  This paper develops a comparative framework for the design of actuated
inertial appendages for planar, aerial reorientation. We define the Inertial
Reorientation template, the simplest model of this behavior, and leverage its
linear dynamics to reveal the design constraints linking a task with the body
designs capable of completing it. As practicable inertial appendage designs
lead to morphology that is generally more complex, we advance a notion of
"anchoring" whereby a judicious choice of physical design in concert with an
appropriate control policy yields a system whose closed loop dynamics are
sufficiently captured by the template as to permit all further design to take
place in its far simpler parameter space. This approach is effective and
accurate over the diverse design spaces afforded by existing platforms,
enabling performance comparison through the shared task space. We analyze
examples from the literature and find advantages to each body type, but
conclude that tails provide the highest potential performance for reasonable
designs. Thus motivated, we build a physical example by retrofitting a tail to
a RHex robot and present empirical evidence of its efficacy.
