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.

翻译：多体动力学仿真器在包括机器人学习与控制在内的许多领域中都是重要工具。然而，许多现有动力学仿真器在处理受约束机械系统时，由于使用能量行为不佳且存在约束违反问题（例如接触相互作用）的不当积分器，会导致不准确。变分积分器是一种数值离散化方法，可减少模拟机械系统时的物理不准确性，而采用最大坐标形式化动力学可轻松且数值稳健地纳入运动学闭环或接触等约束。因此，本文推导了适用于最大坐标下含等式与不等式约束机械系统的变分积分器。此外，还提供了利用稀疏性的高效图算法来求解该积分器，并将其实现为开源仿真器。对该仿真器的评估显示，变分积分器改善了物理精度，稀疏求解器也具有优势。与最小坐标算法的比较表明，数值稳健性得到提升，而行走机器人和外骨骼等具有显式约束的应用示例则展示了最大坐标的必要性和能力。