Time-Optimal Guidance for Intercepting Moving Targets with Impact-Angle Constraints

Abstract

The minimum-time path for intercepting a moving target with a prescribed impact angle is studied in the paper. The candidate paths from Pontryagin's maximum principle are analyzed, so that each candidate is related to a zero of a real-valued function. It is found that the real-valued functions or their first-order derivatives can be converted to polynomials of at most fourth degree. As a result, each canidate path can be computed within a constant time by embedding a standard polynomial solver into the typical bisection method. The control strategy along the shortest candidate eventually gives rise to the time-optimal guidance law. Finally, the developments of the paper is illustrated and verified by three numerical examples.