A realistic model of frequency-based multi-robot polyline patrolling

There is growing interest in multi-robot frequency-based patrolling, in which a team of robots optimizes its frequency of point visits, for every point in a target work area. In particular, recent work on patrolling of open polygons (e.g., open-ended fences) has proposed a general cooperative patrolling algorithm, in which robots move back and forth along the polygon, in an synchronized manner, such that their assigned areas of movement overlap. If the overlap factor is carefully chosen---based on the motion models of the robots---specific performance criteria are optimized. Unfortunately, previous work has presented analysis of motion models in which there are no errors in the movement of the robots, and no velocity changes. We go a step beyond existing work, and develop a realistic model of robot motion, that considers velocity uncertainties. We mathematically analyze the model and show how to use it to find optimal patrolling parameters, given known bounds of uncertainty on the motion. We then use the model to analyze the independently-programmed patrolling movements of physical robots, in extensive experiments. We show that the model predicts the behavior of the robots much more accurately than previously-described models.