Data-Driven Anomaly Detection in Robots Using Matrix Chernoff Bounds

Abstract

This work proposes a novel data-driven anomaly detection framework for robotic systems, grounded in statistical concentration inequalities. The method leverages the Matrix Chernoff Inequality to establish probabilistic bounds on the eigenvalues of cumulative error covariance matrices computed over a sliding window of robot state deviations. An anomaly is flagged when the eigenvalues, computed in real time, violate these theoretical bounds. The proposed approach is model independent, computationally efficient, and straightforward to implement, requiring only the numerical solution of two transcendental equations to determine the bounds. It further offers design flexibility via tunable parameters such as the confidence level and window size. The effectiveness of the detector is validated through both simulation and hardware experiments across distinct anomaly scenarios for different robots, including input delay, sensor corruption, and external perturbations. A comprehensive performance evaluation is also presented using standard metrics such as Detection Rate, False Positive Rate, Accuracy, and Receiver Operating Characteristics (ROC), along with a method for effective parameter selection and comparison with existing works.