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

TL;DR

This paper develops a method to compute the minimum-time intercept path with impact-angle constraints using polynomial solutions and demonstrates its effectiveness through numerical examples.

Contribution

It introduces a polynomial-based approach to efficiently find time-optimal guidance laws for intercepting moving targets with impact-angle constraints.

Findings

Polynomial solutions enable constant-time computation of candidate paths.

The proposed guidance law is proven to be time-optimal.

Numerical examples validate the effectiveness of the method.

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.