Virtual target approach-based optimal guidance law with both impact time and terminal angle constraints

To attack a stationary target with both impact time and angle constraints, a novel two-stage guidance strategy is proposed based on the virtual target approach. A moving virtual target that satisfies both impact time and angle requirements is introduced, which substantially simplifies the problem without estimating the time-to-go and its feasibility has been theoretically proved in this paper. For the first stage, taking into account the nonlinear engagement dynamics, an energy optimal closed-loop guidance law is derived to intercept the virtual target with zero impact angle, which is in an analytical form so it can be implemented without any numerical algorithms. Then for the second stage, the proportional navigation guidance law is employed to enhance the robustness against potential disturbances, which also offers the property that the overall two-stage guidance law is almost-smooth at the switching time. The proposed methodology is capable to accommodate the all-aspect attacking scenario with arbitrary initial conditions and arbitrary terminal impact constraints. At last, the effect of navigation coefficients as well as the performance of the proposed guidance law in different engagement scenarios is assessed by several numerical simulations.