闭链机构的分块运动学约简：基于路径装配与缺陷同伦

中文摘要 AI 辅助

闭式运动链通过非线性闭式约束耦合主动与被动坐标，使模块化建模复杂化。本文提出一种路径装配闭式微分映射（PACDM）框架，用于模块化闭式求解与运动学约简。每个闭式单元比较两条具有共同端点的有序变换路径，其不匹配通过SE(3)上的对数表示，相应的雅可比矩阵由局部变换导数装配而成。多路径模块由最小成对闭式单元集合构建，而秩揭示分析选择局部独立的标量约束。缺陷同伦沿可行且正则的连续路径从近似估计恢复闭式一致的被动坐标。在正则构型下，隐式微分得到局部主动到被动微分映射，随后用于预测-校正连续过程以执行规定运动。该框架在包含两路径和三路径闭链模块的七自由度重型机械臂上评估。与Simscape Multibody比较，轨迹均方根误差低于8.5×10^-10弧度，而预测-校正连续比在每个轨迹样本应用缺陷同伦快约45.8倍。

英文摘要

Closed kinematic chains complicate modular modeling by coupling active and passive coordinates through nonlinear closure constraints. This paper presents a Path-Assembled Closure Differential Mapping (PACDM) framework for modular closure resolution and kinematic reduction. Each closure element compares two ordered transformation paths with common endpoints, with their mismatch expressed through the logarithm on SE(3) and the corresponding Jacobian assembled from local transformation derivatives. Multi-path modules are constructed from a minimal set of pairwise closure elements, while rank-revealing analysis selects locally independent scalar constraints. A defect homotopy recovers closure-consistent passive coordinates from approximate estimates along a feasible and regular continuation path. At regular configurations, implicit differentiation yields the local active-to-passive differential mapping, which is subsequently used in a predictor-corrector continuation procedure for prescribed motion. The framework is evaluated on a seven-degree-of-freedom heavy-duty manipulator containing two-path and three-path closed-chain modules. Comparison with Simscape Multibody yields trajectory root-mean-square errors below 8.5 x 10^-10 rad, while predictor-corrector continuation is approximately 45.8 times faster than applying defect homotopy at every trajectory sample.

发表机构

• Tampere University（坦佩雷大学）

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