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Perfectly Undetectable Reflection and Scaling False Data Injection Attacks via Affine Transformation on Mobile Robot Trajectory Tracking Control

Jun Ueda, Hyukbin Kwon

TL;DR

This work shows that perfectly undetectable false data injection attacks can be realized on nonlinear mobile-robot trajectory tracking by coordinated affine transformations of observables and control commands. By exploiting the partially linear structure of typical two‑wheel robot dynamics, the authors derive explicit reflection and scaling attack strategies and prove their indistinguishability to the controller under two key conditions, including initial-state consistency. They validate the concept with Turtlebot 3 experiments and introduce a state monitoring signature function (SMSF) that can resist affine transformations, outlining construction principles and limitations. The results highlight a practical cybersecurity risk for CPS and motivate the development of resilient control and monitoring strategies, including moving-target SMSFs and potential cryptographic safeguards. Overall, the paper advances understanding of attack feasibility in nonlinear cyber-physical systems and proposes a concrete countermeasure framework with empirical demonstration.

Abstract

With the increasing integration of cyber-physical systems (CPS) into critical applications, ensuring their resilience against cyberattacks is paramount. A particularly concerning threat is the vulnerability of CPS to deceptive attacks that degrade system performance while remaining undetected. This paper investigates perfectly undetectable false data injection attacks (FDIAs) targeting the trajectory tracking control of a non-holonomic mobile robot. The proposed attack method utilizes affine transformations of intercepted signals, exploiting weaknesses inherent in the partially linear dynamic properties and symmetry of the nonlinear plant. The feasibility and potential impact of these attacks are validated through experiments using a Turtlebot 3 platform, highlighting the urgent need for sophisticated detection mechanisms and resilient control strategies to safeguard CPS against such threats. Furthermore, a novel approach for detection of these attacks called the state monitoring signature function (SMSF) is introduced. An example SMSF, a carefully designed function resilient to FDIA, is shown to be able to detect the presence of a FDIA through signatures based on systems states.

Perfectly Undetectable Reflection and Scaling False Data Injection Attacks via Affine Transformation on Mobile Robot Trajectory Tracking Control

TL;DR

This work shows that perfectly undetectable false data injection attacks can be realized on nonlinear mobile-robot trajectory tracking by coordinated affine transformations of observables and control commands. By exploiting the partially linear structure of typical two‑wheel robot dynamics, the authors derive explicit reflection and scaling attack strategies and prove their indistinguishability to the controller under two key conditions, including initial-state consistency. They validate the concept with Turtlebot 3 experiments and introduce a state monitoring signature function (SMSF) that can resist affine transformations, outlining construction principles and limitations. The results highlight a practical cybersecurity risk for CPS and motivate the development of resilient control and monitoring strategies, including moving-target SMSFs and potential cryptographic safeguards. Overall, the paper advances understanding of attack feasibility in nonlinear cyber-physical systems and proposes a concrete countermeasure framework with empirical demonstration.

Abstract

With the increasing integration of cyber-physical systems (CPS) into critical applications, ensuring their resilience against cyberattacks is paramount. A particularly concerning threat is the vulnerability of CPS to deceptive attacks that degrade system performance while remaining undetected. This paper investigates perfectly undetectable false data injection attacks (FDIAs) targeting the trajectory tracking control of a non-holonomic mobile robot. The proposed attack method utilizes affine transformations of intercepted signals, exploiting weaknesses inherent in the partially linear dynamic properties and symmetry of the nonlinear plant. The feasibility and potential impact of these attacks are validated through experiments using a Turtlebot 3 platform, highlighting the urgent need for sophisticated detection mechanisms and resilient control strategies to safeguard CPS against such threats. Furthermore, a novel approach for detection of these attacks called the state monitoring signature function (SMSF) is introduced. An example SMSF, a carefully designed function resilient to FDIA, is shown to be able to detect the presence of a FDIA through signatures based on systems states.
Paper Structure (21 sections, 36 equations, 17 figures)

This paper contains 21 sections, 36 equations, 17 figures.

Table of Contents

  1. Introduction
  2. Preliminaries on Mobile robot dynamic and control
  3. Perfectly Undetectable FDIA: Coordinating Attacks on Observables and Control Commands
  4. Fundamental equations
  5. Specific conditions of perfectly undetectable FDIA on mobile robot control
  6. Problem formulation using affine transformation-based FDIA
  7. Solution to the perfectly undetectable FDIA problem
  8. Attackability analysis of mobile robot Jacobian matrix
  9. Main result: perfectly undetectable FDIA solutions
  10. Stability of the closed-loop system with perfectly undetectable FDIAs
  11. Experiments
  12. Mobile robot experimental setup
  13. Attack scenarios and results
  14. Perfectly undetectable FDIA resilient state monitoring
  15. Affine transformation resilient state monitoring signature functions
  16. ...and 6 more sections

Figures (17)

  • Figure 1: Conceptual diagram of false data injection attack (FDIA) on remote mobile robot control system.
  • Figure 2: Mobile robot desired and current postures. The same notations are used as in Kanayama.
  • Figure 3: Perfectly undetectable false data injection attack (FDIA) on remote mobile robot control system based on affine transformations: (a) Attacked control system with coordinated FDIA on the commands and observables. (b) Plant dynamics as perceived by the controller, indistinguishable from the nominal robot behavior and thus undetectable.
  • Figure 4: Affine transformation-based coordinated FDIA on mobile robot control system
  • Figure 5: Perfectly undetectable FDIA solutions: (a) reflection and (b) scaling attacks
  • ...and 12 more figures