论文标题
刚体和表面接触的刚体动态模拟
Rigid Body Dynamic Simulation with Line and Surface Contact
论文作者
论文摘要
在本文中，我们开发了一种原则性方法，以模拟与点接触（我们称之为同等的接触点）的表面接触和表面接触，该方法与基于物理的表面（线）接触模型一致。假设一组触点形成了凸组集，我们通过将问题作为混合非线性互补性问题同时解决触点检测和动态仿真步骤。这使我们能够同时计算等效接触点（与摩擦模型一致）处的等效接触点以及扳手（力和力矩）以及刚体对象的构型和速度。此外，我们证明还满足了对象之间无渗相的触点约束。我们提出了一个几何隐含的时间步态，用于动态模拟，以进行具有凸接触区域的两个物体之间的接触，其中包括线接触和表面接触。我们证明，对于表面和线接触，对于物体质量中心的速度的任何值，有一个独特的接触点和接触扳手解决方案，可以满足离散的运动方程。模拟示例显示出可以证明我们方法的有效性，并表明通过我们的方法，我们可以在点，线和表面接触之间无缝过渡。
In this paper, we develop a principled method to model line and surface contact with point contact (we call this point, equivalent contact point) that is consistent with physics-based models of surface (line) contact. Assuming that the set of contact points form a convex set, we solve the contact detection and dynamic simulation step simultaneously by formulating the problem as a mixed nonlinear complementarity problem. This allows us to simultaneously compute the equivalent contact point as well as the wrenches (forces and moments) at the equivalent contact point (consistent with the friction model) along with the configuration and velocities of the rigid objects. Furthermore, we prove that the contact constraints of no inter-penetration between the objects is also satisfied. We present a geometrically implicit time-stepping scheme for dynamic simulation for contacts between two bodies with convex contact area, which includes line contact and surface contact. We prove that for surface and line contact, for any value of the velocity of center of mass of the object, there is a unique solution for contact point and contact wrench that satisfies the discrete-time equations of motion. Simulation examples are shown to demonstrate the validity of our approach and show that with our approach we can seamlessly transition between point, line, and surface contact.
