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In this paper, we address the visibility-based target tracking problem in which a mobile observer moving along a p-route, which we define as a fixed path for target tracking, tries to keep a mobile target in its field-of-view. By drawing a connection to the watchman's route problem, we find a set of conditions that must be satisfied by the p-route. Then we propose a metric for tracking to estimate a sufficient speed for the observer given the geometry of the environment. We show that the problem of finding the p-route on which the observer requires minimum speed is computationally intractable. We present a technique to find a p-route on which the observer needs at most twice the minimum speed to track the intruder and a reactive motion strategy for the observer. 

This work explores a variation of the art gallery problem in which a team of static and mobile guards track a mobile intruder with unknown maximum speed. We consider the special case when the mobile guards are restricted to move along the diagonals of a polygonal environment. First, we present an algorithm to identify candidate vertices in a polygon at which either static guards can be placed or they can serve as an endpoint of the segment on which mobile guards move. Next, we present a technique to partition the environment based on the triangulation of the environment, and allocate guards to each partition to track the intruder. The allocation strategy leads to a classification of the mobile guards based on their task and coordination requirements. Finally, we present a strategy to activate/deactivate static guards based on the speed of the intruder. Simulation results are presented to validate the efficacy of the proposed techniques.