Rigid Body Dynamic Simulation with Multiple Convex Contact Patches
Rigid Body Dynamic Simulation with Multiple Convex Contact Patches
复制标题
具有多个凸接触面片的刚体动态仿真
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
N. Chakraborty
中科院分区：
文献类型：
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作者：
Jiayin Xie;N. Chakraborty
提出了一种刚体间歇接触动力学仿真的原则性方法，其中接触假设为非凸面接触面片，可建模为凸面面片的并集。在模拟相互间歇接触的刚体时，普遍的假设是接触是点接触。在最近的工作中，我们介绍了一种模拟具有凸面接触面片(线接触和面接触)的刚体的方法。本文将非凸面接触面片建模为凸面面片的并集，建立了离散时间混合互补问题，同时解决了接触检测和运动方程的积分问题。因此，我们的方法是一种几何隐式方法，我们证明了在我们的公式中，接触的刚体之间不存在人工渗透。我们同时求解每个接触片的等效接触点(ECP)和接触冲量以及物体的状态，即物体的形状和速度。我们提供的经验证据表明，如果两个物体之间的接触块数目小于或等于3，那么物体的状态演化是唯一的，尽管接触冲量和ECP可能不是唯一的。我们还给出了仿真结果，结果表明我们的方法可以在仿真过程中无缝地捕捉非凸面片到点(或线接触)等不同接触模式之间的转换。
We present a principled method for dynamic simulation of rigid bodies in intermittent contact with each other where the contact is assumed to be a non-convex contact patch that can be modeled as a union of convex patches. The prevalent assumption in simulating rigid bodies undergoing intermittent contact with each other is that the contact is a point contact. In recent work, we introduced an approach to simulate contacting rigid bodies with convex contact patches (line and surface contact). In this paper, for non-convex contact patches modeled as a union of convex patches, we formulate a discrete-time mixed complementarity problem where we solve the contact detection and integration of the equations of motion simultaneously. Thus, our method is a geometrically-implicit method and we prove that in our formulation, there is no artificial penetration between the contacting rigid bodies. We solve for the equivalent contact point (ECP) and contact impulse of each contact patch simultaneously along with the state, i.e., configuration and velocity of the objects. We provide empirical evidence to show that if the number of contact patches between two objects is less than or equal to three, the state evolution of the bodies is unique, although the contact impulses and ECP may not be unique. We also present simulation results showing that our method can seamlessly capture transition between different contact modes like non-convex patch to point (or line contact) and vice-versa during simulation.