Multi-surface interactions occur frequently in articulated-rigid-body systems such as robotic manipulators. Real-time prediction of contact-interaction forces is challenging for systems with many degrees of freedom (DOFs) because joint and contact constraints must be enforced simultaneously. While several contact models exist for systems of free rigid bodies, fewer models are available for articulated-body systems. In this paper, we extend the method of Ruspini and Khatib and develop the contact-space resolution (CSR) model by applying the operational space theory of robot manipulation. Through a proper choice of contact-space coordinates, the projected dynamics of the system in the contact space is obtained. We show that the projection into the dynamically consistent null space preserves linear and angular momentum in a subspace of the system dynamics complementary to the joint and contact constraints. Furthermore, we illustrate that a simultaneous collision event between two articulated bodies can be resolved as an equivalent simultaneous collision between two non-articulated rigid bodies through the projected contact-space dynamics. Solving this reduced-dimensional problem is computationally efficient, but determining its accuracy requires physical experimentation. To gain further insights into the theoretical model predictions, we devised an apparatus consisting of colliding 1-, 2-, and 3-DOF articulated bodies where joint motion is recorded with high precision. Results validate that the CSR model accurately predicts the post-collision system state. Moreover, for the first time, we show that the projection of system dynamics into the mutually complementary contact space and null space is a physically verifiable phenomenon in articulated-rigid-body systems.

中文翻译：

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用于关节体系统中同时碰撞的物理一致视图的接触空间分辨率模型：理论和实验结果

多表面相互作用经常发生在铰接式刚体系统中，例如机器人操纵器。接触相互作用力的实时预测对于具有多个自由度 (DOF) 的系统具有挑战性，因为必须同时强制执行关节和接触约束。虽然自由刚体系统存在多种接触模型，但铰接体系统可用的模型较少。在本文中，我们扩展了 Ruspini 和 Khatib 的方法，并通过应用机器人操作的操作空间理论开发了接触空间分辨率（CSR）模型。通过正确选择接触空间坐标，获得了在接触空间中的系统的投影动态。我们表明，到动态一致零空间的投影在与关节和接触约束互补的系统动力学子空间中保留了线性和角动量。此外，我们说明了两个铰接体之间的同时碰撞事件可以通过投影接触空间动力学解析为两个非铰接刚体之间的等效同时碰撞。解决这个降维问题的计算效率很高，但确定其准确性需要物理实验。为了进一步深入了解理论模型预测，我们设计了一种由碰撞 1、2 和 3 自由度关节体组成的装置，其中关节运动被高精度记录。结果验证了 CSR 模型准确预测了碰撞后系统状态。此外，我们第一次表明，系统动力学在相互补充的接触空间和零空间中的投影是铰接刚体系统中的物理可验证现象。