The Mercy Variable: Asymptotic Stability of Context-Aware Architecture

Safety-critical autonomous systems are traditionally governed by strict Control Barrier Functions (CBF), which prioritize forward invariance of safe sets above all else. While mathematically robust, this binary approach creates the 'Frozen Robot' problem in Human-Robot Interaction (HRI), where essential empathetic actions are blocked by safety violations. This paper introduces the 'Mercy Variable' architecture: a hierarchical control strategy that introduces a context-aware slack variable into the CBF formulation. By coupling the relaxation of safety constraints to a real-time 'Stability Budget', we demonstrate that robots can exhibit 'mercy'—intentional, bounded violation of laws—without sacrificing global system stability.