  As a model is only an abstraction of the real system, unmodeled dynamics,
parameter variations, and disturbances can result in poor performance of a
conventional controller based on this model. In such cases, a conventional
controller cannot remain well tuned. This paper presents the control of a
spherical rolling robot by using an adaptive neuro-fuzzy controller in
combination with a sliding-mode control (SMC)-theory-based learning algorithm.
The proposed control structure consists of a neuro-fuzzy network and a
conventional controller which is used to guarantee the asymptotic stability of
the system in a compact space. The parameter updating rules of the neuro-fuzzy
system using SMC theory are derived, and the stability of the learning is
proven using a Lyapunov function. The simulation results show that the control
scheme with the proposed SMC-theory-based learning algorithm is able to not
only eliminate the steady-state error but also improve the transient response
performance of the spherical rolling robot without knowing its dynamic
equations.
