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Distributed Nonlinear Control of Networked Two-Wheeled Robots under Adversarial Interactions

Moh Kamalul Wafi, Ahmad Ataka, Yul Y. Nazaruddin, Bayu Jayawardhana

Abstract

This paper studies distributed trajectory tracking for networks of nonholonomic mobile robots under adversarial information exchange. An exact global input--output feedback linearization scheme is developed to regulate planar position outputs, yielding linear error dynamics without prescribing internal state trajectories. To mitigate corrupted neighbor information, a resilient desired-signal construction is proposed that combines local redundancy with trusted in-neighbor signals, without requiring adversary detection or isolation. When sufficient redundancy is available, the method suppresses adversarial influence and recovers nominal tracking performance. If redundancy conditions are violated, adversarial effects enter as bounded disturbances and the tracking error remains ultimately bounded. Simulation results on star, cyclic, and path topologies validate the analysis and demonstrate the superior resilience of cyclic networks due to distributed information propagation.

Distributed Nonlinear Control of Networked Two-Wheeled Robots under Adversarial Interactions

Abstract

This paper studies distributed trajectory tracking for networks of nonholonomic mobile robots under adversarial information exchange. An exact global input--output feedback linearization scheme is developed to regulate planar position outputs, yielding linear error dynamics without prescribing internal state trajectories. To mitigate corrupted neighbor information, a resilient desired-signal construction is proposed that combines local redundancy with trusted in-neighbor signals, without requiring adversary detection or isolation. When sufficient redundancy is available, the method suppresses adversarial influence and recovers nominal tracking performance. If redundancy conditions are violated, adversarial effects enter as bounded disturbances and the tracking error remains ultimately bounded. Simulation results on star, cyclic, and path topologies validate the analysis and demonstrate the superior resilience of cyclic networks due to distributed information propagation.

Paper Structure

This paper contains 15 sections, 2 theorems, 40 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Communication Network
  3. Problem Formulation and Preliminaries
  4. Nominal Problem Formulation
  5. Non-Nominal Problem Formulation
  6. Motivation for Distributed Nonlinear Control
  7. Distributed Nonlinear Control of Nonholonomic Networks
  8. Nonholonomic Network Model
  9. Global Feedback Linearization
  10. Distributed Nonlinear Control
  11. Distributed Control Under Adversarial Interactions
  12. Resilient $z_i$ via Trusted Redundancy
  13. Robustness without Graph Redundancy
  14. Numerical Simulations
  15. Conclusion

Key Result

Proposition 1

Consider eq:Robots:control and select $\bar{u}^+ = \mathbf{K}\bar{\eta}$ such that $\mathbf{A}+\mathbf{B}\mathbf{K}$ is Hurwitz. Then the origin $\bar{\eta}=0$ of eq:Robots:linear_cl is exponentially stable, i.e., there exist $c_1,c_2>0$ such that Moreover, $\bar{\epsilon}(t)\to 0$ exponentially as $t\to\infty$. If, in addition, $\mathbb{L}=\mathbb{L}_m+\mathbb{A}_0$ is invertible and satisfies t

Figures (4)

  • Figure 1: Example of a graph $\mathcal{G}$ with $m=5$, vehicle-to-vehicle subgraph $\mathcal{G}_m$, and navigator-to-vehicle subgraph $\mathcal{G}_0$, showing the decoupling and assignment of $w_{ij}$.
  • Figure 2: Nonlinear dynamics of a nonholonomic two-wheeled robot
  • Figure 3: Three network topologies $(\mathcal{G}_{\mathrm{s}}, \mathcal{G}_{\mathrm{c}}, \mathcal{G}_{\mathrm{p}})$ with weights used in the simulations.
  • Figure 4: Networked trajectory tracking for three directed topologies. Top row (non-adversarial case): vehicle trajectories under star ($\mathcal{G}_{\mathrm{s}}$), cyclic ($\mathcal{G}_{\mathrm{c}}$), and path ($\mathcal{G}_{\mathrm{p}}$) graphs, and the corresponding averaged tracking and disagreement errors. Bottom row (adversarial case): trajectories and errors under the same topologies with corrupted information exchange. The error plots report the average leader-tracking error $\tilde{e}(t)=\frac{1}{m}\sum_{i=1}^m\|y_i-y_0\|$ and the average disagreement $\tilde{\epsilon}(t)=\frac{1}{m}\sum_{i=1}^m\|y_i-z_i\|$.

Theorems & Definitions (6)

  • Remark 1: Navigator reachability
  • Remark 2
  • Proposition 1
  • Proof 1
  • Proposition 2
  • Proof 2