Control of a mobile robot with an onboard robot arm is examined in this paper. Since controllers are implemented on a digital computer, a fuzzy logic controller ( FLC) is designed in discrete-time. This FLC performs feedback linearization of the composite system and provides an inner loop that accounts for possible motion of the onboard arm. A repeatable design algorithm and stability proof is examined for the adaptive FLC that uses basis vectors based on the fuzzy basis function (FBF) system, unlike most standard adaptive control approaches which use basis vectors depending on the unknown plant (e.g. a tediously computed ‘regression matrix’). Novel fuzzy system parameter update schemes are investigated. Using this discrete-time adaptive FLC the uniform ultimate boundedness of the closed-loop signals is presented for the composite system and the controller achieves tracking under a persistence of excitation condition. The fuzzy system parameter updates yield passivity of the closed-loop system. In fact, the fuzzy logic (FL) system designed is a model-free fuzzy controller that can be applied for any state feedback linearizable nonlinear system including non-holonomic systems in the given class of systems. Finally, the cases of maintaining a desired course and speed and that of achieving a desired final orientation (docking angle) as the onboard arm moves to its desired orientation, are considered. Simulation results are presented in order to justify the theoretical conclusions