arXiv 2301.020182023-01eess.SYcs.ROcs.SY

基于李代数微分动态规划的矩阵李群约束轨迹优化

Constrained Trajectory Optimization on Matrix Lie Groups via Lie-Algebraic Differential Dynamic Programming

Mechanical Engineering, Tampere University, Finland（塔尔库大学机械工程系）；Mechanical Engineering Program, Division of Engineering, New York University Abu Dhabi, United Arab Emirates（纽约大学阿布扎克分校工程学院机械工程项目）；Department of Electrical Engineering（电气工程系）；Automation, Aalto University, Finland（自动化，艾尔沃斯大学）

Gokhan Alcan, Fares J. Abu-Dakka, Ville Kyrki

备注：: 12 pages, 6 figures
DOI：: 10.1016/j.sysconle.2025.106220

阅读 PDF

arXiv 页面 ↗HTML 原文 ↗

AI总结：

本文提出一种基于增广拉格朗日的约束离散微分动态规划方法，可在通用矩阵李群上进行轨迹优化，能有效处理约束且计算高效，在SE(3)机械系统及四旋翼轨迹优化中表现出鲁棒性与稳定性。

摘要：

矩阵李群是控制和机器人学中常用的一类重要流形，在这些流形上优化控制策略是一个基础问题。本文提出一种基于增广拉格朗日的约束离散微分动态规划（DDP）方法，用于矩阵李群上的轨迹优化，具有计算高效性。该方法在反向传播时将优化问题提升到李代数，正向传播时回缩回流形。与仅针对特定矩阵李群类处理约束的现有方法不同，本文方法为通用矩阵李群的非线性约束处理提供了通用解决方案。我们在SE(3)中具有刚体动力学的机械系统中评估了所提DDP方法处理约束的有效性，并与现有直接优化求解器比较了其计算效率。此外，该方法在SE(3)上作为李代数反馈控制策略应用时，在外部扰动下表现出鲁棒性，并能在具有挑战性的真实场景中优化四旋翼轨迹。实验表明，所提方法能在优化过程中有效处理配置、速度和输入上的通用约束，同时在闭环执行所得控制策略时保持对外部扰动的稳定性。

英文摘要：

Matrix Lie groups are an important class of manifolds commonly used in control and robotics, and optimizing control policies on these manifolds is a fundamental problem. In this work, we propose a novel computationally efficient approach for trajectory optimization on matrix Lie groups using an augmented Lagrangian-based constrained discrete Differential Dynamic Programming (DDP). The method involves lifting the optimization problem to the Lie algebra during the backward pass and retracting back to the manifold during the forward pass. Unlike previous approaches that addressed constraint handling only for specific classes of matrix Lie groups, the proposed method provides a general solution for nonlinear constraint handling across generic matrix Lie groups. We evaluate the effectiveness of the proposed DDP method in handling constraints within a mechanical system characterized by rigid body dynamics in SE(3), assessing its computational efficiency compared to existing direct optimization solvers. Additionally, the method demonstrates robustness under external disturbances when applied as a Lie-algebraic feedback control policy on SE(3), and in optimizing a quadrotor's trajectory in a challenging realistic scenario. Experiments show that the proposed approach effectively manages general constraints defined on configuration, velocity, and inputs during optimization, while also maintaining stability under external disturbances when executing the resultant control policy in closed-loop.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

AI总结：

摘要：

英文摘要：

相关论文