| A two-dimensional numerical
model of a horse is presented that predicts the locomotory behaviors of
galloping horses, including how stride frequency, stride length, and metabolic
rate change from a slow canter to a fast gallop. In galloping, each limb
strikes the ground sequentially, one after the other, with distinct time
lags separating hind and forelimb footfalls. In the model, each stance limb
is represented as an ideal linear spring, and both feed-forward and feedback
control strategies determine when each limb should strike the ground. In
a feed-forward strategy, the first hindlimb and the first forelimb to strike
the ground are phase-locked such that the time separating their adjacent
footfalls is held constant by the controller. In distinction, in a feedback
strategy, the footfalls of the second hindlimb and the second forelimb begin
when the first hindlimb and the first forelimb are perpendicular to the
model's trunk, respectively. While any limb is in contact with the ground,
the controller also employs a feedback control to move each stance foot
at a constant tangential velocity relative to the model's trunk. With these
color schemes, the galloping model remains balanced without sensory knowledge
of its postural orientation relative to vertical. This work suggests that
a robot will exhibit behavior that is mechanically similar to that of a
galloping horse if it employs spring-like limbs and simple feed-forward
and feedback control strategies for which postural stabilization is an emergent
property of the system. |
