Mobile edge computing (MEC)-empowered spaceair-ground integrated Internet-of-Things (IoT) networks (SAGIINs) provide a promising solution for computation-intensive tasks generated by mobile IoT devices (IDs). However, task offloading in SAGIINs is challenging due to time-varying IDto-unmanned aerial vehicle (UAV) channels, intermittent LEO satellite service availability, and the coupling among UAV trajectory, communication, computation, and energy decisions. This paper investigates an energy-efficient task offloading and UAV trajectory planning problem in an MEC-empowered SAGIIN, where one UAV acts as both an aerial relay and an MEC server, and multiple LEO satellites provide supplementary computing resources. The UAV trajectory planning, task splitting, and computing resource allocation are jointly optimized to minimize the total system energy consumption under task completion, communication, computation, flight region, and satellite service window constraints. The resulting non-convex problem is decomposed into a UAV trajectory planning subproblem and a task splitting and computing resource allocation subproblem. To solve the former, a retrieval-augmented generation (RAG)-assisted large language model (LLM)-enhanced deep deterministic policy gradient (DDPG) algorithm, termed RLD, is proposed. The latter is shown to be convex and can be solved by using CVXPY for a given UAV trajectory. A weighted retrieval score is further designed to balance ID mobility-pattern similarity and historical UAV trajectory energy performance. Simulation results show that RLD completes all computational tasks in previously unseen test scenarios while consuming less total energy than the benchmark algorithms.

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