Time-to-go Polynomial Guidance with Impact Angle Constraint for Missiles of Time-Varying Velocity

In this paper, a Time-to-go Polynomial Guidance (TPG) law satisfying impact angle constraints for missiles of time-varying velocity against stationary target is investigated. The guidance law assumes the magnitude of guidance commands as a polynomial function of time-to-go with two unknown coefficients. The coefficients are determined to satisfy the two terminal constraints, which are the terminal impact angle and zero miss distance. The derivation of the guidance law is constructed for exponentially decreasing velocity. The main contribution of this study is expansion of the concept of TPG for constant velocity missiles to missiles of time-varying velocity. The proposed guidance law is identical to typical TPG when the velocity of missile is constant. To verify the performance of the proposed guidance law, numerical simulation is performed. The simulation shows that the proposed guidance law is a sub-optimal solution of minimizing timeto-go weighted energy cost function.