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·2025
A Distributed Method for First-Order Optimization With Expansive Projection for Powered Descent Guidance
Jiwoo Choi, Jong-Han Kim
초록

This paper introduces an efficient parallel optimization framework specifically designed for powered descent guidance (PDG) problems, leveraging consensus-based first-order methods. PDG problems are known to encounter significant computational challenges due to their extended planning horizons and inherent nonconvexity. Traditional approaches, such as the proportional integral proximal gradient (PIPG) and the parallel direction method of multipliers (PDMM), are aimed at large-scale optimization but tend to suffer from slower convergence when dealing with extended planning horizons. Although some PDG problems can be made convex through a process known as lossless convexification (LCvx), this method can sometimes produce suboptimal or infeasible solutions. To address this, a first-order approach with expansive projection (ExProj) was recently introduced. In this paper, we distribute the LCvx and ExProj formulations using a novel time-splitting method and integrate a consensus-based alternating direction method of multipliers (ADMM) to further enhance convergence rates. To tackle the computational challenges posed by the split and nonconvex nature of these problems, we introduce several innovative numerical techniques. Our proposed algorithm is rigorously tested across a range of scenarios, including both convexified and nonconvex PDG problems, and its performance is benchmarked against current state-of-the-art approaches. Additionally, we implemented our method on a GPU to significantly enhance the convergence speed. We also conducted a real-time PDG trajectory optimization test in an indoor flight test arena. The results from these tests demonstrate the efficiency and robustness of our framework, underscoring its potential for practical applications in PDG systems. These results are promising and demonstrate the ability of the method to effectively handle real-world operational demands.

키워드
ExpansiveComputer scienceDescent (aeronautics)Projection (relational algebra)Order (exchange)Mathematical optimizationAlgorithmMathematicsEngineeringAerospace engineering
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2025