Mobile robots interact with a dynamically changing, physical environment. All tasks controlling such interactions must be performed reliably and in real-time. Information from the local sensors often is incomplete or inconsistent. Distributed sensor fusion is a technique that enables a team to get a more complete view of the world with a better quality of the provided information. In this paper we address the problem of scheduling the local processing tasks that are part of the overall fusion process. The particular problem to be addressed lies in the unpredictable execution times of these tasks, which do not allow for scheduling using worst-case execution times. The Time-Aware Fault-Tolerant (TAFT) scheduler allows working with expected-case execution times instead, and still achieves a predictable timing behavior. The paper details an efficient scheduling strategy for TAFT based on Earliest Deadline algorithms, formalizing the adopted task model and the underlying scheduling mechanism. Results are presented showing the achieved real-time behavior with an increased acceptance rate, a higher throughput, and a graceful degradation in transient overload situations compared to standard schedulers. Additionally, it describes the implementation of TAFT in the real-time platform that is embedded in our robot team.