The One-Wheel Cubli project provides an experimental validation that a 3D inverted pendulum, featuring two degrees of freedom, can be stabilized on one of its corners using only a single reaction wheel. 

This is achieved by carefully designing the mass moment of inertia in such a way that the inertia along the two principal tilt axes significantly differs. The consequence is a time-scale separation of the underlying tilt dynamics, which renders the underactuated system controllable. A theoretical investigation reveals that controllability is maximized when the ratio of the two principal inertia values amounts to the square of the silver ratio. A model-based control approach is applied that compensates for cantilever deflections, which arise from the lightweight design of the system.

VIDEO

This video introduces the One-Wheel Cubli, a three-dimensional pendulum system that can balance using just a single reaction wheel. June 28, 2022