Quotient method for stabilising a ball-on-a-wheel system — Experimental results

This paper extends the quotient method proposed in [1] and applies it to stabilize a “ball-on-a-wheel” system. The quotient method requires a diffeomorphism to obtain the normal form of the input vector field and uses canonical projection to obtain the quotient. However, the whole process can be done without computing the normal form, which requires defining a quotient generating function and a quotient bracket. This paper presents the steps necessary to apply the quotient method without obtaining the normal form. Furthermore, a Lyapunov function is introduced to prove stability. This paper also presents the experimental implementation of the quotient method to stabilize a ball-on-a-wheel system.