In Canada over 70 thousand people are reported missing each year. Autonomous robotic systems can provide a fast method for responding to such situations and have been proposed for a variety of settings. This Thesis considers the use of an autonomous team of unmanned aerial vehicles (UAVs) to perform a sparse, mobile target search for someone who has gotten lost and is missing in an urban environment. A novel multi-UAV search-trajectory planning method, which relies on the prediction of the missing person’s motion, given a known map of the search environment, is the primary focus. The proposed method incorporates periodic updates of the estimates of where the missing person may be, allowing for intelligent re-coverage of previously searched areas. Additional significant contributions of this work include a behavior-based motion-prediction method for missing persons and a novel non-parametric estimator for iso-probability based (missing-person-location) curves. Simulated experiments are presented to illustrate the effectiveness of the proposed search-planning method, demonstrating a 63% increase in the rate of missing person detection in shorter times as compared to other methods.