Many problems in robotics involve creating or breaking multiple contacts nearly simultaneously or in an indeterminate order. We present a novel general purpose numerical integrator based on the theory of Event Selected Systems (ESS). Many multicontact models are ESS, which has recently been shown to imply that despite a discontinuous vector field, the flow of these systems is continuous, piecewise smooth, and has a well defined orbital derivative for all trajectories, which can be rapidly computed. We provide an elementary proof that our integrator is first-order accurate and verify numerically that it is in fact second-order accurate as its construction anticipated. We also compare our integrator, implemented in NumPy, to a MuJoCo simulation on models with 2 to 100 contacts, and confirm that the increase in simulation time per contact is nearly identical. The results suggest that this novel integrator can be invaluable for modelling and control in many robotics applications.

翻译：机器人学中的许多问题涉及几乎同时或以不确定顺序建立或断开多个接触。我们提出了一种基于事件选择系统（ESS）理论的新型通用数值积分器。许多多接触模型都属于ESS，近期研究表明，尽管其向量场不连续，但这些系统的流动是连续、分段光滑的，且所有轨迹均具有定义明确的轨道导数，可快速计算。我们提供了一个基本证明，表明我们的积分器具有一阶精度，并通过数值验证确认其实际上具有二阶精度，符合其构造预期。我们还将在NumPy中实现的积分器与MuJoCo仿真进行了对比，针对接触数从2到100的模型进行了测试，结果证实每个接触的仿真时间增长几乎相同。该结果表明，这种新型积分器在众多机器人应用的建模与控制中具有重要价值。