Figure 1.
Illustration of experiment and modeling approach.
A guinea fowl running a step down (A), and schematic drawing of the spring-loaded inverted pendulum (SLIP) model with swing-leg trajectory control applied as a function of fall time (B). The gray areas indicate the stance phases, and the line represents the body centre of mass (CoM) trajectory. The green dotted line indicates the time between apex and touch down (TD) during which the leg angle of the SLIP is adjusted according to the applied control strategy (see Methods).
Table 1.
Experimental Data.
Table 2.
Experimental Data.
Figure 2.
Swing-leg control strategy simulations of leg angle and leg length adjustment.
Contours lines of constant peak force (blue solid lines) and constant axial impulse (green dashed lines) as a function of TD leg angle and TD leg length, predicted by the model simulations for one forward speed (experimentally observed average forward speed for level running). The gray square highlights the area of experimentally observed TD leg angles and TD leg lengths (lower and upper quartile). The slope of the contour lines reveals that TD leg angle has a much higher influence on both peak force and axial impulse than TD leg length. We subsequently focused our swing-leg control policies on leg angle adjustment only.
Figure 3.
Experimental data: trajectories over time.
Mean values (solid lines) and standard deviation (colored area) of leg angle (A), and leg length (B) (stance leg in blue, swing leg in green), and leg force (C) (axial force in red, fore-aft force in black) against step time for level running and the three step types −1, 0, and +1. The gray areas indicate the stance phases. The leg angle of both stance and swing leg follows a sinusoidal trajectory (A). Compared to the other step types, the compression of the stance leg is lower during the drop step (step 0) (B). In the drop step (step 0), the axial peak force is not significantly different from the previous step (step −1) or level running, but the fore-aft force indicates an acceleration (C).
Figure 4.
Experimental data: landing conditions.
Boxplots of five TD parameters leg angle (A), leg angular velocity
(B), leg length
(C), speed-corrected leg length velocity
(D), and leg stiffness
(E) for level running and the three step types −1, 0, and +1. The boxes indicate the median (black line) and the range between the lower quartile (Q1) and the upper quartile (Q3). The whiskers show the range between the lowest and the highest value still within 1.5× IQR (inter quartile range IQR = Q3 - Q1). For simplicity, individuals and drop heights have been pooled together (see table 2 for more detailed information). Asterisks indicate a significant difference (
) compared to level running (post-hoc t-test). The drop step (step 0) differs significantly from level running for all five variables.
Figure 5.
Experimental measures of stance dynamics, overlaid with simulation predictions.
Boxplots of three stance measures from the running birds: speed corrected axial peak force (A), axial impulse
(B), and fore-aft impulse
for level running and the three step types −1, 0, and +1. Asterisks indicate a significant difference (
) compared to level running. See tables 1 and 2 for more detailed statistical results. The colored lines show the simulation predictions for the three swing-leg control policies applied to the drop step: constant peak force (blue), constant impulse (green), and equilibrium gait (red). Swing-leg trajectories optimized for equilibrium gait predict higher
(A) and
(B) during the drop step (step 0), which is not experimentally observed. Swing-leg trajectories optimized for constant peak force or constant impulse both result in a good match between measured and predicted dynamics. Analysis of simulation fits across all drop perturbation trials suggest these two policies are equally good at predicting changes in landing conditions (table 3, figure 7).
Figure 6.
Representative simulations illustrating the divergence between equilibrium gait (steady gait) and constant peak force control strategies.
CoM trajectories (A) and force profiles (B) of the simulation results for two swing-leg control strategies: constant peak force (blue solid lines) and equilibrium gait (red dashed lines). The equilibrium gait strategy achieves steady dynamics but demands high forces; whereas the constant peak force strategy results in non-steady dynamics in the drop step, and requires adjustment in subsequent steps to return to a steady gait.
Table 3.
Simulated control strategies compared to experimental data.
Figure 7.
Model predicted late-swing leg angular trajectories, in comparison with experimental data.
Predicted swing-leg trajectories, shown as leg angle against fall time (time from apex until TD), derived from SLIP simulations to achieve constant peak force (blue solid lines), constant axial impulse (green dashed lines), or equilibrium gait (red line) at touchdown. Predictions are for a single forward speed . The thick peak force (blue) and impulse (green dashed) contours indicate the predicted swing-leg trajectories, with thinner contours illustrating the gradient in force and impulse as the trajectory deviates from this. The mean measured leg trajectory is overlaid (dotted black line), along with the mean TD conditions for level running (white circle), 4 cm drop (gray circle) and 6 cm drop (black circle). The equilibrium gait trajectory (red) crosses loading contours, leading to increased force and impulse. The linearity of the constant peak force and impulse contours indicates that these strategies can be approximated by leg retraction with a constant angular velocity, whereas equilibrium gait requires leg protraction. The experimental data follows constant loading contours, suggest that guinea fowl do not use swing-leg trajectory to target equilibrium gait.
Figure 8.
Late-swing leg angular trajectories predicted for the equilibrium gait policy, targeting steady gait.
The equilibrium gait policy predicts a shift from late-swing retraction to protraction with increasing speed. Shown are the swing-leg angle trajectories predicted from simulations optimized for equilibrium gait, for a range of speeds . The simulations predict late-swing leg retraction for low speeds (
), and protraction for higher speeds (
).