System-Level Error Propagation and Tail-Risk Amplification in Reference-Based Robotic Navigation

Image guided robotic navigation systems frequently rely on reference-based geometric perception pipelines, where accurate spatial mapping is established through multi-stage estimation processes. In biplanar X-ray–guided navigation, such pipelines are widely adopted due to their real-time capability and geometric interpretability. However, navigation reliability is often constrained by an overlooked system-level failure mechanism in which installation-induced structural perturbations introduced at the perception stage can be progressively amplified along the perception–reconstruction–execution chain and ultimately dominate execution-level error and tail-risk behavior. This paper investigates this mechanism from a system-level perspective and presents a unified error propagation modeling framework that explicitly characterizes how installation-induced structural perturbations propagate and couple with pixel-level observation noise through biplanar imaging, projection matrix estimation, triangulation, and coordinate mapping. By combining first order analytic uncertainty propagation with large-scale Monte Carlo simulations, we analyze dominant sensitivity channels and quantify worst-case error behavior beyond mean accuracy metrics. The results demonstrate that rotational installation error acts as a primary driver of system level error amplification, whereas translational misalignment of comparable magnitude plays a secondary role under typical biplanar geometries. Moreover, installation-induced structural perturbations fundamentally alter the system’s sensitivity to perception noise, leading to pronounced tail-risk amplification that cannot be captured by additive error models. Real biplanar X-ray bench-top experiments further confirm that the predicted error amplification trends persist under realistic imaging and feature extraction uncertainty. Beyond the specific context of biplanar X-ray navigation, the findings reveal a broader structural limitation of reference-based, multi-stage geometric perception pipelines in robotics. By explicitly modeling system-level error propagation and tail-risk behavior, this work formulates a systematic framework for reliability assessment, sensitivity analysis, and risk-aware design in safety-critical robotic navigation systems.