Abstract: Aiming at the three-dimensional (3D) trajectory shaping guidance problem for high-speed flight vehicles, an analytical guidance law with both impact vector and flight distance constraints is proposed. First, a 3D vector guidance model described in the arc-length domain is presented, along with the orthogonal decomposition of the lateral acceleration commands. The model exhibits a natural decoupling characteristic for multiple constraints. Second, based on classical differential geometry principles, the proposed 3D impact vector constrained guidance law under the assumption of constant speed is extended to the time-varying speed scenario. This guidance law possesses a globally analytical solution for the remaining flight distance in a concise form. Then, by introducing a bias vector command to adjust the remaining flight distance, a trajectory shaping guidance method is derived with dual capabilities for both impact vector control and flight distance control. Finally, numerical simulations validate the effectiveness and superiority of the proposed guidance law when applied to a high-speed vehicle in realistic environments.

Key words: varying speed, analytical flight profile, impact vector constraint, flight distance constraint, trajectory shaping guidance