We show how the limited electrical power and FPGA compute resources available in a swarm of small UAVs can be shared by moving FPGA tasks from one UAV to another. A software and hardware infrastructure that supports the mobility of embedded FPGA applications on a single FPGA chip and across a group of networked FPGA chips is an integral part of the work described here. It is shown how to allocate a single FPGA's resources at run time and to share a single device through the use of application checkpointing, a memory controller, and an on-chip run-time reconfigurable network. A prototype distributed operating system is described for managing mobile applications across the swarm based on the contents of a fuzzy rule base. It can move applications between UAVs in order to equalize power use or to enable the continuous replenishment of fully fueled planes into the swarm.