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<p>This paper investigates the hierarchical three-dimensional (3-D) output tracking problem for networked uncertain robotic systems (NURSs) endowed with Byzantine fault-tolerant (BFT) capability, where both parametric uncertainties and external disturbances are explicitly considered. To address the vulnerabilities introduced by adversarial Byzantine robots and model uncertainties, a hierarchical control framework is developed, consisting of a BFT estimation layer and an output-space tracking layer. In the BFT estimation layer, a distributed BFT mechanism is constructed over a directed interaction graph, enabling each robot to suppress falsified state broadcasts and asymptotically recover the trusted virtual leader trajectory. Once a Byzantine node is detected, a BFT-based structural isolation strategy is activated to eliminate corrupted information while maintaining the connectivity of the remaining network. In the output-space tracking layer, a nonlinear 3-D tracking controller is designed using Jacobian-based output-space transformation and robust compensation terms to counteract uncertainties and disturbances in robot dynamics. The closed-loop stability of the hierarchical architecture is rigorously established through Lyapunov analysis. Numerical simulations further verify that the proposed method achieves resilient estimation, reliable Byzantine isolation, and high-precision 3-D output tracking for NURSs operating under adversarial conditions.</p>

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Hierarchical three-dimensional output tracking for networked uncertain robotic systems with Byzantine fault-tolerant capability

  • 期刊论文

  • 发表日期：

    2026年4月30日

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  • Kai-Lun Huang,
  • Chang-Duo Liang,
  • Menghu Hua,
  • Xisheng Zhan,
  • Ming-Feng Ge

摘要

This paper investigates the hierarchical three-dimensional (3-D) output tracking problem for networked uncertain robotic systems (NURSs) endowed with Byzantine fault-tolerant (BFT) capability, where both parametric uncertainties and external disturbances are explicitly considered. To address the vulnerabilities introduced by adversarial Byzantine robots and model uncertainties, a hierarchical control framework is developed, consisting of a BFT estimation layer and an output-space tracking layer. In the BFT estimation layer, a distributed BFT mechanism is constructed over a directed interaction graph, enabling each robot to suppress falsified state broadcasts and asymptotically recover the trusted virtual leader trajectory. Once a Byzantine node is detected, a BFT-based structural isolation strategy is activated to eliminate corrupted information while maintaining the connectivity of the remaining network. In the output-space tracking layer, a nonlinear 3-D tracking controller is designed using Jacobian-based output-space transformation and robust compensation terms to counteract uncertainties and disturbances in robot dynamics. The closed-loop stability of the hierarchical architecture is rigorously established through Lyapunov analysis. Numerical simulations further verify that the proposed method achieves resilient estimation, reliable Byzantine isolation, and high-precision 3-D output tracking for NURSs operating under adversarial conditions.