Abstract: During the recovery of reusable rockets, traditional numerical guidance methods suffer from high computational burden and challenges in ensuring real-time performance. Moreover, they often neglect attitude smoothness, leading to drastic fluctua-tions in control commands. To address these issues, this paper proposes an analytical guidance law designed with optimal attitude smoothness as the objective. First, an optimal control problem is formulated, and it is proven that the optimal solution takes a simple cubic function form. This transforms the complex trajectory optimization problem into an analytical parameter optimization problem, significantly improving computational efficiency. Furthermore, by introducing a dual-phase guidance framework, adaptive determination of the ignition point is achieved. A constant-thrust baseline design is adopted to reduce the requirement for deep throttling of the engine. Combined with an aerodynamic compensation strategy, the algorithm's adaptability in complex flight environments is enhanced. Simulation results demonstrate that the attitude command profile generated by the proposed method closely matches the theoretical optimal solution, with extremely short computation time, indicating excellent potential for online real-time application. Even under harsh conditions such as limited thrust adjustment range and parameter deviations, the method stably achieves high-precision terminal state control, demonstrating promising prospects for engineering applications.

Key words: Analytical guidance, Iterative guidance, Optimal control, Trajectory optimization, Vertical landing