Heading Error Shaping Guidance Laws Using Generalized Finite-Time Convergence Error Dynamics

This paper introduces a new methodology for designing guidance laws that directly shape the pattern of the heading error as desired. To this end, the concept of generalized finite-time convergence error dynamics is introduced. By leveraging this specific error dynamics, the proposed guidance laws can ensure that the heading error decreases according to the desired pattern while guaranteeing finite-time convergence. The resulting guidance laws take the form of proportional navigation guidance laws, but with a previously unexplored time-varying gain. The paper conducts a theoretical analysis to examine the properties of the proposed guidance laws, including the closed-form solutions of the heading error and acceleration command. Compared to existing methods, the proposed guidance laws provide a more direct and versatile approach to addressing various guidance operational goals. Accordingly, several illustrative examples are presented to demonstrate the process of designing guidance laws using the proposed approach. Furthermore, numerical simulations are conducted to validate the characteristics of the designed guidance laws.