Swing-Leg Trajectory of Running Guinea Fowl Suggests
Task-Level Priority of Force Regulation Rather than
Disturbance Rejection
Yvonne Blum1, Hamid R. Vejdani2, Aleksandra V. Birn-Jeffery1,3, Christian M. Hubicki2,
Jonathan W. Hurst2, Monica A. Daley1*
1 Department of Comparative Biomedical Sciences, Royal Veterinary College, Hatfield, Hertfordshire, United Kingdom, 2 Mechanical, Industrial and Manufacturing
Engineering, Oregon State University, Corvallis, Oregon, United States of America, 3 Department of Biology, University of California Riverside, Riverside, California, United
States of America
Abstract
To achieve robust and stable legged locomotion in uneven terrain, animals must effectively coordinate limb swing and
stance phases, which involve distinct yet coupled dynamics. Recent theoretical studies have highlighted the critical
influence of swing-leg trajectory on stability, disturbance rejection, leg loading and economy of walking and running. Yet,
simulations suggest that not all these factors can be simultaneously optimized. A potential trade-off arises between the
optimal swing-leg trajectory for disturbance rejection (to maintain steady gait) versus regulation of leg loading (for injury
avoidance and economy). Here we investigate how running guinea fowl manage this potential trade-off by comparing
experimental data to predictions of hypothesis-based simulations of running over a terrain drop perturbation. We use a
simple model to predict swing-leg trajectory and running dynamics. In simulations, we generate optimized swing-leg
trajectories based upon specific hypotheses for task-level control priorities. We optimized swing trajectories to achieve i)
constant peak force, ii) constant axial impulse, or iii) perfect disturbance rejection (steady gait) in the stance following a
terrain drop. We compare simulation predictions to experimental data on guinea fowl running over a visible step down.
Swing and stance dynamics of running guinea fowl closely match simulations optimized to regulate leg loading (priorities i
and ii), and do not match the simulations optimized for disturbance rejection (priority iii). The simulations reinforce previous
findings that swing-leg trajectory targeting disturbance rejection demands large increases in stance leg force following a
terrain drop. Guinea fowl negotiate a downward step using unsteady dynamics with forward acceleration, and recover to
steady gait in subsequent steps. Our results suggest that guinea fowl use swing-leg trajectory consistent with priority for
load regulation, and not for steadiness of gait. Swing-leg trajectory optimized for load regulation may facilitate economy
and injury avoidance in uneven terrain.
Citation: Blum Y, Vejdani HR, Birn-Jeffery AV, Hubicki CM, Hurst JW, et al. (2014) Swing-Leg Trajectory of Running Guinea Fowl Suggests Task-Level Priority of
Force Regulation Rather than Disturbance Rejection. PLoS ONE 9(6): e100399. doi:10.1371/journal.pone.0100399
Editor: Amir A. Zadpoor, Delft University of Technology (TUDelft), Netherlands
Received January 24, 2014; Accepted May 27, 2014; Published June 30, 2014
Copyright:  2014 Blum et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: This study was funded by grant RGY0062/2010 of the Human Frontier Science Program (HFSP). The funders had no role in study design, data collection
and analysis, decision to publish, or preparation of the manuscript.
Competing Interests: The authors have declared that no competing interests exist.
* Email: mdaley@rvc.ac.uk
Introduction
Legged locomotion involves coordination of limb swing and
stance phases with distinct yet tightly coupled dynamics. Studies of
legged locomotion often focus primarily on the dynamics of the
stance phase, during which an animal’s legs experience the
greatest demands for force and power [1–8]. Yet, recent research
highlights the critical role of swing-leg trajectory on locomotor
dynamics—experimental evidence shows that leg loading is
critically sensitive to the initial landing conditions (leg angle, leg
length and body velocity) at the swing-stance transition [9–11],
which are influenced by swing-leg trajectory. Running animals
must effectively coordinate the interplay of swing-leg trajectory,
landing conditions and stance leg loading [12–16]. For example,
when running guinea fowl encounter an unexpected pothole, late-
swing leg retraction leads to variation in leg contact angle, which
explains 80% of the variance in stance leg impulse [17]. Thus, the
swing-leg trajectory is a critical factor in the dynamics of legged
locomotion, particularly during movement over uneven terrain.
Recent theoretical studies have highlighted inherent trade-offs
in swing-leg trajectory for walking and running in uneven terrain.
Simple walking and running models have revealed that swing-leg
velocity just before the stance transition influences numerous
aspects of locomotor dynamics, including stability [14–16,18],
robustness [19], leg work [19,20], disturbance rejection and
collision impact energy losses [18]. Previous studies suggest these
factors cannot be simultaneously optimized—resulting in a trade-
off between two families of performance objectives: swing-leg
velocity can be optimized to minimize peak forces, work and
collision impacts [16,18–20], or to provide stability, disturbance
rejection and robustness of body centre of mass (CoM) dynamics
[15,16,18–20], but not all simultaneously. Thus, a potential trade-
off has emerged between optimal swing-leg trajectory to regulate
leg loading for injury avoidance, or alternatively, to facilitate steady
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gait through disturbance rejection. Yet, while theoretical studies
suggest such a trade-off, there is no experimental data on how
running animals optimize swing-leg trajectory for non-steady
locomotion.
Do running animals favor one end of this trade-off, or
alternatively, find a compromise solution? Both disturbance
rejection and injury avoidance have potential to be important
task-level priorities for running animals. Disturbance rejection
refers to minimizing the effect of perturbations on the body center
of mass (CoM) trajectory [21]. Buffering the CoM motion against
disturbances reduces the risk of fall, and may minimize need for
active control intervention [22,23]. Furthermore, some experi-
mental evidence has suggested steady CoM dynamics as an
important task-level goal in legged locomotion [9,24]. However,
minimizing leg impacts and peak forces may also be critical,
because animal legs have relatively constant safety factors in
musculoskeletal structures around 2–46 the peak forces of steady
locomotion [25,26]. Perfect disturbance rejection can demand
large leg forces [18–20], which could lead to musculoskeletal
injury. Building legs to withstand very large forces would require
carrying extra weight, so limited safety factors in animal legs may
reflect a compromise between safety and economy. Specialized
runners like cursorial ground birds appear to have a structure that
is more optimized for economy, with relatively light legs and thin
tendons, which could inherently limit safety factors [6,26,27],
making them prone to injury [28,29]. Based on these consider-
ations, we reason that both disturbance rejection and injury
avoidance
have
potential
to
be
important,
yet
sometimes
conflicting, task-level priorities in animal locomotion.
In this paper, we test the hypothesis that running guinea fowl
use
swing-leg
trajectory
optimized
to
regulate
leg
loading
(reflecting priority for injury avoidance), against an alternative
hypothesis that they use swing-leg trajectory optimized for
disturbance rejection (reflecting priority for steady body dynam-
ics). These hypotheses represent the two ends of the theoretical
trade-off in swing-leg trajectory described above, providing useful
points of comparison to animal behavior. In reality, animal swing-
leg trajectory could reflect an intermediate compromise solution,
which can be revealed by comparing experimentally observed
swing trajectories to simulation predictions for the two hypothet-
ical extremes. We experimentally measured swing-leg trajectory
and stance dynamics of guinea fowl running over a visible step
down in terrain, when given ample practice, distance and time to
anticipate the drop. This contrasts with previous studies of the
intrinsic-dynamic response to an unexpected terrain drop [10,17].
Here, we are focused on understanding the task-level priorities
reflected in the ‘optimized’ locomotor behavior.
To generate simulation predictions, we use a simple approach
with swing-leg geometry that evolves as a function of time during
the flight phase, according to a prescribed trajectory optimized to
meet a specific performance objective [20,30]. The swing-leg
trajectory determines the landing conditions at the swing-stance
transition, and the landing conditions are used to predict stance
dynamics based on a simple running model (see methods for
model details). We generate simulations with swing-leg trajectory
optimized for three specific performance objectives, the first two
reflecting a priority to regulate leg loading, and the third reflecting
a priority for disturbance rejection. Specifically, we optimize swing
trajectory to achieve i) constant peak force, ii) constant axial
impulse, or iii) perfect disturbance rejection (steady gait) in the step
immediately following a downward step in terrain. Similar swing-
leg control policies have been investigated previously in simula-
tion:
Ernst
and
colleagues
investigated
swing-leg trajectory
optimized to target steady gait (constant speed and bounce
height), to provide disturbance rejection in uneven terrain [30],
and Vejdani and colleagues compared several possible priorities in
simulation, including steady gait, constant leg work and constant
leg loading [20]. Here we directly compare simulation predictions
to new experimental data on guinea fowl running over a visible
step down, to understand how task-level priorities influence swing-
leg control in running birds.
Optimization of swing-leg trajectory to achieve well-defined
intrinsic-dynamic characteristics could be particularly important
for animal locomotion because neuromuscular delays limit the rate
of feedback-mediated responses to perturbations, and terrain
conditions are not often perfectly known. Neuromuscular delays
(synaptic, conduction, electromechanical and force development)
can represent a large fraction of the step cycle in animals [10,31],
and therefore limit the rate of feedback in both stance and swing.
These neural delays are likely to be especially problematic at the
swing-stance transition, when small changes in landing conditions
have large influence on stance leg loading and body dynamics [9–
11]. If the animal’s knowledge of the terrain is imperfect, variation
in terrain height leads to a disturbance, with the immediate
response determined by feed-forward muscle activation and the
system’s intrinsic dynamics [9,10,17]. Application of a prescribed
swing-leg trajectory can provide well-defined intrinsic-dynamic
response in terms of stability, disturbance rejection and leg loading
characteristics, bridging neuromuscular delays and minimizing
need for rapid neural feedback. The focus of this paper is to
understand the task-level mechanical priorities reflected in the
swing-leg trajectory used by running animals.
Methods
1 Experiments
Avian running trials were conducted on a 0:6|4:5 m runway.
Five 0:6|0:9 m force plates (model 9287B, Kistler, Winterthur,
Switzerland) were arranged in a row to record the ground reaction
forces (sampling frequency 500 Hz). A camera system (Qualisys,
Gothenburg, Sweden), consisting of eight high speed infrared
cameras, was used to capture body kinematics (sampling frequency
of 250 Hz). For further analysis, both force data and kinematic
data were interpolated to a frequency of 500 Hz. We used three
experimental terrain conditions: a level runway, a runway with a
4 cm drop and a runway with a 6 cm drop (figure 1(A)).
Five
guinea
fowl
(Numida
meleagris)
(body
mass
m~1:39+0:24 kg, touch down (TD) leg length during level
running LTD,Level~0:21+0:02 m) were encouraged to run from
one end of the runway to the other (running the step down). We
wanted to understand the birds’ optimized strategy, as opposed to
an unexpected perturbation response, so we trained the birds for a
week before data collection. Before data collection, the birds were
accustomed both to the task and to being handled by humans.
Trials for each terrain condition (level, 4 cm drop, 6 cm drop)
were collected in a single block (not randomized), to allow the
birds to correctly anticipate the terrain. We collected 10 steady
running trials per bird per condition, in which the approach up to
the ‘22 step’ (before the middle of the runway) was in straight-line
and approximately steady. Since we could not control the birds’
running speed, we also analyzed their velocity and acceleration
during post-processing, as explained in further detail in 2. Neither
surgery or anesthesia were used in this study because no invasive
procedures were involved. The Royal Veterinary College Ethics
and Welfare Committee approved all of the animal experiment
protocols under the project title ‘Kinematics and kinetics in birds
running over an uneven terrain’.
Swing Leg Trajectory of Running Guinea Fowl
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To approximate the CoM position and the foot point, two
markers were attached to the birds’ back (cranial and caudal), one
at digit III and one at the tarsometatarsophalangeal joint. The
marker placement and techniques used to estimate the initial
position and velocity of the CoM were the same as reported in
[13]. The initial position of the CoM was determined by the
average of the cranial and caudal marker position, and the initial
velocity condition was derived from kinematics using the path-
match optimization technique as described by [17]. We further
corrected the initial position estimate based on the assumption that
the birds’ pitch angular momentum during level running should be
minimized (the body should not pitch forward or backward during
steady running). This optimization led to an estimate of the true
CoM location as positional offsets from the original markers placed
on the birds back (horizontal offset xoffset~0:032+0:015 m,
vertical offset yoffset~{0:040+0:016 m) [13]. We then calculated
the CoM position trajectories by integrating the ground reaction
forces twice.
The following variables were extracted from the experimental
data for further analysis: the length of the virtual leg L, which is
defined as the distance between the CoM and the foot point, and
its derivative, leg length velocity _L (figure 1(B)), the virtual leg
angle a, which is measured anti-clockwise with respect to the
horizontal, and its derivative, leg angular velocity
_a, their
corresponding TD conditions LTD and _LTD, aTD, _aTD, the axial
(directed along the virtual leg) and fore-aft horizontal ground
reaction force Faxial and Fx, respectively, the axial peak force
Faxial,max, the axial and fore-aft impulse Iaxial and Ix, respectively,
which are calculated by integrating the corresponding force
trajectories over stance time, and the net CoM work DECoM,
which is the net change in CoM Energy over the course of stance.
2 Statistical Analysis
We made all parameters non-dimensional by normalizing them
with respect to body mass m, gravitational acceleration g, body
weight BW~mg, average TD leg length during level running
L0~LTD,Level and periodic time of a pendulum T~
ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
L0=g
p
. The
steps were categorized into four step types: level running (Level),
two steps before drop (step 22), the pre-drop step (step 21), the
drop step itself (step 0) and the first post-drop step (step +1). Since
we could not control the birds’ running speed, we analyzed the
fore-aft impulse of step 22 during post-processing and selected
steady trials (i.e. DIxDƒ0:15 BW T, which corresponds to a change
in fore-aft velocity of less than 0:22 m=s) [13]. Step 22 was used
only to assess steadiness of the approach, and not further analyzed.
We analyzed a total of 367 running steps at speeds between
_x~½1:64,4:07m=s with following sample sizes: Level = 167, Step
21 = 73, Step 0 = 70, and Step +1 = 57.
The statistical analysis of the experimental data was performed
in Matlab (R2012a, Mathworks Inc., Natick, MA, USA). We ran a
mixed model multi-way ANOVA on the entire dataset with fixed
effects ‘step type’ nested within ‘drop height’, ‘individual’ as a
random effect and ‘speed’ as a continuous effect (table 1). We then
performed post-hoc pair-wise t-tests for the differences between
the level mean values and the three step types (21, 0, and +1),
separated into the two drop height conditions (4 cm, 6 cm)
(table 2).
As expected, some parameters of gait dynamics were signifi-
cantly influenced by forward speed _x [32,33] (table 1). For
comparison to simulation results, we were interested in under-
standing the effect of the drop perturbation independent from
variance in speed. For the factors that exhibited significant speed
effect in the mixed model ANOVA, we further analyzed the speed
effect using a simple regression analysis. We pooled the normalized
data together (all birds, all trials and all step categories) and
calculated each parameter’s linear regression with respect to _x,
after confirming that the residuals from this regression were
approximately normally distributed. If this analysis revealed a
substantial speed effect by the criteria R2w0:15 and pv0:01, we
recalculated the corresponding parameter (here, we use Y as a
placeholder) by taking the residuals of the linear speed-regression
(YRes) and adding the mean value of level running ( YLevel):
^Y~YResz YLevel:
ð1Þ
Based on these results, for further analysis we used the speed-
corrected leg length velocity ^_L_LTD (R2~0:43, pv0:001) and the
speed-corrected axial peak force ^Faxial,max (R2~0:29, pv0:001).
3 Model
We used the passive, planar spring-loaded inverted pendulum
(SLIP) as a reduced-order representation of whole-body dynamics
of animal locomotion. This model is based on the observation that
animals move with bouncing, spring-like gaits, with ground
reaction forces approximated by a model with a point mass body
and massless legs that resist only compressive loads [34–37]. This
model has been widely used in biomechanics and robotics [38],
because it qualitatively reproduces the dynamics of both walking
[37] and running [34,35]. The SLIP model is a passive, energy
conservative dynamic template of locomotion [39]. While active
stance models have also been suggested as templates for legged
locomotion [40–45], the most appropriate choice of active stance
model for running animals remains unclear. In this study, we are
focused specifically on the influence of swing-leg trajectory on
landing conditions and, consequently, the peak force and impulse
of the leg during stance. The passive SLIP model provides good
prediction of the stance peak force, impulse and overall body
dynamics given specified landing conditions [5,17,34,35,37].
Consequently, the SLIP model is the most appropriate dynamic
template for this study, because it allows us to focus specifically on
the effects of swing-leg trajectory on running dynamics.
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 trajec-
tory 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).
doi:10.1371/journal.pone.0100399.g001
Swing Leg Trajectory of Running Guinea Fowl
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The SLIP model has a multitude of possible solutions,
depending on initial conditions (body position and velocity) and
leg parameters (leg stiffness and leg length). In this model, the body
is represented by a point mass m supported by a linear leg spring
of stiffness k and resting leg length L0, touching the ground with
the angle of attack aTD (figure 1(B)). During flight phase the CoM
follows a ballistic curve, determined by the acceleration of gravity.
The transition from flight to stance occurs when the landing
condition y~L0 sin(aTD) is fulfilled. During stance phase the
equation of motion is given by
m€r~k L0
r {1


r{mg,
ð2Þ
with r~(x,y)T being the position of the point mass with respect to
the foot point, r its absolute value and g~(0,g)T the gravitational
acceleration, with g~9:81 m=s2. Take off occurs when the leg
length (distance between the CoM and toe) exceeds the resting leg
length L0. Since the system is energetically conservative, its state is
fully described by the apex condition (y0, _x0
ð
ÞT, with x0~0 and
_y0~0 (the apex is the highest point of the CoM trajectory).
To estimate appropriate SLIP model leg stiffness k and TD
angle of the virtual leg aTD,SLIP, we optimized these model leg
parameters to match the experimentally observed average ‘steady
gait’ values for forward velocity, apex height, peak axial leg force
and total axial leg impulse. As noted earlier, the peak force,
impulse and body CoM dynamics of animal locomotion can be
well approximated by the SLIP model [5,17,34,35,37]. In level
terrain, all steady steps were included in the average used to fit a
reference steady SLIP model. For the simulations in uneven
terrain (4 cm and 6 cm drop), we used the step prior to the
disturbance (step 21) to generate the reference steady gait,
optimizing the leg parameters to match the peak force, axial
impulse, apex height and forward velocity of this step. The model
leg stiffness remained fixed within a terrain condition, and was
therefore unchanged between step 21 and step 0, but was allowed
to vary between terrains (level versus 4 cm, 6 cm drop runways),
reflecting potential shifts in the reference ‘steady’ gait. The model
was implemented in Matlab (R2012a, Mathworks Inc., Natick,
MA, USA).
4 Running Simulations with Swing-Leg Trajectory
To simulate running, we used the SLIP model with initial
conditions and parameters of the reference steady gait (see above),
and applied a prescribed swing-leg trajectory as a function of fall
time during the flight phase to control TD conditions at the swing-
stance transition. We assume our model has an anticipated time of
ground contact for the nominal steady gait at a given speed, but no
specific information about the terrain, including the size and
location of the drop. We prescribe a continuous evolution of
swing-leg angle as a function of time during the flight phase, from
the instant of apex until the actual ground contact (figure 1). This
means that if the ground is contacted early or late compared to the
reference steady gait, the TD conditions are altered.
During stance, no control was applied, and stance dynamics
were solely determined by the TD conditions applied to the
passive SLIP model. Thus, the only control applied to the model
was the swing-leg trajectory as a function of fall time. We used the
apex to initialize the swing-leg trajectory because it is a unique
event that can be easily detected. Note, we do not assume any
specific mechanisms of control to be analogous between the model
and experiment. We are focused specifically on understanding
how different swing-leg trajectories influence dynamics following a
drop perturbation. A specified swing-leg trajectory could be
achieved through a number of different control mechanisms,
which are not the focus of the current study.
We generated optimized swing-leg trajectories based on three
different objective functions for the subsequent SLIP-modeled
stance phase: i) constant peak force, ii) constant axial impulse, or
iii) equilibrium (steady) gait. For each proposed objective function,
we solved for a swing-leg trajectory as a function of fall time based
on the relationship between landing conditions and predicted
stance phase dynamics using the SLIP model. We focused our
attention specifically on the effects of swing-leg trajectory because
previous experimental studies have suggested leg geometry at
contact as a primary control target in running [5,14,16,17,46].
We performed an initial simulation analysis to reveal the
consequences of simultaneous adjustment of swing-leg length and
angle on the predicted stance peak force and axial impulse of the
SLIP running model. Figure 2 shows the contour lines of constant
peak force (solid lines) and axial impulse (dashed lines) as a
function of TD leg angle and TD leg length, predicted by the SLIP
model for a single forward speed _x~2:84 m=s (average experi-
mentally observed level running speed). Within the region of
Table 1. Experimental Data.
F-ratio
Parameter
Drop Height(Step Type)
Individual
Speed
aTD
[deg]
49.1*
140.6*
0.9
_aTD
[deg/T]
29.8*
36.3*
106.9*
LTD
[L0]
15.2*
25.7*
24.6*
_LTD
[L0/T]
20.6*
145.3*
259.9*
kLeg
[BW/L0]
13.4*
92.2*
8.3*
Faxial,max
[BW]
9.1*
150.3*
67.8*
Iaxial
[BW T]
8.1*
250.0*
77.1*
Ix
[BW T]
15.6*
4.9*
16.5*
DECoM
[BW L0]
11.2*
15.9*
19.1*
Analysis of variance (ANOVA) with four factors: Step type nested within drop height, individual as a random effect, and speed as a continuous effect. N = 367 steps.
Significant differences (pƒ0:05) are indicated by asterisks.
doi:10.1371/journal.pone.0100399.t001
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Table 2. Experimental Data.
Parameter
Level Mean (s.d.)
Drop
Step Type Mean - Level Mean (s.d.)
21
0
+1
aTD
[deg]
122.6
(5.4)
4 cm
0.83
(6.0)
27.1
(6.2)*
21.8
(6.8)
6 cm
20.3
(5.4)
29.7
(6.0)*
21.5
(5.6)
_aTD
[deg/T]
280.9
(15.5)
4 cm
7.0
(16.6)*
220.2
(9.6)*
21.8
(13.1)
6 cm
2.8
(17.6)
224.1
(14.2)*
20.3
(17.8)
LTD
[L0]
1.00
(0.03)
4 cm
20.01
(0.03)*
0.02
(0.03)*
20.01
(0.04)
6 cm
20.02
(0.04)*
0.03
(0.03)*
0.00
(0.04)
^_L_LTD
[L0/T]
1.25
(0.22)
4 cm
0.03
(0.22)
20.18
(0.26)*
0.02
(0.24)
6 cm
0.01
(0.22)
20.24
(0.22)*
0.08
(0.26)
kLeg
[BW/L0]
11.9
(3.8)
4 cm
3.4
(5.3)*
4.1
(4.2)*
3.3
(4.1)*
6 cm
3.1
(4.7)*
4.3
(3.9)*
4.3
(4.0)*
^Faxial,max
[BW]
2.21
(0.36)
4 cm
0.14
(0.47)
0.10
(0.44)
0.21
(0.49)*
6 cm
0.04
(0.45)
20.03
(0.47)
0.33
(0.51)*
Iaxial
[BW T]
1.01
(0.20)
4 cm
0.04
(0.19)
20.04
(0.21)
0.02
(0.22)
6 cm
0.00
(0.26)
20.14
(0.25)*
0.04
(0.28)
Ix
[BW T]
0.01
(0.08)
4 cm
20.03
(0.07)*
0.07
(0.08)*
20.03
(0.09)
6 cm
20.03
(0.06)*
0.08
(0.06)*
20.06
(0.08)*
DECoM
[BW L0]
0.02
(0.17)
4 cm
20.05
(0.17)
0.03
(0.17)
20.12
(0.20)*
6 cm
20.08
(0.14)*
0.01
(0.12)
20.21
(0.28)*
Post-hoc t-test to compare the three step types 21, 0, and +1 to level running. Significant differences (pƒ0:05) are indicated by asterisks.
doi:10.1371/journal.pone.0100399.t002
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experimentally observed TD leg postures (gray square), the force
and impulse contour lines are nearly vertically oriented (figure 2).
This reveals that peak force and axial impulse are strongly
influenced by leg angle at TD, whereas leg length at TD has a
relatively small influence on SLIP-predicted stance leg loading.
These observations suggest leg angle is the more effective target for
swing-leg control of a SLIP running model. Furthermore,
experimentally observed variation in leg length at touchdown is
small in magnitude [17]. Animals tend to run with a consistent leg
posture because variation in leg length influences gearing and
muscle dynamics [10,25]. Consequently, for simplicity, we focused
our predictions on simulations of leg angle adjustment only,
without changes in leg length.
Leg stiffness can also be adjusted as a function of fall time, as a
potential control strategy for running [15]. However, leg stiffness is
a stance parameter, and not a component of the ‘swing-leg
trajectory’ per se. Although we did not directly investigate
adjustment of leg stiffness as a function of fall time, we did
nonetheless account for between-terrain shifts in leg stiffness, by
fitting the nominal steady gait that observed in the ‘21 step’
position on the runway (see Methods section 3). This allowed the
nominal steady gait to change between terrains, but not from step-
to-step. We did, however, measure the experimentally observed
step-by-step variance in effective leg stiffness (see Results and
Discussion).
In the ‘constant peak force policy’, we optimized the leg angle as
a function of fall time such that the resulting peak force during
stance remains constant for all steps. Specifically, we solve for a
trajectory such that if the foot contacts the ground after apex, the
landing conditions lead to a specified SLIP-modeled peak leg
force. When this swing trajectory is applied to the model in the
presence of a drop perturbation, the leg angle evolves until foot
contact, and the peak force of the perturbed step (0) matches the
peak force of the previous step (21).
In the ‘constant axial impulse policy’, we regulate axial leg
impulse rather than peak force, following similar methods. We
solve for a swing-leg angular trajectory as a function of fall time to
maintain a specific constant axial leg impulse achieved by the
SLIP model. When this swing trajectory is applied to the model in
the presence of a drop perturbation, the axial impulse of the
perturbed step (0) matches that of the previous step (21).
The ‘equilibrium gait policy’ has been suggested in theoretical
literature as a method for achieving perfect disturbance rejection
in uneven terrain [20,30,47]. This strategy ensures that the model
achieves a steady gait (constant velocity and bounce height from
apex to apex), with a symmetric CoM trajectories with respect to
the vertical axis defined by mid-stance (TD and take off conditions
are symmetrical). By choosing the appropriate TD leg angle for
each velocity vector during the ballistic flight phase _r~(_x,_y)T, an
equilibrium gait is obtained regardless of when the foot contacts
the ground. We used this relationship to solve for a leg angle
trajectory as a function of fall time to ensure steady gait of the
SLIP model. While birds may not use a perfect equilibrium gait
running, we consider the possible strategy that they optimize
swing-leg trajectory to minimize deviations from an equilibrium
gait for disturbance rejection.
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 _x~2:84 m=s (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.
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Further analysis of simulations using the methods above, as well
as discussion of stability implications, can be found in Vejdani et
al. 2013 [20].
Results
We first report the experimentally observed changes in running
dynamics (section 1), followed by a description of the simulation
predictions (section 2), and comparison between experimental
results and simulation predictions (section 3).
1 Experimental Data
When guinea fowl negotiate an anticipated drop step, the
trajectories over time of leg angle and axial leg force remain
remarkably similar to level terrain locomotion. Figure 3 shows the
measured trajectories over time of the birds’ leg angle (A), leg
length (B), and leg force (C) for the different step types (Level, 21,
0, +1). Notable shifts occur in the stance fore-aft impulse and leg
length trajectory of step 0 (figure 3). The results of the ANOVA for
experimentally measured variables are listed in table 1, with post-
hoc pairwise comparisons in table 2 and boxplots of data in
figures 4 and 5. These findings are summarized below.
Swing-Leg Kinematics in the Drop Step.
The leg angle
follows a consistent sinusoidal trajectory (figure 3(A), blue: stance
leg, green: swing-leg), with little apparent change during negoti-
ation of the drop step. Nonetheless, landing conditions vary in the
drop step due to the extension of the ballistic flight phase at the
transition between steps 21 and step 0. In the elongated flight
phase, continuing leg retraction causes the bird to land with a
steeper leg angle aTD at step 0 compared to level running (table 1).
The leg length trajectory (figure 3(B), green line) also shows a
relatively consistent trajectory across the the step types, but with a
slowed rate of lengthening during the elongated flight phase. This
results in a small but significant increase in leg length LTD, but a
decrease in leg velocity ^_L_LTD at touchdown in step 0 compared to
level running.
Anticipatory Changes in Step 21.
In step 21, preceding
the drop, the leg length LTD, leg angular velocity ^_a_aTD and leg
length velocity ^_L_LTD differ slightly but significantly from level
terrain running (figure 4 and table 2). These findings suggest the
birds tune their gait in anticipation of the drop step, which has also
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 21, 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 21) or level running, but the fore-aft force indicates an acceleration (C).
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been observed during negotiation of visible obstacles [13]. In step
21, the birds reduced leg retraction speed, adopted a 1–2% more
crouched leg posture, and increased effective leg stiffness. The
increase in leg stiffness was maintained across all three steps of the
drop terrain (steps 21,0,+1), whereas the other leg parameters
varied between steps (table 2) across the drop terrain. Nonetheless,
the swing-leg trajectories remain very similar to level running
(figure 3), suggesting that the overall task-level swing-leg control
strategy may be maintained across step types within each terrain,
with variation in the timing of ground contact causing step-by-step
variations in landing conditions.
Body
Dynamics
and
Stance
Leg
Forces.
The
body
dynamics during negotiation of the drop (step 0) are very similar
to those observed by guinea fowl negotiating an unexpected
pothole [17]. The axial peak force remains consistent in the step
preceding (step 21) and during the perturbation (step 0), with no
statistically significant change until step +1 (figure 3(C), and
table 2). The total axial impulse ^Iaxial (integral of force over time)
does not change in step 21, but decreases slightly in step 0, due to
reduced stance duration. The net fore-aft impulse indicates
acceleration in step 0 (figure 5 and table 2), but DECoM does not
differ significantly from level terrain. This indicates that gravita-
tional potential energy of the drop is passively converted to
forward kinetic energy, increasing velocity, similar to unexpected
pothole experiments [17]. The increased velocity is not main-
tained, because the negative fore-aft impulse Ix and the negative
net CoM work DECoM in the subsequent step (step +1) indicate
that the bird actively absorbs energy, slowing down (table 2).
In the step preceding the drop (step 21), the net fore-aft impulse
Ix indicates slight deceleration, and the net change in body CoM
energy DECoM is slightly negative (figure 5 and table 2). Thus, the
results indicate a small active deceleration in anticipation of the
drop.
2 Simulation Results
We generated optimized swing-leg trajectories based upon three
hypothesized task-level priorities: i) constant peak force, (ii)
constant impulse, and iii) equilibrium (steady) gait. The optimized
swing-leg trajectories were applied to a simple running model (see
Methods section 3) to predict the swing and stance dynamics in
‘step 0’ of the drop perturbation.
The simulations of swing-leg trajectory targeting constant peak
force and constant impulse predict relatively similar dynamics
during the drop step (table 3 and figure 5). As an illustration of the
simulation results for a drop perturbation, figure 6 shows the CoM
trajectories (A) and force profiles (B) of the SLIP model with two
swing-leg control strategies—constant peak force (solid lines), and
equilibrium gait (dashed lines). During level running the CoM
trajectories and force profiles are identical, but when the flight
phase duration differs from the expected nominal steady gait, the
predictions of the two control strategies diverge. The predicted
Figure 4. Experimental data: landing conditions. Boxplots of five
TD parameters leg angle aTD (A), leg angular velocity _aTD (B), leg length
LTD (C), speed-corrected leg length velocity ^_L_LTD (D), and leg stiffness
kLeg (E) for level running and the three step types 21, 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 1.56 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 (pƒ0:05)
compared to level running (post-hoc t-test). The drop step (step 0)
differs significantly from level running for all five variables.
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peak force and axial impulse in the drop step increase drastically
for the equilibrium gait strategy. This lends further evidence to the
trade-off suggested from previous theoretical studies (see Intro-
duction). The constant peak force and constant impulse control
strategies both result in a non-steady stance in the drop step,
indicated by a positive fore-aft impulse (figure 5, green and blue
lines).
Thus,
gravitational
potential
energy
from
the
drop
perturbation is converted into horizontal kinetic energy, and the
running model accelerates. This forward acceleration is in
agreement with the experimentally observed dynamics (figure 5C).
3 Comparison between Experimental Data and
Simulation Results
Simulations of constant peak force or constant impulse policies
both result in a reasonably good match between measured and
predicted dynamics. The constant peak force policy provides a
slightly better match to median peak forces and axial impulse;
however 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). Consequently, we
cannot conclusively distinguish between them.
To quantitatively compare simulation predictions to experi-
mental data, the most relevant parameters are TD leg angle in step
0 and the predicted changes in stance dynamics resulting from the
altered landing conditions. The TD leg angle is predicted by
applying the optimized swing-leg angular trajectory during the
ballistic flight phase. The simulations allow us to evaluate the
interaction between swing and stance dynamics, and identify
aspects of bird running that match and deviate from the model
predictions. To determine which swing-leg control policy was most
consistent with guinea fowl behavior, we ran a simulation for each
running trial, predicting the drop step dynamics by applying the
three control policies to the SLIP model as described in the
methods (Methods section 4). For each control policy, table 3
reports the average differences DaTD and root mean squared
errors (RMSE) between the predicted touchdown virtual leg angle
aTD,Policy and experimentally measured aTD (Methods section 3).
Compared to equilibrium gait, both constant peak force and
constant axial impulse control result in smaller deviations between
predicted and measured TD leg angle DaTD and smaller RMSE,
suggesting a more accurate prediction of the TD leg angle across
all three step types simulated (level, 21 and 0).
Stance phase peak force Faxial,max, axial impulse Iaxial, and fore-
aft impulse Ix were simulated by applying the TD conditions
resulting from each swing-leg control policy to the SLIP model
(table 3). The simulation predictions are compared to experimen-
tal data in figure 5, with boxplots showing the distribution of
experimental data and colored lines indicating predictions of each
control strategy. Simulations of the equilibrium gait policy predict
considerable increases in ^Faxial,max and Iaxial during the drop step
(step 0), which is not experimentally observed (figure 5).
To further illustrate the divergence between the force and
equilibrium gait policies, figure 7 shows the swing-leg trajectories
predicted by the different control strategies for one constant
forward speed _x~2:84 m=s (average experimentally observed
forward speed). Contour lines of constant peak force (blue lines)
and constant axial impulse (green lines) are plotted as a function of
TD leg angle (y-axis) and fall time (x-axis), indicating the
trajectories for each control policy (a single predicted swing-leg
trajectory follows a single contour line). The red line indicates the
leg angle trajectory that leads to equilibrium gait (here indicating
swing-leg protraction as a function of fall time). The experimen-
tally measured TD leg angles are shown for level running (white
circle), 4 cm drop (gray circle) and 6 cm drop (black circle). The
experimentally observed TD conditions lie between contour lines
for constant peak force (blue) and constant axial impulse (green),
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 ^Faxial,max (A),
axial impulse Iaxial (B), and fore-aft impulse Ix for level running and the
three step types 21, 0, and +1. Asterisks indicate a significant difference
(pƒ0:05) 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 ^Faxial,max (A) and Iaxial (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).
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but differ markedly from the predictions of equilibrium gait. The
approximate linearity of the contour lines for constant peak force
and constant axial impulse indicate that these policies can be
closely approximated by retracting the leg with a constant angular
velocity (_a&28 deg=T for peak force control, and _a&26 deg=T for
impulse control at the representative forward velocity shown).
For the equilibrium gait policy, the simulation predicted swing-
leg angular trajectory varies between late-swing retraction and
protraction, depending on forward speed. Figure 8 shows the
simulation predicted swing-leg angle trajectories resulting in
equilibrium gait for forward speeds between _x~½0:5,3:5m=s,
with constant leg length and leg stiffness. The simulations predict
late-swing retraction for low speeds (_xv1:68 m=s), and protraction
for higher speeds(_xw1:68 m=s). For a system with the body mass
and virtual leg length of a guinea fowl, running at a forward speed
of _x~1:68 m=s, an equilibrium gait can be achieved with a
constant leg angle (a~120:1 deg), without adjusting the leg angle
during swing (_a~0). Within the observed speed range of guinea
fowl, the equilibrium gait policy predicts late-swing protraction.
Yet, experimental data show that birds consistently retract their
legs in late swing (table 1 and figure 4) across all speeds and step
types.
Although experimentally observed TD leg angles for steady
level running (white circle) lie close to equilibrium gait predictions
Table 3. Simulated control strategies compared to experimental data.
Control Policy
DaTD [deg]
RMSE [deg]
^Faxial,max [BW]
Iaxial [BW T]
Ix [BW T]
Level
Constant Peak Force
20.6
5.4
2.33
1.00
0.03
Constant Impulse
20.5
3.1
2.46
1.08
0.02
Equilibrium Gait
2.0
5.9
2.56
1.20
0
Step 21
Constant Peak Force
20.2
5.0
2.42
1.03
0.04
Constant Impulse
20.4
3.0
2.53
1.10
0.03
Equilibrium Gait
2.5
5.6
2.80
1.22
0
Step 0
Constant Peak Force
20.3
4.5
2.42
0.92
0.08
Constant Impulse
2.0
4.2
2.75
1.10
0.06
Equilibrium Gait
9.0
10.7
4.79
2.21
0
Difference DaTD and root mean squared error (RMSE) of the predicted virtual leg angle at TD aTD,Policy and the experimentally measured virtual leg angle at TD aTD.
Axial peak force ^Faxial,max, axial impulse Iaxial, and fore-aft impulse Ix are the predicted values of the corresponding control strategies. Compared to the equilibrium gait
strategy, the RMSE suggest that both constant peak force and constant impulse control predict the TD leg angle more accurately.
doi:10.1371/journal.pone.0100399.t003
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.
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(red line), there is no evidence that the swing-leg trajectory directly
targets equilibrium gait, because the drop perturbations lead to a
sharp deviation from equilibrium gait predictions. Instead, the
results suggest that the guinea fowl behavior more closely match
predictions of swing-leg trajectory optimized to maintain constant
peak leg force or constant leg impulse.
Discussion
Perturbation experiments [13,17] and theoretical models of
walking and running [14–16,18–20,22] have suggested swing-leg
trajectory as a critical target of control for legged locomotion
because stance dynamics are highly sensitive to landing conditions.
Swing-leg trajectory influences the timing of ground contact, the
landing leg posture and body velocity at contact. These landing
conditions, in turn, influence stability [14–16,18], robustness [19],
leg work [19,20], disturbance rejection and collision impact energy
losses [18]. Swing-leg trajectory can be optimised for consistent leg
loading and economy, or alternatively, for steady body dynamics,
but not all of these simultaneously [15,16,18–20]. We investigated
how running guinea fowl manage this potential trade-off by
measuring their ‘optimized’ locomotor strategy for negotiating a
visible and well-practiced step down in terrain. The simulation
results in figures 6 and 5 provide further evidence of the suggested
trade-off in swing-leg trajectory. The specific swing-leg angular
trajectory used by running guinea fowl is consistent with task-level
priority to regulate leg loading (limiting fluctuations in peak force
and impulse), rather than priority to maintain steady body
dynamics. The birds’ swing-leg angular trajectory is consistent
with both the constant peak force and constant impulse policies,
but clearly deviates from the predictions of the equilibrium gait
policy.
The constant peak force and constant leg axial impulse policies
both predict leg retraction in late swing with nearly constant
angular velocity (figure 7). Previous studies have shown that
running animals tend to retract the leg in late swing [14,17,48];
however, these studies could not explain the specific leg retraction
velocities used by animals, because a wide range of retraction
velocities can provide stability [14–16]. ‘Stability’ simply refers to
whether or not the system recovers—whether a deviation in body
dynamics decays (stable) or grows (unstable) over time [49,50].
Priority for stability alone is not sufficient to predict a specific leg
angular trajectory. The equilibrium gait policy predicts a specific
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 _x~2:84 m=s. 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.
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leg angular trajectory by targeting a perfectly steady gait, which
can theoretically provide perfect disturbance rejection in the face
of terrain height variation [20,47]. However, this policy can
demand large increases in force and impulse in the stance phase.
Furthermore, the equilibrium gait policy can predict either leg
protraction or retraction of the leg in late swing (figure 8). While
stable spring mass running with swing-leg protraction is possible
(with appropriately tuned leg stiffness) [16], this strategy would
result in higher leg impacts due to increased velocity of the foot
with respect to the ground [15] (e.g., the opposite of ‘ground speed
matching’, [48]). This might explain why, to our knowledge, only
swing-leg retraction, never protraction, has been experimentally
observed in bipedal locomotion of humans [51] and birds
[12,16,17].
We found that stance dynamics immediately following the drop
perturbation (step 0) are consistent with a passive energy-
conservative leg model, albeit with a non-steady response in
which gravitational potential energy is converted to kinetic energy,
causing forward acceleration. In fact, the overall body dynamics of
step 0 are remarkably similar to those of an unexpected drop step
[17], despite evidence of anticipatory changes to gait in the drop
terrain. The anticipatory adjustments include small but significant
changes in the nominal gait of step 21 preceding the drop (table 2),
and an increase in effective leg stiffness across all steps in the drop
terrain (figure 4). These findings suggest that guinea fowl tune gait
dynamics depending on context including the anticipated ‘rough-
ness’ of terrain.
Nonetheless, leg angular trajectory remains remarkably con-
stant and rhythmic across steps within each terrain (figure 3),
suggesting that birds target a consistent optimized trajectory within
a terrain context and avoid step-by-step adjustments. A prescribed
swing-leg trajectory has potential to be implemented through feed-
forward control, with minimal feedback, circumventing neuro-
muscular delays. However, our results do not reveal the underlying
neural control mechanisms used to achieve the observed swing-leg
trajectory. A consistent leg angular trajectory could be achieved
through a combination of feedforward and feedback mechanisms,
making use of internal models of dynamics as well as vestibular,
visual and proprioceptive sensory information. Whatever the
underlying control mechanisms, our findings are consistent with
the idea that animals optimize swing-leg trajectory to achieve well-
defined intrinsic-dynamic characteristics at the swing-stance
transition, to bridge neuromuscular delays and minimize the need
for rapid neural modulation.
Although the results confirm that step 0 dynamics can be well
approximated by a passive, energetically conservative leg model,
the dynamics of the 2nd stance (step +1) clearly indicate net energy
absorption, which cannot be achieved with a passive model.
Consequently, a full dynamic model of the birds’ recovery over
several steps requires a more sophisticated stance leg model that
includes actuation. It will be interesting in future work to further
investigate alternative task-level templates of running that allow for
non-conservative stance dynamics following terrain perturbations.
Actuated template models have been proposed and analyzed from
a theoretical perspective [40–45], but it is not yet clear which of
these is most appropriate for animal legged locomotion. Elabora-
tions of stance models were not considered here because we were
primarily focused on the effects of swing-leg trajectory on the
swing-stance transition. Non-conservative stance models would
have confounded the interpretation of swing-leg trajectories. The
initial step down response (step 0) is energetically conservative and
matches well with SLIP leg loading predictions, so we concluded
that a more complex model was not justified for the current study.
Nonetheless, future work should investigate more complex stance
models to further explore the interactions between swing and
stance dynamics in non-steady locomotion, in particular to
understand the full time course of recovery from a perturbation.
Additionally, we observed asymmetry in the force trajectory
across all running conditions—which has also been noted
previously [52] and likely reflects the complex underlying
musculoskeletal structure and dynamics of animal legs. The
passive SLIP model does not predict the precise shape of the
biologically observed leg force trajectory, because it is also
influenced by factors such as damping in tissues, muscle contractile
properties and musculoskeletal gearing effects. The SLIP model
serves only as a general ‘template’ of the overall body dynamics of
running gaits [39], and does not reflect the specific underlying
neuromuscular and musculoskeletal mechanisms. Nonetheless,
template models such as SLIP provide a convenient approxima-
tion of legged locomotion because animals tend to use periodic
gaits with ground reaction forces and body dynamics that can be
approximated by a point mass body with massless legs that resist
only compressive loads [34–37]. The SLIP model is not the only
model that provides a reductionist approximation of locomotor
dynamics [40–45,49,53–56]; however, it is the most widely
validated choice for simulations of running (see Methods section
3). These caveats aside, we have found that a simple reductionist
model can reproduce many aspects of avian running dynamics
during negotiation of a drop in terrain, by optimizing swing-leg
angular trajectory to target landing conditions that meet the
specific task-level priority of regulating stance leg loading.
The observed strategy of minimizing fluctuations in peak force
and impulse may also minimize energy cost of transport. Cost of
transport is influenced by both muscular force and work [6,56],
which is therefore strongly related to ground reaction force [57].
Additionally, a separate simulation study has compared swing-leg
trajectories optimized for force, impulse and leg work, and found
that all three of these policies predict similar swing-leg trajectories,
yet diverge from the predictions of an equilibrium gait policy [20].
Thus, it appears that load regulation and economy are closely
aligned priorities. A swing-leg trajectory optimized to regulate leg
loading may have the dual benefits of minimizing injury risk and
maximizing economy of uneven terrain locomotion.
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
_x~½0:5,3:5m=s. The simulations predict late-swing leg retraction for
low speeds ( _xv1:68 m=s), and protraction for higher speeds
(_xw1:68 m=s).
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The majority of animal locomotion studies have focused on
steady-state locomotion, and many studies either implicitly or
explicitly assumed that steady gait is an overriding priority and
therefore a direct target of active control. While animals must
avoid falling in uneven terrain, ‘stability’ and ‘disturbance
rejection’ or ‘steadiness’ of gait may not be exceptionally pressing
priorities for the control of swing-leg trajectory compared to other
task-level demands, such as injury avoidance and economy.
Applying a swing-leg trajectory that enforces a steady gait could
dramatically increase the peak force and impulse experienced by
the leg in the presence of a terrain drop. These forces could easily
exceed the safety factors of animal musculoskeletal tissues, which
are around 2–46 peak force of steady locomotion [25,26].
Therefore, minimizing fluctuations in peak force and impulse to
prevent damage to musculoskeletal structures might be a more
pressing priority than immediate recovery to a nominal steady gait
following perturbations.
Nonetheless, disturbance rejection is likely an important priority
over slightly longer timescales. This conclusion is supported by the
experimental finding that guinea fowl consistently recover from
terrain perturbations within about 2–3 strides [10,11,13], but do
not exhibit perfect, immediate disturbance rejection, even for
small terrain perturbations [13]. We suggest that the immediate
imperatives of swing-leg control in animal legged locomotion are
related
to
injury
avoidance
and
economy,
not
immediate
stabilization to a nominal steady gait, while stance phase
mechanisms (e.g., energy absorption/insertion) facilitate recovery
to steady gait over multiple steps.
Our simulations suggest a simple method for generating target
swing-leg trajectories for implementation in legged robots to
achieve performances similar to that of running animals. The
‘equilibrium gait’ policy has been suggested for legged robots for
its disturbance rejection properties [30,47]; however, we suggest
that it may be undesirable for systems with significant force
limitations. A separate recent paper explores in more detail
simulations of running dynamics with multiple alternative swing-
leg control policies [20], and this paper also further discusses
potential implications for bio-inspired robots. This systematic
approach of comparing predictions based on multiple potential
task-level priorities could help engineers design and control robots
to benefit from passive-dynamic structures, minimize actuator
demands and minimize control effort.
Conclusions
We have presented a novel approach combining simulations
and experiment that allows us to investigate the task-level priorities
in non-steady animal locomotion, including disturbance rejection,
injury avoidance and economy. Guinea fowl negotiate a down-
ward step using unsteady dynamics with forward acceleration, and
recover to steady gait in subsequent steps. ‘Steadiness’ of gait does
not appear to be the direct or immediate priority governing swing-
leg trajectory used by running animals. Our results suggest,
instead, that guinea fowl use swing-leg trajectories that reflect
priority for load regulation, which may facilitate injury avoidance
and economy in uneven terrain.
Supporting Information
Text S1
List of symbols, terms and definitions.
(PDF)
Acknowledgments
The authors thank D. Renjewski, S. D. Wilshin and J. Gordon for fruitful
discussions and feedback on the manuscript.
Author Contributions
Conceived and designed the experiments: MAD JWH. Performed the
experiments: YB ABJ. Analyzed the data: YB HRV MAD. Contributed
reagents/materials/analysis tools: ABJ HRV. Wrote the paper: YB HRV
MAD JWH. Discussed and interpreted data: YB HRV ABJ CMH MAD
JWH.
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Swing-leg trajectory of running guinea fowl suggests task-level priority of force regulation rather than disturbance rejection.
Blum, Yvonne,Vejdani, Hamid R,Birn-Jeffery, Aleksandra V,Hubicki, Christian M,Hurst, Jonathan W,Daley, Monica A