Zero-Effort-Miss/Zero-Effort-Angle-Error Guidance for UAV Interception in Nonadvantageous Engagements With Terminal Angle Constraint

This paper develops two three-dimensional optimal guidance laws based on zero-effort variables for unmanned aerial vehicle (UAV) interception engagements under non-advantageous conditions. First, a zero-effort-miss (ZEM) optimal guidance law is derived directly in 3D space, minimizing a quadratic control-effort cost while enforcing the terminal zero-miss condition at a designated impact time. To improve terminal geometry, a zero-effort-angle-error (ZEAE) concept is introduced, leading to a unified ZEM/ZEAE guidance law that simultaneously enforces a prescribed terminal impact angle and zero miss distance. Both laws admit closed-form expressions and are amenable to real-time onboard implementation. Using Lyapunov-based analysis, the stability of the resulting closed-loop systems is established for the ideal continuous-time model under the stated assumptions, implying convergence of the zero-effort variables to zero as the terminal time is approached. Numerical simulations over multiple engagement scenarios, including highly challenging cases where the defender does not have a clear advantage in speed or maneuverability, indicate that the proposed guidance laws reduce control effort and limit peak acceleration compared with classical proportional navigation. Furthermore, the robustness of the proposed method against estimation errors in target maneuver parameters is validated. In addition, the ZEM/ZEAE law provides accurate terminal impact-angle control, improving terminal engagement geometry. This study provides a theoretically grounded and practically implementable approach for control-efficient precision interception in autonomous UAV engagements under non-advantageous conditions.