Before revision:  In this work, we show that an underactuated system as a spin-rolling sphere on a plane with three inputs and five states can be transformed into a fully-actuated model by the given Darboux-frame transformation.
After revision:  In this work, we show that an underactuated system as a spin-rolling sphere on a plane with five states and three inputs can be transformed into a fully-actuated model by the given Darboux-frame transformation.