科里奥利因子化与黎曼几何的联系
摘要
许多能量基类的控制策略对于机械系统需要选择满足偏斜对称性质的科里奥利因子化。在本文中，我们（a）探讨控制设计者在此选择中拥有灵活性的条件，（b）发展了一个与克里斯托费尔符号相关的规范选择，（c）描述了如何有效地对受约束的机械系统进行控制计算。我们将科里奥利因子化的选择与配置流形上的仿射联结的概念联系起来，并展示了联结的性质如何与相关的因子化相关系。特别地，基于克里斯托费尔符号的因子化与无挠性相关联，这可以限制基于被动性控制的系统轨迹的扭曲。我们 then develop a method to induce Coriolis factorizations for constrained mechanisms from unconstrained ones, which provides a pathway to use the theory for efficient control computations with high-dimensional systems such as humanoids and quadruped robots with open- and closed-chain mechanisms. A collection of algorithms is provided (and made available open source) to support the recursive computation of passivity-based control laws, adaptation laws, and regressor matrices in future applications.
引用
@article{arxiv.2312.14425,
title = {Coriolis Factorizations and their Connections to Riemannian Geometry},
author = {Patrick M. Wensing and Jean-Jacques E. Slotine},
journal= {arXiv preprint arXiv:2312.14425},
year = {2025}
}
备注
working draft; comments welcome