Impact time and angle control guidance for homing missiles using sequential convex programming

Abstract

In this paper, a computational guidance method using Sequential Convex Programming (SCP) technique is applied to an Impact Time and Angle Control Guidance (ITACG) problem and its variants for homing missiles. ITACG for tactical missiles aims to satisfy prescribed terminal flight angle and flight time condition. Typical homing missile guidance schemes ensures target interception, yet those methods cannot control the impact angle and time of the missile. Consequently, demand for ITACG method existed in order to realize cooperative mission by multiple missiles. Some explicit closed-form ITACG methods were proposed based on classical linear-quadratic optimal control theory. These methods suggest explicit closed-form guidance laws, while crucial nonlinear operational constraints had to be removed during the derivation process.

Modern computational guidance methods attempts to solve the given nonlinear optimal control problem in real-time. The advantage of real-time numerical optimization method over closed-form guidance method is that every crucial nonlinear constraints can be considered. Among various computational guidance approach, SCP method is widely investigated nowadays. SCP on optimal control problem approximates the given optimal control problem into Second-Order Cone Programming (SOCP) subproblems. SOCP problem, a form of convex programming problem, can be solved in polynomial time using interior-point method. Hence, given optimal control problem can be solved rapidly by solving numbers of approximated SOCP subproblems, and successively substituting the new solution.

Exploiting the advantage of SCP method, a computational guidance method for ITACG problem is suggested, satisfying additional nonlinear constraints. Especially, two crucial operational constraints: maximum maneuver acceleration limit, and maximum field-of-view limit are considered. In order to improve numerical stability and versatility of standard SCP method, novel L1 penalized SCP(LPSCP) algorithm is proposed. Moreover, convexification methods for ITACG problem and its variants: Impact Time Control Guidance(ITCG), Impact Angle Control Guidance(IACG), and Minimum Time Impact Angle Control Guidance(minT IACG) are developed. Proposed methods are applied to various guidance scenarios, imitating warm start with good initial guess, cold start without initial guess, and perturbation of objectives. Furthermore, LPSCP method is applied to various guidance problems to show its versatility. The performance of suggested computational guidance methods are verified through suggested scenarios, including comparison with standard pseudospectral method.