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Despite thousands of years of changes in medical practice, healthcare delivery remains highly dependent on manual human effort. Mobile robots can help clinicians by automating the execution of tasks that do not directly demand medical knowledge (e.g. transporting medications to nurses). Yet, healthcare is a dynamic environment with a constantly mobile workforce. The present work describes a solution to the problem of autonomous robotic tracking of mobile targets in large, dynamic environments supported by a high-resolution, real-time, ultra wideband radio-frequency localization technology. The solution consists of a navigation system able to perform both global and local path planning simultaneously based on an evolutionary computation approach. A priori information and instant sensorial stimuli are integrated by the system in order to evolve efficient trajectories in real-time. The system proposed was tested with dynamic obstacles and targets and was demonstrated to be both highly adaptive and responsive.