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<p>Aimed at addressing the three-dimensional (3D) high-speed maneuvering target rendezvous problem under uncontrollable speed, uncertainties, and specified approaching direction, this study developed an incremental finite-time angle-constrained guidance law, combining the incremental nonlinear dynamic inverse (INDI) and super-twisting (ST) frameworks. An angle-constrained guidance model was constructed as a baseline according to the 3D rendezvous relative motion model. To avoid the unbounded perturbation generated near rendezvous and ensure that the guidance states converge in finite time, a nonsingular sliding surface including guidance states was used for formulating an INDI-ST angle-constrained guidance law. This guidance law could not only enhance the robustness but also smoothen the guidance command with reduced guidance gains as compared to the NDI-ST-based method. In the incremental domain, the sliding surface and guidance states were shown to converge in finite time. To implement the INDI-ST guidance law, a multivariate super-twisting differentiator with guaranteed convergence was designed to approximate the latest derivatives of the sliding surface. Furthermore, the robustness of the NDI-ST and INDI-ST-based guidance laws under measurement uncertainties was compared analytically, revealing that the incremental finite-time guidance law required relatively small guidance gains and resulted in relatively narrow system perturbations in each sampling period. Extensive Monte Carlo simulations demonstrated the robustness and feasibility of the proposed guidance algorithm.</p>

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Incremental finite-time three-dimensional angle-constrained guidance approaching high-speed targets

  • 期刊论文

  • 发表日期：

    2026年6月17日

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  • Zhenlin Zhang,
  • Tuo Han,
  • Qinglei Hu,
  • Yuan Li,
  • Dongyu Li

摘要

Aimed at addressing the three-dimensional (3D) high-speed maneuvering target rendezvous problem under uncontrollable speed, uncertainties, and specified approaching direction, this study developed an incremental finite-time angle-constrained guidance law, combining the incremental nonlinear dynamic inverse (INDI) and super-twisting (ST) frameworks. An angle-constrained guidance model was constructed as a baseline according to the 3D rendezvous relative motion model. To avoid the unbounded perturbation generated near rendezvous and ensure that the guidance states converge in finite time, a nonsingular sliding surface including guidance states was used for formulating an INDI-ST angle-constrained guidance law. This guidance law could not only enhance the robustness but also smoothen the guidance command with reduced guidance gains as compared to the NDI-ST-based method. In the incremental domain, the sliding surface and guidance states were shown to converge in finite time. To implement the INDI-ST guidance law, a multivariate super-twisting differentiator with guaranteed convergence was designed to approximate the latest derivatives of the sliding surface. Furthermore, the robustness of the NDI-ST and INDI-ST-based guidance laws under measurement uncertainties was compared analytically, revealing that the incremental finite-time guidance law required relatively small guidance gains and resulted in relatively narrow system perturbations in each sampling period. Extensive Monte Carlo simulations demonstrated the robustness and feasibility of the proposed guidance algorithm.