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Recent years have witnessed the deployments of wireless sensor networks in a class of mission-critical applications such as object detection and tracking. These applications often impose stringent QoS requirements including high detection probability, low false alarm rate and bounded detection delay. Although a dense all-static network may initially meet these QoS requirements, it does not adapt to unpredictable dynamics in network conditions (e.g., coverage holes caused by death of nodes) or physical environments (e.g., changed spatial distribution of events). This paper exploits reactive mobility to improve the target detection performance of wireless sensor networks. In our approach, mobile sensors collaborate with static sensors and move reactively to achieve the required detection performance. Specifically, mobile sensors initially remain stationary and are directed to move toward a possible target only when a detection consensus is reached by a group of sensors. The accuracy of final detection result is then improved as the measurements of mobile sensors have higher signal-to-noise ratios after the movement. We develop a sensor movement scheduling algorithm that achieves near-optimal system detection performance within a given detection delay bound. The effectiveness of our approach is validated by extensive simulations using the real data traces collected by 23 sensor nodes.