发表机构
Institute of Robotics, Johannes Kepler University（约翰内斯·开普勒大学机器人研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究约束刚体时间步长方案中运动表示和构型更新问题，从几何角度探讨，表明若约束定义c - 空间子群，数值积分方案可精确满足约束，得出SE(3)是合适c - 空间，不过结果不能直接用于MBS。
AI 中文摘要
完整约束刚体的动力学可由受几何约束的牛顿 - 欧拉方程建模，常被表述为指标为1的微分代数方程（DAE）系统。在多体系统（MBS）动力学中，常见的做法是：（1）通过常微分方程的积分方案数值求解该系统；（2）在直积李群SO(3)×R3上处理刚体运动，而刚体运动实际构成半直积李群SE(3)。已观察到约束满足情况取决于用作构型空间（c - 空间）的李群。本文从几何角度考虑该问题，表明若约束定义了c - 空间的一个子群，则数值积分方案能精确满足约束。SE(3)的子群对机械系统建模有重要意义，包括低运动学（勒洛）副，且在MBS建模中被隐含使用。结论是SE(3)是约束刚体数值DAE建模的合适c - 空间，但该结果不能直接应用于MBS。
英文摘要
The dynamics of a holonomically constrained rigid body can be modeled by Newton-Euler equations subjected to geometric constraints. This is frequently formulated as a differential-algebraic equation (DAE) system of index 1. Inmultibody system (MBS) dynamics it is common (1) to numerically solve this system by means of integration schemes for ordinary differential equations, and (2) to treat the rigid body motion on the direct product Lie group SO (3)R3, although rigid body motions form the semidirect product Lie group SE (3). It is has been observed that the constraint satisfaction depends on which Lie group is used as configuration space (c-space). In this paper the problem is considered from a geometric perspective. It is shown that the constraints are exactly satisfied by a numerical integration scheme if they define a subgroup of the c-space. The subgroups of SE (3) have a significance for modeling mechanical systems, including lower kinematic (Reuleaux) pairs and are implicitly used in MBS modeling. It is concluded that SE (3) is the appropriate cspace for numerical DAE modeling of a constrained rigid body. This result does not immediately apply to MBS, however.
Commentspages 995-1015
Journal refBit Numer Math 56, 995-1015 (2016)
