In recent papers we proposed a novel approach for mobile robot localization based on set theoretic methods. In this paper we complete this set-based approach by introducing a novel set-based mobile robot path planning algorithm, which can handle the outputs of the set-based localization. In opposite to most known path planning algorithms the approach considers not only kinematic and dynamic constraints of the robot but also noisy measurements from its employed sensors. Realistic simulation experiments validate the effectiveness of the proposed approach.