Certified Robustness in Machine Learning Against Adversarial Attacks in Real-Time Autonomous Navigation Systems

Autonomous navigation systems, ranging from unmanned aerial vehicles (UAVs) to autonomous ground vehicles (AGVs), are increasingly dependent on deep neural networks (DNNs) for high-stakes decision-making. Despite their success, these models are notoriously vulnerable to adversarial attacks, deliberate perturbations to sensor inputs that cause misclassification or catastrophic policy failures. While empirical defenses such as adversarial training are common, they provide no formal safety guarantees. Certified robustness, which offers provable bounds on model behavior within a specified input range, has emerged as a critical requirement for safety-critical robotics. This article provides an in-depth examination of the state-of-the-art in certified robustness, evaluates the trade-offs between formal verification and real-time execution constraints, and proposes a conceptual framework for integrating certified monitors into autonomous navigation pipelines to ensure provable safety in dynamic environments. We further discuss the transition from static verification to temporal safety-critical architectures, the necessity of standardized benchmarks in physical hardware-in-the-loop (HITL) testing, and the socio-technical challenges of integrating formal verification into existing regulatory frameworks. We conclude by advocating for a paradigm shift toward certified training, where robustness is an architectural prerequisite rather than a post-processing patch.