig 3.
Sway movements generated by the simulation of the DIP/VIP hybrid model.
Blue trace: ankle joint rotation; Red trace: hip joint rotation.
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.
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).
Table 4.
Range of variation.
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.
Table 5.
Influence of the hip stiffness.