Iterative solution to differential geometric guidance problem

Abstract

PurposeTo study the application of three‐dimensional differential geometric (DG) guidance commands to a realistic missile defense engagement, and the application of the Newton's iterative algorithm to DG guidance problems.Design/methodology/approachThe classical differential geometry theory is introduced firstly to transform all the variables in DG guidance commands from an arc length system to the time domain. Then, an algorithm for the angle‐of‐attack and the sideslip angle is developed by assuming the guidance curvature command and guidance torsion command equal to its corresponding value of current trajectory. Furthermore, Newton's iteration is utilized to develop iterative solution of the stated algorithm and the two‐dimensional DG guidance system so as to facilitate easy computation of the angle‐of‐attack and the sideslip angle, which are formulated to satisfy the DG guidance law.FindingsDG guidance law is viable and effective in the realistic missile defense engagement, and it is shown to be a generalization of gain‐varying proportional navigation (PN) guidance law and performs better than the classical PN guidance law in the case of intercepting a maneuvering target. Moreover, Newton's iterative algorithm has sufficient accuracy for DG guidance problem.Originality/valueProvides further study on DG guidance problem associated with its iterative solution.