Contact dynamics modelling for robotic task simulation
Contact dynamics modelling for robotic task simulation
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发表时间：
2008
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通讯作者：
Y. Gonthier
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作者：
Y. Gonthier
本文介绍了基于顺应接触模型的接触动力学建模系统的理论推导和实现。该系统被设计用作通用建模工具，以支持基于空间的机器人操纵器系统的任务规划过程。除了通常的保真度和准确性之外，这种操作环境对接触动力学建模系统提出了额外的要求。该系统不仅必须能够生成准确可靠的模拟结果，而且必须在相当短的时间内完成，以便运维工程师可以在几个小时内调查多个场景。该系统很容易与现有的模拟设施连接。接触模型的所有物理参数可以通过实验确定，也可以根据材料特性通过分析或理论推导通过其他方式获得。类似地，可以自动选择数值参数，也可以使用启发式规则来选择数值参数，这些规则给出了值的范围指示，以确保模拟结果在质量上是正确的。接触动力学建模系统由两个接触模型组成。一方面，提出了点接触模型来解决涉及具有非共形表面的物体的模拟。由于它基于赫兹理论，因此接触表面必须光滑且没有间断，即没有角或锐边。点接触模型包括法向阻尼和切向摩擦，并假设接触表面非常小，因此假设接触力通过点作用。给出了将法向阻尼设置为有效恢复系数函数的表达式。引入了新的七参数摩擦模型。该摩擦模型基于刷毛摩擦模型，并通过引入与负载相关的刷毛刚度和阻尼项以及以矢量形式表达刷毛变形来适应 3 维摩擦冲击建模的背景。该模型具有驻留时间粘滞力依赖性，并且能够再现摩擦现象的动态性质。然后提出了基于温克勒弹性地基模型的第二个接触模型来处理更一般的几何形状。这种所谓的体积接触模型适用于广泛的接触几何形状，只要接触表面可以近似为平坦的即可。还提出了一种处理后一种近似不合理的对象的方法。接触表面上的接触压力分布的影响以滚动阻力矩和旋转摩擦力矩的形式来解释。结果表明，接触力和力矩可以用两个物体之间干涉体积的体积特性来表示，定义为碰撞体的两个未变形几何形状相交所跨越的体积。感兴趣的属性是：干扰体积的体积、其质心的位置以及关于质心的惯性张量。该分析还引入了一种定义接触法线的新方法；结果表明，接触法线必须对应于惯性张量的特征向量之一。该研究还研究了库仑摩擦力如何受到物体相对运动的影响。引入平均表面速度的概念。它考虑了接触表面的相对平移和角运动。然后使用平均表面速度来查找与库仑摩擦引起的摩擦力和旋转扭矩相关的无量纲因子。后面这些因素被标记为 Contensou 因素。此外，干涉体积关于接触法线的转动惯量的回转半径被证明与旋转库仑摩擦扭矩与平移库仑摩擦力相关。然后提出了七参数刷毛摩擦模型的体积版本。摩擦模型包括切向摩擦力和旋转摩擦扭矩。 Contensou 因子用于控制库仑摩擦的行为。对于这两种接触模型，方程都是根据第一原理推导出来的，并且对每个接触模型特性的行为进行了研究和模拟。如果可用，将模拟结果与文献中的基准结果进行比较。使用持有半球形有效负载并与平板接触的六自由度机械臂进行实验来验证点接触模型。模拟结果与实验结果之间具有良好的一致性。
This thesis presents the theoretical derivations and the implementation of a contact dynamics modelling system based on compliant contact models. The system was designed to be used as a general-purpose modelling tool to support the task planning process space-based robot manipulator systems. This operational context imposes additional requirements on the contact dynamics modelling system beyond the usual ones of fidelity and accuracy. The system must not only be able to generate accurate and reliable simulation results, but it must do it in a reasonably short period of time, such that an operations engineer can investigate multiple scenarios within a few hours. The system is easy to interface with existing simulation facilities. All physical parameters of the contact model can be identified experimentally or can be obtained by other means through analysis or theoretical derivations based on the material properties. Similarly, the numerical parameters can be selected automatically or by using heuristic rules that give an indication of the range of values that would ensure that the simulations results are qualitatively correct. The contact dynamics modelling system is comprised of two contact models. On one hand, a point contact model is proposed to tackle simulations involving bodies with non-conformal surfaces. Since it is based on Hertz theory, the contacting surfaces must be smooth and without discontinuity, i.e., no corners or sharp edges. The point contact model includes normal damping and tangential friction and assumes the contact surface is very small, such that the contact force is assumed to be acting through a point. An expression to set the normal damping as a function of the effective coefficient of restitution is given. A new seven-parameter friction model is introduced. The friction model is based on a bristle friction model, and is adapted to the context of 3-dimensional frictional impact modelling with introduction of load-dependent bristle stiffness and damping terms, and with the expression of the bristle deformation in vectorial form. The model features a dwell-time stiction force dependency and is shown to be able to reproduce the dynamic nature of the friction phenomenon. A second contact model based on the Winkler elastic foundation model is then proposed to deal with a more general class of geometries. This so-called volumetric contact model is suitable for a broad range of contact geometries, as long as the contact surface can be approximated as being flat. A method to deal with objects where this latter approximation is not reasonable is also presented. The effect of the contact pressure distribution across the contact surface is accounted for in the form of the rolling resistance torque and spinning friction torque. It is shown that the contact forces and moments can be expressed in terms of the volumetric properties of the volume of interference between the two bodies, defined as the volume spanned by the intersection of the two undeformed geometries of the colliding bodies. The properties of interest are: the volume of the volume of interference, the position of its centroid, and its inertia tensor taken about the centroid. The analysis also introduces a new way of defining the contact normal; it is shown that the contact normal must correspond to one of the eigenvectors of the inertia tensor. The investigation also examines how the Coulomb friction is affected by the relative motion of the objects. The concept of average surface velocity is introduced. It accounts for both the relative translational and angular motions of the contacting surfaces. The average surface velocity is then used to find dimensionless factors that relate friction force and spinning torque caused by the Coulomb friction. These latter factors are labelled the Contensou factors. Also, the radius of gyration of the moment of inertia of the volume of interference about the contact normal was shown to correlate the spinning Coulomb friction torque to the translational Coulomb friction force. A volumetric version of the seven-parameter bristle friction model is then presented. The friction model includes both the tangential friction force and spinning friction torque. The Contensou factors are used to control the behaviour of the Coulomb friction. For both contact models, the equations are derived from first principles, and the behaviour of each contact model characteristic was studied and simulated. When available, the simulation results were compared with benchmark results from the literature. Experiments were performed to validate the point contact model using a six degrees-of-freedom manipulator holding a half-spherical payload, and coming into contact with a flat plate. Good correspondence between the simulated and experimental results was obtained.