Terminal acceleration stabilizing guidance law for impact angle constrained interception of a non-maneuvering target

Abstract

A practical homing guidance scheme is newly proposed in order to meet the impact angle and terminal acceleration constraints, simultaneously. Provided that the homing guidance loop is modeled as a linear time-varying differential equation by approximating the missile dynamics as a firstorder system, its closed-form solution is expressed as a linear combination of hypergeometric functions. It implies that the instability of the homing guidance loop is mainly due to the missile dynamic lags and, furthermore, the non-diverging homing trajectory could be obtained by introducing the additional biased acceleration command as a rational function of time-to-go. These inspirational observations motivate us to formulate an impact angle control problem as designing an appropriate biased term which generates a non-diverging time-to-go polynomial homing trajectory for given terminal constraints. The resultant guidance command has a similar form used in conventional guidance laws but its feedback gains vary with time-to-go. This similarity means that, during the flight, the proposed guidance law adaptively embraces existing guidance laws derived by intentionally ignoring the effect of missile dynamic lags. Through the numerical simulations, the performance of the proposed guidance scheme is evaluated.