From Passive Monitoring to Active Defence: Resilient Control of Manipulators Under Cyberattacks

Abstract

Cyber-physical robotic systems are vulnerable to false data injection attacks (FDIAs), in which an adversary corrupts sensor signals while evading residual-based passive anomaly detectors such as the chi-squared test. Such stealthy attacks can induce substantial end-effector deviations without triggering alarms. This paper studies the resilience of redundant manipulators to stealthy FDIAs and advances the architecture from passive monitoring to active defence. We formulate a closed-loop model comprising a feedback-linearized manipulator, a steady-state Kalman filter, and a chi-squared-based anomaly detector. Building on this passive monitoring layer, we propose an active control-level defence that attenuates the control input through a monotone function of an anomaly score generated by a novel actuation-projected, measurement-free state predictor. The proposed design provides probabilistic guarantees on nominal actuation loss and preserves closed-loop stability. From the attacker perspective, we derive a convex QCQP for computing one-step optimal stealthy attacks. Simulations on a 6-DOF planar manipulator show that the proposed defence significantly reduces attack-induced end-effector deviation while preserving nominal task performance in the absence of attacks.

Figures (4)

• Figure 1: Closed-loop system under FDIA. Sensor signals are corrupted by injection $\bm{a}_k$, yielding attacked output $\tilde{\bm{y}}_k$. The Kalman filter generates the innovation $\bm{r}_k$, which is monitored by the ADS.
• Figure 2: End-effector trajectories: attacker's reference $\bar{\boldsymbol{p}}^{\text{A}}$, defended only by the passive detector (PO) and by the proposed active defence (D). The latter defence limits drift toward the malicious target.
• Figure 3: Attack tracking error $\|\bar{\boldsymbol{p}}^{\text{A}}_k - \bm{p}_k\|_2$, Mahalanobis distances $z_k$ and $\tilde{z}_k$ of \ref{['eq:mahalanobis_distance', 'eq:anomalyScore']}, and scaling $f(\tilde{z})$ of \ref{['eq:exp_decreasing_gain_law_zero']}. With active defence (D), $\tilde{z}_k$ increases until scaling becomes effective, then settles, limiting attacker-realizable accelerations.
• Figure 4: Adversary and control signals. Optimal increment $\bm{\Delta}^\star_k$ of \ref{['eq:optimProb']}, attack sequence $\bm{a}_k$ of \ref{['eq:incremental']}, and resulting actuation $\bm{u}_k$ of \ref{['eq:pid_actuation_task', 'eq:finalControl']}. Under the proposed active defence (D), the attacker escalates $\bm{\Delta}^\star_k$ but scaling suppresses the realized $\bm{u}_k$, constraining task-space manipulation.

Theorems & Definitions (15)

• Lemma 1: Innovation whiteness
• proof
• Lemma 2: Chi-squared distribution
• proof
• Corollary 1: Threshold calibration
• Theorem 1: Actuation-projected residual covariance
• proof
• Theorem 2: Confidence for the Anomaly Measure
• proof
• Theorem 3