可快速计算的粘性摩擦和无滑移刚性接触模型
Rapidly computable viscous friction and no-slip rigid contact models
摘要：
本文提出了两种特殊情况下的刚性接触建模计算效率高的算法--接触只有粘性摩擦和接触没有滑动-有特别有用的应用在机器人的运动和把握。对具有库仑摩擦的刚性接触进行建模通常在接触点的数量方面表现出$O(n^3)$预期的时间复杂度和$2^{O(n)}$最坏情况的复杂度。我们考虑的特殊情况在预期情况下表现出$O(m^3 + m^2n)$时间复杂度（$m$是多刚体系统中独立坐标的数量），在最坏情况下表现出多项式复杂度;因此，渐近复杂度不再由接触点的数量（可以想象是无限的）驱动，而是更多地依赖于系统中的物体数量（通常是固定的）。这些特殊情况下，还需要相当少的约束非线性优化变量，从而产生运行时间的显着改善。最后，这些特殊情况还提供了另一个优点：非线性优化问题在数值上更容易求解。
英文摘要：
This article presents computationally efficient algorithms for modeling two special cases of rigid contact---contact with only viscous friction and contact without slip---that have particularly useful applications in robotic locomotion and grasping. Modeling rigid contact with Coulomb friction generally exhibits $O(n^3)$ expected time complexity in the number of contact points and $2^{O(n)}$ worst-case complexity. The special cases we consider exhibit $O(m^3 + m^2n)$ time complexity ($m$ is the number of independent coordinates in the multi rigid body system) in the expected case and polynomial complexity in the worst case; thus, asymptotic complexity is no longer driven by number of contact points (which is conceivably limitless) but instead is more dependent on the number of bodies in the system (which is often fixed). These special cases also require considerably fewer constrained nonlinear optimization variables thus yielding substantial improvements in running time. Finally, these special cases also afford one other advantage: the nonlinear optimization problems are numerically easier to solve.
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