Multi-Phase Rocket Landing Guidance Using Sequential Convex Programming

This paper presents a Sequential Convex Programming (SCP) framework for solving nonconvex optimal control problems with improved numerical efficiency and robustness. The proposed algorithm iteratively linearizes the system dynamics and constraints, formulating a sequence of convex subproblems that are solved using a high-performance conic solver. Key innovations include the use of of diagonal scaling matrices and centering vectors to transform state, control, and parameter variables into scaled quantities, ensuring better numerical conditioning and solver performance. The framework also incorporates trust regions and virtual states to handle artificial infeasibility and ensure convergence. The effectiveness of the approach is demonstrated through a multi-phase rocket landing guidance problem, where the algorithm achieves real-time performance while maintaining high accuracy. The results highlight the scalability and robustness of the proposed method, making it suitable for complex nonlinear control applications in aerospace and beyond.