This paper presents the development of a low-complexity wheel slip-based vehicle model for an omnidirectional vehicle equipped with Mecanum wheels that is suited for optimal control. Augmenting a vehicle model with wheel slip properties allows for better trajectory tracking, while the reduced model complexity allows for manageable parameter estimation and motion planning with lower computation times. The wheel slip model and optimal motion planning are validated on an in-house developed omnidirectional vehicle for three different surfaces. The estimation procedure of the slip model parameters for these surfaces is discussed and the effective application of these models in optimal motion planning is demonstrated. The results encourage to use simplified wheel slip models in motion planning problems to keep the computation time low and to increase the position accuracy, which reduces the need for positional feedback and fast online motion replanning if slip would occur.