Bank-to-turn guidance law with terminal impact-angle constraint

To avoid the mathematical singularity of polar converting in bank-to-turn (BTT) guidance and to provide the specified terminal impact angle, a BTT guidance law with impact-angle constraint (BTT-GL/IA) is presented. Considering the influence of the impact-angle control and target maneuver to the miss-distance, a new form zero-effort miss-distance with impact angle (ZEM/IA) is introduced. Referring to the Lyapunov-like approach used to drive the guidance law in the prior literature, a Lyapunov function is constructed in terms of ZEM/IA. Based on the Lyapunov stability theorem, a negative definite function is designed, and the BTT-GL/IA is derived. Next, BTT-GL/IA is implemented in another form with the variables as the line-of-sight angle and its rate, which are easily measured by the seeker. When using BTT-GL/IA, the guidance law tends to maintain smooth and continuously-varied body acceleration and roll-angle commands while satisfying the impact position and angle constraints. The problem of a mathematical singularity in normal BTT polar converting logic is avoided. Finally, both the maneuverable and stationary targets with different impact-angle constraints are considered in numerical simulations. Through various simulation results, the effectiveness and practicality of the BTT-GL/IA are demonstrated.