arXiv subjects

Dai Shen

Publications and source records attributed to Dai Shen.

3 recordsLinked to original sources

arXiv2026

Dual-Thrust Switching Analytical Guidance Algorithm for Powered Landing with Attitude Smoothness Optimization

Traditional numerical guidance methods for powered landing of reusable rockets are typically constrained by high computational complexity and inadequate real-time performance. Moreover, insufficient consideration of attitude smoothness often induces severe fluctuations in control commands; meanwhile, most existing approaches are tailored for single-thrust scenarios, failing to accommodate the guidance requirements of multi-engine thrust switching. To mitigate these limitations, this paper proposes an analytical guidance method optimized for attitude smoothness, which supports dual-thrust-mode switching. First, a corresponding optimal control problem is formulated, and it is theoretically proven that the optimal attitude command takes a concise piecewise cubic function form. This transforms complex trajectory optimization into a parametric analytical optimization problem, yielding a substantial improvement in computational efficiency. Further, a three-phase guidance framework is designed to enable adaptive determination of the guidance activation point and thrust switching point; when integrated with an aerodynamic correction strategy, this framework enhances the method's adaptability in complex flight environments particularly under high lift-to-drag ratio conditions. Simulation results demonstrate that the attitude command profile generated by the proposed method aligns closely with the theoretical optimal solution, with an ultra-short computation time, confirming its strong potential for online real-time implementation. Even under stringent conditions (e.g., limited thrust adjustment range, high lift-to-drag ratios, and parameter deviations), the method consistently achieves high-precision landing, showcasing promising prospects for engineering applications.

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arXiv2026

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

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.

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arXiv2026

Microsecond-Class Powered-Descent Optimization via Exact Condensation and Strong Convex Regularization

Fuel-dominant powered descent can be written as a convex program, but the usual full-state epigraph formulation still carries many state variables, fuel epigraph variables, and dynamics equalities. In addition, the pure-fuel objective provides no strong-convexity curvature. This paper combines three structural reductions. First, a dimensionally consistent low-weight energy term makes the control solution unique. Second, a terminal-state sensitivity recursion eliminates every intermediate state exactly; invertible row normalization turns the 30-node baseline with 300 primal variables and 174 equality multipliers into a problem with 90 control variables and six terminal multipliers. Third, the shared radial structure of the fuel norm and thrust ball gives an exact closed-form proximal operator consisting of group shrinkage followed by magnitude clipping. The condensed problem is solved with a fixed-budget extrapolated proportional--integral projected-gradient iteration implemented in fixed-size C17 arrays. In a Mars powered-descent case with energy weight 0.02 and relative reference-solution tolerance $10^{-3}$, the iteration count decreases from 2744 for the pure-fuel full-state epigraph baseline to 93, while the fuel metric increases by only 0.033\%. The mean end-to-end solve time is \SI{68.2}{\micro\second}, and P99 is \SI{128.1}{\micro\second}, on an Intel i7-10875H. Because the thrust set in this test case is already a convex ball, the contribution is fast solution of the convex core rather than a new lossless-convexification theorem.

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