Submillisecond Sequential Convex Optimization for Powered Landing via Dynamics Condensation and xPIPG

Abstract

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.