The performance of a driving simulator depends on the efficiency of the embedded motion cueing algorithm. An explicit model predictive control was established recently as a pertinent design framework for the motion cueing algorithm. The complexity of the explicit solution increases manifold when the human vestibular model is considered. The present paper focuses on the complexity reduction of explicit solution using low complexity contractive sets for the motion cueing algorithm. The low-complexity explicit controller is formulated for the efficient control of the motion cueing system for the ULTIMATE driving simulator available in Renault.