Till John, Aloi Vincent, Riojas Katherine E, Anderson Patrick L, Webster Robert J, Rucker Caleb
Department of Mechanical, Aerospace, and Biomedical Engineering, The University of Tennessee, Knoxville, TN.
Department of Mechanical Engineering, Vanderbilt University, Nashville, TN 37235 USA.
IEEE Trans Robot. 2020 Dec;36(6):1704-1718. doi: 10.1109/TRO.2020.3000290. Epub 2020 Jul 27.
Existing static and kinematic models of concentric tube robots are based on the ordinary differential equations of a static Cosserat rod. In this paper, we provide the first dynamic model for concentric tube continuum robots by adapting the partial differential equations of a dynamic Cosserat rod to describe the coupled inertial dynamics of precurved concentric tubes. This generates an initial-boundary-value problem that can capture robot vibrations over time. We solve this model numerically at high time resolutions using implicit finite differences in time and arc length. This approach is capable of resolving the high-frequency torsional dynamics that occur during unstable "snapping" motions and provides a simulation tool that can track the true robot configuration through such transitions. Further, it can track slower oscillations associated with bending and torsion as a robot interacts with tissue at real-time speeds. Experimental verification of the model shows that this wide range of effects is captured efficiently and accurately.
现有的同心管机器人静态和运动学模型基于静态柯塞尔杆的常微分方程。在本文中，我们通过采用动态柯塞尔杆的偏微分方程来描述预弯曲同心管的耦合惯性动力学，首次为同心管连续体机器人提供了动态模型。这产生了一个初边值问题，该问题能够捕捉机器人随时间的振动。我们使用时间和弧长的隐式有限差分在高时间分辨率下对该模型进行数值求解。这种方法能够解析不稳定“突然折断”运动期间出现的高频扭转动力学，并提供一种模拟工具，该工具可以通过此类转变跟踪机器人的真实构型。此外，当机器人以实时速度与组织相互作用时，它可以跟踪与弯曲和扭转相关的较慢振荡。对该模型的实验验证表明，能有效且准确地捕捉到这一系列广泛的效应。
