Maintaining visibility of a moving holonomic target at a fixed distance with a non-holonomic robot

In this paper we consider the problem of maintaining surveillance of a moving the target by a nonholonomic mobile observer. The observer's goal is to maintain visibility of the target from a predefined, fixed distance, l. The target escapes if (a) it moves behind an obstacle to occlude the observer's view, (b) it causes the observer to collide with an obstacle, or (c) it exploits the nonholonomic constraints on the observer motion to increase its distance from the observer beyond the surveillance distance l. We deal specifically with the situation in which the only constraint on the target's velocity is a bound on speed (i.e., there are no nonholonomic constraints on the target's motion), and the observer is a nonholonomic, differential drive system having bounded speed. We develop the system model, from which we derive a lower bound for the required observer speed. Finally, we consider the effect of obstacles on the observer's ability to successfully track the target.