  We present a recipe for rendering a submanifold normally hyperbolic and
invariant within a stability basin. The construction includes the ability to
choose the asymptotic phase map. We are motivated by the notion of "templates
and anchors" -- the biomechanical observation that animal motions are often
governed by low dimensional dynamics -- and the growing applications in
robotics which desire means for making such biologically derived templates
govern the dynamics of robots. Our approach is fairly universal, in the sense
that a broad range of model reduction constructions must be normally hyperbolic
if they are robust, and a broad range of such normally hyperbolic systems can
be produces from our construction.
