Control based on vision data is a growing field of research and it is widespread in industry. The amount of data in each image and the processing needed to obtain control-relevant information from this data lead to significant delays with a large variability in the control loops. This often causes performance deterioration since in many cases the delay variability is not explicitly addressed in the control design. In this paper, we approach this problem by applying the ideas of recently developed model-based control design methods, which are tailored to address stochastic delays directly, to the motion control of an omnidirectional robot with a vision-based self-localization algorithm. The completion time or delay of the Random Sample Consensus (RANSAC) based localization algorithm is identified as a stochastic random variable with significant variability, illustrating the practical difficulties with data processing. Our main aim is to show that the novel deadline-driven and event-driven control designs significantly outperform a traditional periodic control implementation for a stochastic optimal control performance index.