This paper discusses the problem of tracking a moving target by means of a cluster of mobile agents that is able to sense the acoustic emissions of the target, with the aim of improving the target localization and tracking performance with respect to conventional fixed-array acoustic localization. We handle the acoustic part of the problem by modeling the cluster as a sensor network, and we propose a centralized control strategy for the agents that exploits the spatial sensitivity pattern of the sensor network to estimate the best possible cluster configuration with respect to the expected target position. In order to take into account the position estimation delay due to the frame-based nature of the processing, the possible positions of the acoustic target in a given future time interval are represented in terms of a compatible set, that is, the set of all possible future positions of the target, given its dynamics and its present state. A frame-by-frame cluster reconfiguration algorithm is presented, which adapts the position of each sensing agent with the goal of pursuing the maximum overlap between the region of high acoustic sensitivity of the entire cluster and the compatible set of the sound-emitting target. The tracking scheme iterates, at each observation frame, the computation of the target compatible set, the reconfiguration of the cluster, and the target acoustic localization. The reconfiguration step makes use of an opportune cost function proportional to the difference of the compatibility set and the acoustic sensitivity spatial pattern determined by the mobile agent positions. Simulations under different geometric configurations and positioning constraints demonstrate the ability of the proposed approach to effectively localize and track a moving target based on its acoustic emission. The Doppler effect related to moving sources and sensors is taken into account, and its impact on performance is analyzed. We compare the localization results with conventional static-array localization and positioning of acoustic sensors through genetic algorithm optimization, and results demonstrate the sensible improvements in terms of localization and tracking performance. Although the method is discussed here with respect to acoustic target tracking, it can be effectively adapted to video-based localization and tracking, or to multimodal information settings (e.g., audio and video).@en