Gravity-Turn-Assisted Optimal Guidance Law

This paper proposes a new optimal guidance law that directly uses (instead of compensating for) gravity for accelerating missiles. The desired collision triangle that considers both gravity and the vehicle's axial acceleration is analytically derived based on geometric conditions. The concept of instantaneous zero-effort-miss is introduced to allow for analytical guidance command derivation. By formulating a finite time instantaneous zero-effort-miss regulation problem, the proposed optimal guidance law is derived through Schwarz's inequality approach. The relationships of the proposed formulation with conventional proportional navigation guidance and guidance-to-collision are analyzed, and the results show that the proposed guidance law encompasses previously suggested approaches. The significant contribution of the proposed guidance law lies in that it ensures zero final guidance command and enables energy saving with the aid of using gravity turn. Nonlinear numerical simulations clearly demonstrate the effectiveness of the proposed approach.