Terminal Guidance Based on Bézier Curve for Climb-and-Dive Maneuvering Trajectory With Impact Angle Constraint

Abstract

To improve the penetration capability and the damage effectiveness of cruise missiles, maneuvering trajectory with specific impact angle is applied in terminal guidance. In this paper, an innovative online method for terminal guidance is presented, which can guide the cruise missile to a stationary target along a climb-and-dive maneuvering trajectory while meeting the expected impact angle. The basic principles of the proposed guidance method are the Bézier curve theory and the missile inverse dynamics. The maneuvering trajectory is shaped by a third-order Bézier curve based on the missile current state, the target position, and the impact angle constraint. The real-time guidance command represented by attack angle <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> is obtained based on the missile inverse dynamics. The shape of flight trajectory can be modified by regulating the Bézier parameters <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$b_{1}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$b_{2}$ </tex-math></inline-formula> to satisfy different tactical requirements without changing the boundary conditions. Simulation results demonstrate the effectiveness of the proposed method applied in cruise missile terminal guidance.