Zero-effort-miss shaping guidance laws

This paper suggests a new approach in designing homing guidance laws to enable direct shaping of the pattern of zero-effort-miss (ZEM) as desired. The proposed approach uses the concept of weighted ZEM and its specific desired error dynamics: the former is to provide an additional degree of freedom in shaping actual ZEM and the latter is to guarantee a finite-time convergence. Utilization of these two concepts allows simple determination of the guidance law that can achieve the desired pattern of ZEM. The resultant guidance law is shown a type of proportional navigation guidance (PNG) law with the specific form of time-varying gain not revealed in previous studies. It provides unique information on how the time-varying gain should be shaped to obtain the desired pattern of ZEM. Accordingly, the resultant guidance laws can cope with various operational objectives in a more direct way compared with the previously existing approaches. This paper also performs theoretical analysis to investigate the properties of designed guidance laws including the closed-loop solutions of ZEM and acceleration command. Also, we determine the feasible set of desired ZEM patterns that can be achieved in the proposed framework. Two illustrative examples are considered to show how to design guidance laws using the proposed approach. Moreover, the characteristics of the guidance laws designed are validated and demonstrated via numerical simulations.