基于极大坐标的多体动力学变分积分器与图求解器
Variational Integrators and Graph-Based Solvers for Multibody Dynamics in Maximal Coordinates
AI总结：
该研究针对现有多体动力学仿真器约束处理精度差的问题，推导了极大坐标下带约束的变分积分器，提出高效图基稀疏求解算法并实现开源仿真器，验证了其物理精度、鲁棒性及在机器人等场景的适用性。
摘要：
多体动力学仿真器是机器人学习与控制等诸多领域的重要工具。然而，现有许多动力学仿真器在处理受约束机械系统时存在精度不足的问题，原因在于积分器不合适，能量特性差且约束违反问题突出，例如接触相互作用场景。变分积分器是一类数值离散化方法，可减少机械系统仿真中的物理误差，而采用极大坐标表述动力学则能简便且数值鲁棒地纳入运动学闭环、接触等约束。因此，本文推导了一种适用于极大坐标下带等式与不等式约束机械系统的变分积分器。此外，本文还提出了用于求解该积分器的高效基于图的稀疏性利用算法，并将其实现为开源仿真器。仿真器评估结果显示，变分积分器提升了物理精度，稀疏求解器也展现出优势。与极小坐标算法的对比表明其数值鲁棒性更优，步行机器人与带显式约束的外骨骼的应用实例则证明了极大坐标的必要性与性能。
英文摘要：
Multibody dynamics simulators are an important tool in many fields, including learning and control for robotics. However, many existing dynamics simulators suffer from inaccuracies when dealing with constrained mechanical systems due to unsuitable integrators with bad energy behavior and problematic constraint violations, for example for contact interactions. Variational integrators are numerical discretization methods that can reduce physical inaccuracies when simulating mechanical systems, and formulating the dynamics in maximal coordinates allows for easy and numerically robust incorporation of constraints such as kinematic loops or contacts. Therefore, this article derives a variational integrator for mechanical systems with equality and inequality constraints in maximal coordinates. Additionally, efficient graph-based sparsity-exploiting algorithms for solving the integrator are provided and implemented as an open-source simulator. The evaluation of the simulator shows improved physical accuracy due to the variational integrator and the advantages of the sparse solvers. Comparisons to minimal-coordinate algorithms show improved numerical robustness and application examples of a walking robot and an exoskeleton with explicit constraints demonstrate the necessity and capabilities of maximal coordinates.
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