Multibody dynamics simulators are an important tool in many fields, including learning and control in 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 in 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.

多体动力学模拟器是许多领域的重要工具，包括机器人的学习和控制。然而，许多现有的动力学模拟器在处理受约束的机械系统时，由于不合适的积分器具有不良的能量行为和有问题的约束违规（例如在接触相互作用中），因此存在不准确性。变分积分器是一种数值离散方法，可以在模拟机械系统时减少物理误差，并且在最大坐标中制定动力学可以轻松且在数值上稳健地结合运动学环或接触等约束。因此，本文推导了最大坐标中具有等式和不等式约束的机械系统的变分积分器。此外，还提供了用于求解积分器的高效的基于图的稀疏性利用算法，并将其实现为开源模拟器。模拟器的评估表明，由于变分积分器和稀疏求解器的优点，物理精度得到了提高。与最小坐标算法的比较表明数值稳健性得到了提高，步行机器人和具有明确约束的外骨骼的应用示例证明了最大坐标的必要性和能力。