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中断多个接触。我们基于事件选择系统理论提出了一种新颖的通用数值积分器。许多多接触模型属于ESS系统，最近的研究表明：尽管这类系统具有不连续向量场，其流仍保持连续、分段光滑，且对所有轨迹均存在明确定义的轨道导数，并可快速计算。我们给出了该积分器具有一阶精度的基本证明，并通过数值验证其实际达到构造时期望的二阶精度。我们还将基于NumPy实现的积分器与MuJoCo仿真在2至100个接触的模型上进行对比，确认了单位接触的仿真时间增量几乎一致。结果表明，这种新型积分器在众多机器人应用中对于建模与控制具有重要价值。