Three-dimensional blind-cone-avoidance optimal guidance: a robust event-triggered approach

This paper investigates the three-dimensional (3-D) homing guidance problem with blind cone constraint. And an optimal guidance approach is proposed to address this issue. The proposed optimal guidance law is designed based on the optimal 3-D pure proportional guidance (PPN) with an additional bias term by lever-aging the predictor-corrector concept and optimal event-trigged control. The terminal impact vector of PPN is first analytically predicted with the Rodrigues' rotation formula and its impact vector dynamics is established driven by the bias term. Then the bias term is designed as an event-triggered controller with optimal control theory. The controller will be triggered if the impact vector will fall into the blind cone and force the impact vector to deviate from the blind cone. The main benefit of the proposed guidance law lies in its optimal nature and robust characteristics. Hence it outperforms the impact-angle-control guidance law with preassigned an-gle. Theoretical analysis is performed to demonstrate its command characteristics and reveal its working principle. And numerical simulation results are presented to support our findings.