Curvature Constrained Cubic Spline Impact Angle Guidance for Intercepting Stationary Targets

Abstract

In this paper, a cubic spline guidance law is proposed for intercepting a stationary target at a desired impact angle in surface-to-surface engagement scenarios. An inverse method is used, which represents the altitude as a cubic polynomial of the downrange. The paper addresses many shortcomings of earlier work in this area. In particular, an explicit guidance expression is derived, which makes the guidance law effective and accurate in the presence of disturbances and uncertainties. It is also shown that the guidance command can be obtained using a single cubic spline polynomial even for impact angles greater than and equal to $\pi / 2$ , while resulting in substantial improvement in terms of lateral acceleration and length of the trajectory. The paper also obtains an analytically derived capture region. The proposed guidance law is conceptually simple, independent of time-to-go, computationally inexpensive, and does not need linearization.