This paper presents an adaptive backstopping station-keeping control using recurrent wavelet fuzzy cerebella model articulation controller (RWFCMAC) for omnidirectional ball-driven chairs used in indoor environments. Lagrangian mechanics is adopted to establish a coupled mathematical model of the vehicle; when the nutation angle is sufficiently small, this model is shown to be consistent with the well-known decoupled model under two special cases. Based on the derived model with uncertainties caused by different riders, an intelligent adaptive controller is developed by using RWFCMAC, aggregated hierarchical siding-mode control and backstepping control, in order to maintain the nutation angle at zero. The effectiveness and merit of the proposed controller are exemplified by conducting several simulations on the laboratory-built omnidirectional ball-riding vehicle.