大范围时变非线性动力学下的精准定点着陆 Precision Landing Under Large-Envelope, Time-Varying Nonlinear Dynamics
行业挑战Industry Challenge
火箭一级垂直回收是典型的大范围、时变、强非线性动态过程。为了在燃料耗尽前安全定点着陆，系统必须实时规划最优轨迹。不仅要处理质量随燃料消耗骤降、气动变化等非线性动力学，还需严格满足姿态边界和推力锥二阶锥（SOC）约束。传统轨迹规划方案通常面临以下显著瓶颈：
Vertical recovery of a rocket first stage is a typical large-envelope, time-varying, strongly nonlinear dynamic process. To land safely and precisely before fuel depletion, the system must plan optimal trajectories in real time. It must handle nonlinear dynamics such as mass dropping sharply as fuel is consumed and changing aerodynamics, while strictly satisfying attitude bounds and thrust-cone second-order cone (SOC) constraints. Conventional trajectory planning approaches typically face the following major bottlenecks:
计算密集特性与箭载算力不足的矛盾Compute-Intensive Optimization vs. Limited Onboard Computing
在线数值优化求解属于计算密集型任务，而箭载宇航级嵌入式芯片受设计要求限制，算力往往十分有限。开源求解器在这类硬件上难以实施在线计算，传统方案只能选择“在大幅简化模型上实施低精度在线规划”或“离线弹道规划 + 在线局部跟踪”。这一妥协严重削弱了系统应对强侧风、发动机推力衰减等突发摄动的动态调节能力，从根本上制约火箭 GNC 系统的整体抗干扰能力与最终着陆精度。
Online numerical optimization is compute intensive, while aerospace-grade onboard processors provide limited performance under stringent design constraints. Open-source solvers struggle to execute online on this hardware, forcing conventional systems to choose either low-accuracy online planning with heavily simplified models or offline trajectory design plus local online tracking. This compromise weakens dynamic response to sudden disturbances such as strong crosswinds and engine-thrust degradation, fundamentally limiting GNC robustness and landing accuracy.
非凸问题的降维妥协与收敛危机Nonconvex Simplification and Convergence Risk
火箭真实动力学模型表现为高度非凸非线性。在尝试引入在线优化的传统处理中，工程师往往需要将原始问题大幅简化并线性化为简单凸问题。第三方凸优化求解器通常只能处理线性二阶锥，无法直接求解本质上的非凸非线性模型。这种近似处理不仅在规划层限制了火箭的控制边界与机动能力，而且在复杂边界工况下极易引发求解器发散，带来收敛性风险。
Real rocket dynamics are highly nonconvex and nonlinear. Conventional attempts at online optimization require engineers to simplify and linearize the original problem into a basic convex formulation. Third-party convex optimization solvers generally handle only linear second-order cones and cannot directly solve the underlying nonconvex nonlinear model. This approximation restricts the rocket's control envelope and maneuverability at the planning level while introducing solver-divergence and convergence risks near complex operating boundaries.