机器人操作和运动通常涉及几乎同时发生的碰撞——例如一步中脚跟和脚趾的触地——其结果对碰撞发生的顺序极其敏感。机器人仿真器通常缺乏预测这种顺序的准确性，而是通过启发式方法选择一种顺序。当基于模型的控制器和在仿真中学习到的策略被部署到真实机器人上时，这种差异会降低性能。我们通过一个集值刚体模型来调和这一问题，该模型生成同时摩擦碰撞的广泛物理合理结果集合。我们首先通过将 Routh 碰撞模型重新表述为微分包含（DI），将其扩展到多重碰撞，并证明任何解都将在有限时间内解决所有碰撞。通过将时间视为状态，我们将该模型嵌入到另一个捕捉刚体动力学连续时间演化的 DI 中，并保证解的存在性。最后，我们将同时碰撞的仿真转化为线性互补问题（LCP），并开发了一种算法，用于对碰撞后速度集合进行紧近似，并提供概率保证。我们在来自操作和腿足运动的若干示例上展示了我们的方法。
英文摘要：
Robotic manipulation and locomotion often entail nearly-simultaneous collisions -- such as heel and toe strikes during a foot step -- with outcomes that are extremely sensitive to the order in which impacts occur. Robotic simulators commonly lack the accuracy to predict this ordering, and instead pick one with a heuristic. This discrepancy degrades performance when model-based controllers and policies learned in simulation are placed on a real robot. We reconcile this issue with a set-valued rigid-body model which generates a broad set of physically reasonable outcomes of simultaneous frictional impacts. We first extend Routh's impact model to multiple impacts by reformulating it as a differential inclusion (DI), and show that any solution will resolve all impacts in finite time. By considering time as a state, we embed this model into another DI which captures the continuous-time evolution of rigid body dynamics, and guarantee existence of solutions. We finally cast simulation of simultaneous impacts as a linear complementarity problem (LCP), and develop an algorithm for tight approximation of the post-impact velocity set with probabilistic guarantees. We demonstrate our approach on several examples drawn from manipulation and legged locomotion.
Experimental Verification of Stability Theory for a Planar Rigid Body with Two Unilateral Frictional Contacts
Faculty of Mechanical Engineering, Technion - Israel Institute of Technology（以色列理工学院机械工程学院）；Budapest University of Technology and Economics（布达佩斯技术与经济大学）
Intersection-free Robot Manipulation with Soft-Rigid Coupled Incremental Potential Contact
ZenusTech Inc.（泽努斯科技公司）；Shanghai Jiao Tong University（上海交通大学）；SJTU-Yale Joint Center of Biostatistics and Data Science, National Center for Translational Medicine, Shanghai Jiao Tong University（上海交通大学-耶鲁大学生物统计与数据科学联合中心，上海交通大学国家转化医学中心）
The Nonsmooth Impact Direction (NSID) of Robotic Systems
Automation and Control Institute, TU Wien（维也纳工业大学自动化与控制研究所）；Institute of Robotics and Mechatronics, German Aerospace Center (DLR)（德国航空航天中心机器人与机电一体化研究所）
