  This paper addresses the problem of tracking mobile intruders in a polygonal
environment. We assume that a team of diagonal guards is deployed inside the
polygon to provide mobile coverage. First, we formulate the problem of tracking
a mobile intruder inside a polygonal environment as a multi-robot task
allocation (MRTA) problem. Leveraging on guard deployment strategies in art
gallery problems for mobile coverage, we show that the problem of finding the
minimum speed of guards to persistently track a single mobile intruder is
NP-hard. Next, for a given maximum speed of the intruder and the guards, we
propose a technique to partition a polygon, and compute a feasible allocation
of guards to the partitions. We prove the correctness of the proposed
algorithm, and show its completeness for a specific class of inputs. We
classify the guards based on the structural properties of the partitions
allocated to them. Based on the classification, we propose motion strategy for
the guards to track the mobile intruder when it is located in the partition
allocated to the guard. Finally, we extend the proposed technique to address
guard deployment and allocation strategies for non-simple polygons and multiple
intruders.
