极大坐标系下的线性变分积分器
Linear-Time Variational Integrators in Maximal Coordinates
摘要：
大多数动力学仿真工具使用最小坐标（也称为广义坐标或关节坐标）来参数化多体机器人系统的配置。然而，最大坐标的方法有几个优点，最小坐标参数化，包括本地处理封闭的运动回路和非完整约束。本文描述了一个线性时间变分积分器，制定在极大坐标。由于其变分形式，该算法不会遭受约束漂移，并具有良好的能量和动量守恒性质。稀疏矩阵分解技术允许在$O(n)$（线性）时间内计算具有$n$链接的无环铰接机构的动力学。引入循环的其他约束也可以由算法处理，而不会产生太多的计算开销。实验结果表明，我们的方法提供了速度竞争与国家的最先进的最小坐标算法，同时优于他们在几种情况下，特别是当处理闭环和配置奇异。
英文摘要：
Most dynamic simulation tools parameterize the configuration of multi-body robotic systems using minimal coordinates, also called generalized or joint coordinates. However, maximal-coordinate approaches have several advantages over minimal-coordinate parameterizations, including native handling of closed kinematic loops and nonholonomic constraints. This paper describes a linear-time variational integrator that is formulated in maximal coordinates. Due to its variational formulation, the algorithm does not suffer from constraint drift and has favorable energy and momentum conservation properties. A sparse matrix factorization technique allows the dynamics of a loop-free articulated mechanism with $n$ links to be computed in $O(n)$ (linear) time. Additional constraints that introduce loops can also be handled by the algorithm without incurring much computational overhead. Experimental results show that our approach offers speed competitive with state-of-the-art minimal-coordinate algorithms while outperforming them in several scenarios, especially when dealing with closed loops and configuration singularities.
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。
