1
List of abbreviations, deﬁnitions and symbols
Abbreviations
CoM
center of mass
SLIP
spring loaded inverted pendulum model
TD
touch down, referring to landing conditions at the swing-stance transition
Deﬁnitions
Model
A reduced-order mathematical description of the physical sys-
tem. Here we use the highly reductionist spring-mass model
with massless leg.
Landing conditions
Initial conditions of the CoM (position and velocity) at the be-
ginning of stance. These are directly inﬂuenced by the swing-
leg trajectory during ﬂight.
Passive dynamics
Synonymous with intrinsic dynamics—the response of the
physical model. Here, the stance dynamics of the model are
fully determined by landing conditions and leg stiﬀness.
Control policy
Active control applied to the model with a speciﬁc target per-
formance goal. Here the only applied control is late-swing leg
angular trajectory.
Peak force control
Late-swing leg trajectory optimized to target landing condi-
tions for constant peak force of the SLIP model in the drop
step (equal to the peak force of the previous step).
Impulse control
Late-swing leg trajectory optimized to target landing condi-
tions for constant axial impulse of the SLIP model in the drop
step (equal to the impulse of the previous step).
Equilibrium gait control
Late-swing leg trajectory optimized to target landing condi-
tions for perfect disturbance rejection of the SLIP model in
the drop step, resulting in a steady, symmetric gait cycle.
2
Parameters
SI Units
g
gravitational acceleration [m/s2]
m
body mass [kg]
L0
resting leg length [m]
BW = mg
body weight [N]
T =
p
L0/g
periodic time of a pendulum [s]
Non-dimensional
α
leg angle [deg]
αPolicy
angle of the virtual leg (CoM to foot) predicted by a swing-leg control strategy [deg]
αSLIP
angle of the virtual leg for the SLIP model during stance [deg]
˙α
leg angular velocity [deg/T]
∆ECoM
net CoM work [BW L0]
Faxial
axial leg force [BW]
Iaxial
axial leg impulse [BW T]
Ix
fore-aft impulse [BW T]
kLeg
eﬀective linear leg stiﬀness [BW/L0]
L
leg length [L0]
˙L
leg length velocity [L0/T]
r = (x, y)T
CoM position [L0]
˙r = ( ˙x, ˙y)T
CoM velocity [L0/T]
¨r = (¨x, ¨y)T
CoM acceleration [L0/T 2]
t
time [T]

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