MARCH: Margin-Aware Reasoning for CBF-Harnessed Multi-Agent Control

Control Barrier Functions (CBFs) are widely used to enforce safety by activating a low-level Quadratic Program (QP) to correct high-level planning decisions before execution. This CBF-QP-based architecture is attractive for LLM-based planners and works well in simple single-robot or low-constraint settings, where such corrections are only occasionally needed. However, in swarm systems with multiple coupled constraints, frequent CBF-QP activation can make the low-level CBF-QP hard to solve or even infeasible. This suggests a different perspective: maintaining CBF-QP feasibility is not only a low-level optimization problem; it also depends on whether the high-level LLM planner avoids decisions that repeatedly activate the CBF-QP. Based on this view, we propose Predictive Harness-CBF (Predictive H-CBF), a harness-based framework that uses low-level CBF-QP feedback to revise future high-level decisions generated by an LLM-based planner. Specifically, the harness receives CBF margins and related QP feedback, organizes them together with task context and memory, and generates multiple high-level decision candidates. A predictive evaluator then rolls out these candidates over a short horizon and selects the final decision based on task progress, predicted CBF activation, and QP feasibility. The selected decision guides future high-level LLM output, while the low-level CBF-QP continues to enforce safety during execution. Experiments on 3-D swarm-control tasks show that Predictive H-CBF reduces repeated CBF activation, hard CBF-QP infeasibility, and unnecessary CBF interventions while maintaining competitive coverage performance.