Reusable Rocket Pinpoint Landing Under Complex Propulsion System Constraints via Second-Order Cone Programming

Advances in reusable rocket technology have made high-precision landing a critical technical challenge in spaceflight research. Traditional trajectory optimization methods are typically focused on fuel efficiency, terminal accuracy, and fundamental safety constraints but often neglect the dynamic characteristics of the propulsion system, particularly physical limits on the thrust magnitude rate. Ignoring these constraints can produce control commands that exceed maximum throttling capabilities and thereby compromise mission feasibility. To address these challenges, this paper proposes an efficient trajectory optimization algorithm within a lossless convex optimization framework that incorporates thrust magnitude rate, maximum pitch-over, and glide-slope cone constraints to build a realistic rocket landing model under multiple restrictions. To obtain a high-precision solution to the continuous-time optimal control problem, first-order-hold (FOH) discretization is applied to control variables and relaxation variables express thrust rate constraints in differential form. Combined with a convexification strategy, certain nonconvex constraints are transformed and the problem is reformulated as a second-order cone program (SOCP). The algorithm converges rapidly to a high-quality feasible trajectory without requiring an initial guess. These attributes underscore the strong engineering practicality and significant potential of the suggested algorithm for online applications. Simulation results demonstrate that the proposed method can effectively generate fuel-optimal landing trajectories while significantly enhancing the safety and feasibility of the mission. This approach broadens the modeling scope of rocket landing trajectory optimization and offers a robust and practical solution framework for autonomous precision landing missions subject to complex propulsion system constraints.