  Rigid bodies, plastic impact, persistent contact, Coulomb friction, and
massless limbs are ubiquitous simplifications introduced to reduce the
complexity of mechanics models despite the obvious physical inaccuracies that
each incurs individually. In concert, it is well known that the interaction of
such idealized approximations can lead to conflicting and even paradoxical
results. As robotics modeling moves from the consideration of isolated
behaviors to the analysis of tasks requiring their composition, a
mathematically tractable framework for building models that combine these
simple approximations yet achieve reliable results is overdue. In this paper we
present a formal hybrid dynamical system model that introduces suitably
restricted compositions of these familiar abstractions with the guarantee of
consistency analogous to global existence and uniqueness in classical dynamical
systems. The hybrid system developed here provides a discontinuous but
self-consistent approximation to the continuous (though possibly very stiff and
fast) dynamics of a physical robot undergoing intermittent impacts. The
modeling choices sacrifice some quantitative numerical efficiencies while
maintaining qualitatively correct and analytically tractable results with
consistency guarantees promoting their use in formal reasoning about mechanism,
feedback control, and behavior design in robots that make and break contact
with their environment.
