  This paper discusses the problem of designing a self-balancing unicycle where
pedals are used for both power generation and speed control. After developing
the principal physical aspects (in the longitudinal dimension), we describe an
abstract model in the form of a collection of hybrid automata, together with
design requirements to be met by an ideal controller. We discuss
simplifications and assumptions that make this model amenable to verification
and validation tools such as SpaceEx. To enable experimentation with different
prototypical controllers and user behaviours in concrete scenarios, we also
develop a simple simulation framework using digital time.
