基于动力学凝聚和xPIPG的动力着陆亚毫秒级序贯凸优化
Submillisecond Sequential Convex Optimization for Powered Landing via Dynamics Condensation and xPIPG
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中文总结 AI 辅助
该研究针对动力着陆的低延迟需求，提出基于动力学凝聚和xPIPG的序贯凸优化方法，实现亚毫秒级端到端求解，为动力着陆轨迹规划提供高效方案。
中文摘要 AI 辅助
变质量、自由终端时间且含二次气动阻力的动力着陆需反复求解局部凸子问题，其在线主要开销在于长动力学等式链和内部迭代。本文开发了一种专为低延迟设计的凝聚序贯凸近似方法：通过精确块消元从31节点模型中移除217个中间状态分量和210个区间方程，剩余100个原变量由6个终端等式耦合；低权重能量项和固定二次邻近正则化使理想代理函数强凸且曲率可预测；内部求解器为外推比例-积分投影梯度（xPIPG），采用固定大小数组、3×3区间求解及融合单遍节点映射实现，该单遍映射是刻意的低成本近似而非精确联合邻近算子，因此通过非线性轨迹残差和独立物理检查评估计时代码，而非声称精确KKT收敛。单精度C实现在4次外更新和336次xPIPG更新内完成一次规划；在Intel Core i7-10875H上，端到端求解时间中位数为374微秒，P99值为512微秒；所有100种常见初始状态扰动均通过验证，15至51节点时中位数仍低于0.7毫秒；独立高精度一阶保持积分给出终端位置误差为0.183米。在所述模型、硬件、停止规则和计时边界内，据作者所知，这是首个用于单条动力着陆轨迹的亚毫秒级端到端序贯凸求解方案。
英文摘要
Powered landing with variable mass, free final time, and quadratic aerodynamic drag requires the repeated solution of local convex subproblems, whose main online cost lies in the long dynamics-equality chain and the inner iterations. This paper develops a condensed sequential convex approximation designed for low latency. Exact block elimination removes 217 intermediate-state components and 210 interval equations from a 31-node model, leaving 100 primal variables coupled by six terminal equalities. A low-weight energy term and fixed quadratic proximal regularization make the ideal surrogate strongly convex with predictable curvature. The inner solver is an extrapolated proportional--integral projected gradient (xPIPG) implemented with fixed-size arrays, $3\times3$ interval solves, and a fused one-pass node map. The one-pass map is a deliberate low-cost approximation, not the exact joint proximal operator. We therefore evaluate the timed code by nonlinear trajectory residuals and independent physical checks rather than by a claim of exact KKT convergence. The single-precision C implementation completes one plan in four outer updates and 336 xPIPG updates. On an Intel Core i7-10875H, the median end-to-end solve time is \SI{374}{\micro\second} and the P99 value is \SI{512}{\micro\second}. All 100 common initial-state perturbations pass validation, and the median remains below \SI{0.7}{\milli\second} for 15--51 nodes. An independent high-accuracy first-order-hold integration gives a terminal position error of \SI{0.183}{\meter}. Within the stated model, hardware, stopping rule, and timing boundary, this is, to the authors' knowledge, the first submillisecond end-to-end sequential-convex solve for a single powered-landing trajectory.
