Nonsingular Terminal Sliding Mode Guidance with Impact Angle Constraints

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.

Three-dimensional impact angle guidance with coupled engagement dynamics

“…For the guidance problem, the mass of the interceptor, the thrust acting on the interceptor, density variations and the induced, as well as zero-lift, drag coefficients can be found in Kumar et al 16 Due to the effect of gravity, the performance of the guidance law degrades. The effect of gravity in the longitudinal direction cannot be compensated for once the boost or sustain phase is over.…”

“…In fact, the papers [8][9] do not provide an analysis of the sliding mode dynamics for the chosen switching surface and it satisfies the objectives of the guidance law after occurrence of sliding mode. There are several impact angle guidance laws (for example Cho et al 12 ), some of which use SMC (for example, Shima 13 and Lee et al 14 ) and some ensure finite time convergence, [15][16][17][18] but only for two-dimensional engagement scenarios. For a 3D engagement scenario, Zhou et al 19 and Golestani et al 20 present finite-time convergent guidance laws but these address only the problem of interception of targets and not impact angle.…”

Guidance laws based on model predictive control and target manoeuvre estimator

“…In Shima (2011), an SMC-based guidance law was proposed to impose desired intercept angle, which is applicable in head-on, tail-chase and head-pursuit engagement scenarios. Later, in Kumar et al (2012Kumar et al ( , 2014, terminal sliding mode (TSM) and non-singular TSM (NTSM) algorithms are adopted to design guidance laws to cater for desired terminal angles. For implementation of these two guidance laws, the target manoeuvre information is required to design the sliding surface and the equivalent control law.…”

Distributed cooperative guidance of multiple anti-ship missiles with arbitrary impact angle constraint

“…The issue of impact angle control guidance (IACG) has been addressed in an amount of works, from the biased proportional navigation guidance based IACG laws [8,9,13,21,31] to the optimal control theory based IACG laws [12,22,23], from the model predictive static programming technique based IACG laws [1,16] to the sliding mode control theory based IACG laws [4,10,11,14,20,28,32], too numerous to mention one by one.…”