LLM-Enabled Low-Altitude UAV Natural Language Navigation via Signal Temporal Logic Specification Translation and Repair

Natural language (NL) navigation for low-altitude uncrewed aerial vehicles (UAVs) provides an intuitive interface for non-expert operators and supports more accessible aerial services. However, deploying this capability in urban environments requires grounding often underspecified instructions into safety-critical and dynamically feasible motion plans under spatiotemporal constraints. To address this challenge, we propose a unified framework that translates NL instructions into Signal Temporal Logic (STL) specifications and subsequently synthesizes trajectories via mixed-integer convex programming (MICP). Specifically, to generate executable STL formulas from free-form NL, we develop a reasoning-enhanced large language model (LLM) trained with chain-of-thought (CoT) supervision and group-relative policy optimization (GRPO), which improves syntactic validity and semantic consistency. Furthermore, to resolve infeasibilities induced by overly restrictive logical, spatial, or temporal requirements, we introduce a specification repair mechanism. This module combines MICP-based diagnosis with LLM-guided semantic reasoning to select predicate and temporal repair modes, while constraints assigned the no-relaxation mode remain hard in the subsequent optimization. Experiments on NL-to-STL translation, simulation studies, and real-world flight tests show that the proposed framework improves executable specification generation, restores feasibility through semantic repair, and supports safe, interpretable UAV navigation in complex scenarios.