Three-dimensional cooperative guidance law with practical predefined-time approach angle and time-to-go convergence

This paper presents a Three-Dimensional (3D) cooperative guidance law with Practical Predefined-Time (PPT) convergence for multiple missiles considering approach angle (terminal line-of-sight) and simultaneous arrival constraints. To achieve a salvo attack against a maneuvering target from various directions, the guidance problem is tackled by addressing two critical factors: ensuring that the time-of-arrival is consistent and that the desired approach angles can be met. Considering the short duration of the homing guidance process, the convergence with predefined time for guidance states (especially the approach angle and time-to-go) is factored in. First, for the simultaneous arrival, a PPT guidance law is developed, which can meet the same time-to-go convergence rate in the Line-of-Sight (LOS) direction. Then, in the normal LOS direction, a 3D PPT guidance law is presented considering the approach angle constraint so that the desired approach angles can be reached within a user-designed time. The time-based generator technique is employed in the proposed PPT Cooperative Guidance Law (PPTCGL) to avoid the time-varying gain singularity issue. Notably, this technique can allow the convergence time to be preset in advance, independent of initial system conditions and tuning parameters. Additionally, to avoid excessive gain and improve the robustness of guidance law, a PPT disturbance observer is designed against uncertainties and target maneuvers so that the guidance system perturbation can be compensated in real time. It is user-friendly that the convergence of disturbance estimation can be met with a flexible pre-setting time before achieving the terminal guidance constraints. Finally, extensive numerical simulations are conducted to verify the effectiveness and robustness of the proposed PPTCGL in both the nominal cases and the Monte Carlo test.