Nonsingular Terminal Sliding Mode Guidance with Impact Angle Constraints

TLDR

Conventional sliding‑mode guidance guarantees only asymptotic convergence, yet finite‑time impact‑angle attainment is critical in practice, and existing finite‑time laws suffer singularities that cause control saturation. The paper presents nonsingular guidance laws that intercept targets at a specified impact angle from any initial heading. The authors enforce nonsingular terminal sliding mode by selecting lateral acceleration to drive the line‑of‑sight angle to the desired impact angle, with a switching surface based on nonlinear engagement dynamics, and validate the approach via numerical simulations across varied geometries and angles. Simulations show that the guidance laws, though designed for constant‑speed interceptors, remain robust to time‑varying interceptor speeds.

Abstract

Guidance laws based on a conventional sliding mode ensures only asymptotic convergence. However, convergence to the desired impact angle within a finite time is important in most practical guidance applications. These finite time convergent guidance laws suffer from singularity leading to control saturation. In this paper, guidance laws to intercept targets at a desired impact angle, from any initial heading angle, without exhibiting any singularity, are presented. The desired impact angle, which is defined in terms of a desired line-of-sight angle, is achieved in finite time by selecting the interceptor’s lateral acceleration to enforce nonsingular terminal sliding mode on a switching surface designed using nonlinear engagement dynamics. Numerical simulation results are presented to validate the proposed guidance laws for different initial engagement geometries and impact angles. Although the guidance laws are designed for constant speed interceptors, its robustness against the time-varying speed of interceptors is also evaluated through extensive simulation results.