Analytical Foundations and the Shadow Theorem for Resilient Distributed Robotics

This document explores the formalization of the EFIR-Shadow (ESA) algorithm, an analytical framework designed to improve state estimation stability in distributed ROS2 architectures under conditions of severe information decoherence. By modeling uncertainty as a geometric property of the Information Field I(x,t)I(x,t)I(x,t), the work introduces the Shadow Theorem as a mechanism to handle communication scenarios characterized by significant packet loss (e.g., >70%). The proposed approach does not replace classical Bayesian estimators, such as the Kalman filter introduced by Rudolf E. Kalman, but complements them by providing a regime specifically suited for information collapse conditions. Experimental results obtained on heterogeneous Raspberry Pi 4/5 environments indicate a consistent improvement in tracking robustness and stability compared to standard stochastic estimation methods, particularly in the presence of non-Gaussian disturbances and network-induced decoherence.