Optimal trajectory shaping guidance of missiles with time-varying acceleration constraints

A guidance law for a missile with a time-varying acceleration constraint is presented. By using a cost function containing both terminal constraints and a running cost on the ratio between the guidance command and the time-varying command constraint, the resulting guidance law shapes the missile's trajectory in a way that reduces command saturation occurrence and allows the missile to avoid no-capture regions. The optimal control based guidance law is derived for a missile with 1 ^st order autopilot dynamics and a terminal intercept angle constraint against a static target. In the case of aerodynamic steering missiles with a limited angle of attack, the acceleration constraint is usually trajectory dependent and therefore cannot be computed analytically in advance. An iterative solution is proposed for the numeric computation of the time-varying acceleration constraint, producing open-loop guidance gain scheduling. For practical implementation reasons the guidance command is decomposed into two separate optimizations, one for the acceleration constraint where the guidance gains are scheduled by a predicted time-to-go, and the other for 1 ^st order autopilot dynamics with a real-time calculated time-to-go, resulting in a sub-optimal guidance law. In addition, a time-varying weight function is used to control the acceleration clearance in areas of interest, such as near intercept. The performance of the proposed guidance scheme is investigated using nonlinear planar simulation. It is shown that the trajectory can be shaped, inherently, in a way that avoids command saturation.