将刚体动力学导数适配于约束嵌入的闭链模型
Adapting Rigid-Body Dynamics Derivatives for Constraint Embedding Closed-Chain Models
- University of Notre Dame（圣母大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文扩展刚体动力学导数算法至约束嵌入闭链模型，移除局部构型不变假设，支持更一般关节类型，并评估额外计算成本，以提升模型预测控制与可微仿真的精度。
AI中文摘要：
本文将一个现有的刚体动力学一阶导数算法扩展到使用约束嵌入建模的闭链运动学系统。许多标准动力学算法同时适用于开链和约束嵌入模型，但现有的高效导数方法假设关节速度效应在局部是构型不变的。我们移除这一假设，并推导出适配算法，将动力学导数扩展到更一般的关节类型，包括约束嵌入闭链模型中出现的关节类型。我们的结果比较了传统的销钉关节机器人模型与捕获局部闭链的更完整驱动模型。我们表明，这些泛化引入的额外项在仅建模驱动运动学时计算影响较小，但当驱动链中包含额外刚体（如电机转子）或考虑非局部回路时，可能会产生更高成本。总体而言，这些结果使得约束嵌入驱动子机制更精确的动力学计算能够用于模型预测控制和可微仿真。
英文摘要：
This paper extends an existing algorithm for the first-order derivatives of rigid-body dynamics to the case of closed-chain kinematic systems modeled using constraint embed- ding. Many standard dynamics algorithms apply to both open- chain and constraint-embedded models, but existing efficient derivative methods assume joint velocity effects are locally config- uration invariant. We remove this assumption and derive adapted algorithms that extend dynamics derivatives to more general joint types, including those arising in constraint-embedded closed- chain models. Our results compare conventional pin-joint robot models with more complete actuation models that capture local closed chains. We show that the additional terms introduced by these generalizations have low computational impact when mod- eling actuation kinematics alone, but can incur higher cost when additional rigid bodies, such as motor rotors, are included in the actuation chain, or when considering non-local loops. Overall, these results enable more accurate dynamics computations for constraint-embedded actuation submechanisms to be adopted in model-predictive control and differentiable simulation.
