This paper presents a mathematical model for saccadic motion and fixations. We relate this issue to the problem of motion planning and show that a family of artificial potential functions can be used for creating saccadic motion. The advantage of this approach is that finding the next fixation point does not require an explicit visual search-which is computationally costly and may be problematic in real-time applications. Rather, the system naturally 'slides' from the current fixation into the next. Thus real-time performance on cheap hardware can easily be achieved. Experimental results serve to provide insight into the performance of a robot APES implementing this approach.