Data-Driven Anomaly Detection in Robots Using Matrix Chernoff Bounds
Richa Dubey, Niladri Sekhar Tripathy, Suril Vijaykumar Shah
AI summary
Problem
Traditional robot anomaly detection relies on heuristic thresholds, accurate system models, or computationally heavy learning-based methods, which lack theoretical grounding, scalability, or efficiency for resource-constrained platforms.
Approach
The framework computes a cumulative error covariance matrix from a sliding window of state deviations offline, then applies the Matrix Chernoff Inequality to derive probabilistic bounds on its eigenvalues; real-time eigenvalues are compared against these bounds to flag anomalies.
Key results
- Theoretically grounded probabilistic bounds derived via Matrix Chernoff Inequality
- Accurate detection of input delays, sensor corruption, and external perturbations
- High performance across standard metrics with tunable confidence and window parameters
- Model-independent, computationally efficient implementation requiring only two transcendental equations
Why it matters
Enables reliable, scalable, and lightweight fault monitoring for robots in safety-critical and resource-constrained environments without requiring accurate system models or extensive training data.
Abstract
This work proposes a novel data-driven anomaly de- tection framework for robotic systems, grounded in statistical con- centration 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,computedinrealtime,violatethesetheoreticalbounds. The proposed approach is model-independent, computationally efficient, and straightforward to implement, requiring only the nu- merical 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 perturba- tions. 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.