# MAGMA：乘子增强几何运动算法

> 原文链接：https://robotics.hellobike.com/papers/2026-10-15-2610-21852
> 频道：papers | 更新日期：2026-10-15 | 标签：arxiv, cs.RO
> 核心摘要：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。

# MAGMA：乘子增强几何运动算法

::: v-pre
> 原文链接：[MAGMA: Multiplier-Augmented Geometric Motion Algorithm](https://arxiv.org/abs/2610.21852)（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
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## 原始参考来源 (Sources)

- [arXiv 2610.21852：MAGMA: Multiplier-Augmented Geometric Motion Algorithm](https://arxiv.org/abs/2610.21852)