论文/arXiv 2610.21852·13 天前

MAGMA：乘子增强几何运动算法

针对受约束高维机械系统最优控制难题，提出基于AGHF和增广拉格朗日的MAGMA，并在多类受限轨迹生成问题上验证。

AI 整理

• 本体 SDK 与控制
• 评测与安全

原文链接：MAGMA: Multiplier-Augmented Geometric Motion Algorithm（arXiv 2610.21852 · 发布日期：2026-10-15）

MAGMA: Multiplier-Augmented Geometric Motion Algorithm

针对受约束高维机械系统最优控制难题，提出基于AGHF和增广拉格朗日的MAGMA，并在多类受限轨迹生成问题上验证。

核心要点

• 高维机械系统受非线性动力学和非凸可行集影响，约束最优控制求解仍具挑战。
• MAGMA将Affine Geometric Heat Flow轨迹优化与增广拉格朗日框架结合，并用原始-对偶流求解。
• 论文给出原始-对偶AGHF的理论刻画，证明MAGMA是在适当能量上的梯度流。
• 在含障碍、状态限制和驱动限制的难题上，相比先进求解器获得高质量解且调参更少。

验证范围与局限：验证范围为多类带障碍、状态限制和驱动限制的轨迹生成问题。

英文摘要 (Abstract)

Solving optimal control problems for high-dimensional mechanical systems subject to constraints remains challenging due to nonlinear dynamics and non-convex feasible sets. This paper introduces MAGMA(Multiplier-Augmented Geometric Motion Algorithm), an Affine Geometric Heat Flow (AGHF)-based trajectory optimizer that incorporates an augmented Lagrangian framework solved via a primal-dual flow. A theoretical characterization of the primal-dual AGHF is provided, establishing that MAGMA is a gradient flow on an appropriately defined energy. MAGMA is validated across a variety of challenging trajectory generation problems with obstacles, state limits, and actuation limits. Comparative evaluations against state-of-the-art solvers demonstrate that MAGMA achieves high quality solutions with significantly reduced tuning effort on the hardest problems.

作者：César E. Ramos Chuquiure, Vansh Thakur, Challen Enninful Adu, Ram Vasudevan

来源

本页事实对应的公开页面，以原文为准。

1. arXiv 2610.21852：MAGMA: Multiplier-Augmented Geometric Motion Algorithm访问 2026-10-21