Summary
Rolling without slipping is often assumed during modeling unicycles resulting in kinematic constraints and simplified description of the system. However, in real cases, slipping may occur especially in case of low friction coefficients. In this study, the wheel-ground contact of the unicycle is modeled assuming Coulomb friction yielding a limitation on the friction force magnitude. The corresponding dynamical models for the rolling without slipping, and rolling with slipping cases are derived using the Newtonian approach. This limitation on the friction force restricts the feasible steady states and also the realizable maneuvers that can be carried out without the slipping of the wheel as also shown by simulations.
