Three-Dimensional Geometric Descent Guidance With Impact Angle Constraint

A novel trajectory-shaping guidance law with impact angle constraint is proposed for attacking stationary targets in a three-dimensional environment. The guidance concept, derived from the inverse dynamic method, is to design an analytical curve trajectory satisfying the impact angle in advance and obtain reasonable control commands. The vehicle motion is decomposed in the horizontal and vertical planes of the inertial coordinate system. Firstly, the trajectory in the vertical plane is designed as ellipse, which can be shaped by adjusting its axis direction. An improved sliding mode control (SMC) method, which adds position-dependent correction to the weight in sliding mode surface, is adopted to track the nominal trajectory. Therefore, the vehicle approaches the ellipse quickly and smoothly in the early stage and hits the stationary target accurately. Secondly, a third-order Bézier curve with adjustable parameters is employed as the prior nominal trajectory in the lateral plane. When the vehicle deviates from the original trajectory due to perturbation or self-limitation, it will turn to the updated curve in real time according to its own condition. Moreover, coupling of acceleration commands in the two planes is resolved through acceleration decomposition, which qualifies independent trajectory design in two planes and paves a new way to more curve combinations. Nominal testing and Monte Carlo simulations on the proposed method are carried out. Simulation results demonstrate that the proposed guidance law is highly designable and strongly robust.