  We have built a 12DOF, passive-compliant legged, tailed biped actuated by
four brushless DC motors. We anticipate that this machine will achieve varied
modes of quasistatic and dynamic balance, enabling a broad range of locomotion
tasks including sitting, standing, walking, hopping, running, turning, leaping,
and more. Achieving this diversity of behavior with a single under-actuated
body, requires a correspondingly diverse array of controllers, motivating our
interest in compositional techniques that promote mixing and reuse of a
relatively few base constituents to achieve a combinatorially growing array of
available choices. Here we report on the development of one important example
of such a behavioral programming method, the construction of a novel monopedal
sagittal plane hopping gait through parallel composition of four decoupled 1DOF
base controllers.
  For this example behavior, the legs are locked in phase and the body is
fastened to a boom to restrict motion to the sagittal plane. The platform's
locomotion is powered by the hip motor that adjusts leg touchdown angle in
flight and balance in stance, along with a tail motor that adjusts body shape
in flight and drives energy into the passive leg shank spring during stance.
The motor control signals arise from the application in parallel of four
simple, completely decoupled 1DOF feedback laws that provably stabilize in
isolation four corresponding 1DOF abstract reference plants. Each of these
abstract 1DOF closed loop dynamics represents some simple but crucial specific
component of the locomotion task at hand. We present a partial proof of
correctness for this parallel composition of template reference systems along
with data from the physical platform suggesting these templates are anchored as
evidenced by the correspondence of their characteristic motions with a suitably
transformed image of traces from the physical platform.
