This article proposes wheeled mobile robot navigation based on a model predictive control over unimodal potential function. The navigation potential function has a single minimum and no local minima. It is obtained from a discrete graph-based search algorithm that can update the environment changes. Obtained navigation function enables continuous convergent navigation where gradient direction is computed to steer the robot towards the goal. Model predictive control using particle swarm optimization is applied to find the path within areas of the lowest potential and considering the control effort. The proposed solutions feature simple implementation, at moderate computational effort and with good navigation results.