A geometrically implicit time-stepping method for multibody systems with intermittent contact
A geometrically implicit time-stepping method for multibody systems with intermittent contact
复制标题
间歇接触多体系统的几何隐式时间步进方法
DOI：
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发表时间：
2014
期刊：
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通讯作者：
J. Trinkle
中科院分区：
文献类型：
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作者：
N. Chakraborty;Stephen Berard;Srinivas Akella;J. Trinkle
对于广泛的机器人问题，包括零件进给装置的设计、操作和运动学规划以及抓取策略的设计，具有稳健处理间歇接触的精确动力学仿真是必要的。本文提出了一种用于间歇接触多体系统动力学仿真的隐式时间步长格式，将接触约束作为一组互补方程和代数方程加入动力学模型中。我们将每个物体建模为凸不等式的交集，并将接触约束写为接触力与依赖于物体上最近点的距离函数之间的互补约束。最近点满足由最小距离问题的Karush-Kuhn-Tucker(KKT)条件得到的一组代数约束。我们证明了这些代数方程和互补约束共同保证了接触约束的满足。这使得我们能够将几何隐式时间步进格式(即，我们不需要近似距离函数)描述为一个非线性互补问题。因此，所得到的时间步长更准确，并且不依赖于闭合形式的距离函数。我们通过实例模拟演示了该方法对解析解以及前面描述的模拟和实验结果的保真度。
Accurate dynamic simulation with robust handling of intermittent contact is necessary for a wide range of robotics problems, including the design of parts feeding devices, manipulation and kinodynamic planning, and designing grasp strategies. In this paper we present an implicit time-stepping scheme for dynamic simulation of multibody systems with intermittent contact by incorporating the contact constraints as a set of complementarity and algebraic equations within the dynamics model. We model each body as an intersection of convex inequalities and write the contact constraints as complementarity constraints between the contact force and a distance function dependent on the closest points on the bodies. The closest points satisfy a set of algebraic constraints obtained from the Karush–Kuhn–Tucker (KKT) conditions of the minimum distance problem. We prove that these algebraic equations and the complementarity constraints taken together ensure satisfaction of the contact constraints. This enables us to formulate a geometrically implicit time-stepping scheme (i.e. we do not need to approximate the distance function) as a nonlinear complementarity problem. The resulting time-stepper is therefore more accurate and does not rely on a closed-form distance function. We demonstrate through example simulations the fidelity of this approach to analytical solutions and previously described simulation and experimental results.