Abstract This article presents a study of interval estimation approach based on functional interval observers for mecanum‐wheels omnidirectional automated guided vehicle (MOAGV). In the context of MOAGV, the nonlinear system in discrete time incorporates model uncertainty and unknown bounded disturbances. A functional observer is developed by integrating terminal sliding mode and techniques, aiming to reduce the impact of lumped disturbances/uncertainties. Additionally, a novel observer structure is introduced to increase the degrees of freedom in the design process. Subsequently, the linear function bounds are obtained using the reachability analysis of the estimation error. Finally, the performance of the improved functional interval observer is demonstrated by numerical simulations.