The Cubli: Modeling and Nonlinear Attitude Control Utilizing Quaternions

This paper covers the modeling and nonlinear attitude control of Cubli, a cube with three reaction wheels mounted on orthogonal faces that becomes wheel based 3D inverted pendulum when positioned in one its vertices. The proposed approach utilizes quaternions instead Euler angles as feedback states. A nice advantage quaternions, besides usual arguments to avoid singularities trigonometric functions, is it allows working out quite complex dynamic equations completely by hand utilizing vector notation. Modeling performed Lagrange validated through computer simulations Poinsot trajectories analysis. derived law linearization technique, thus being time-invariant equivalent linear dynamically linearized at given reference. Moreover, characterized only straightforward tuning parameters. Experimental results are presented.