Real-time dynamics of soft and continuum robots based on Cosserat rod models
Real-time dynamics of soft and continuum robots based on Cosserat rod models
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DOI：
10.1177/0278364919842269
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发表时间：
2019-05-01
影响因子：
9.2
通讯作者：
Rucker, Caleb
中科院分区：
文献类型：
--
作者：
Till, John;Aloi, Vincent;Rucker, Caleb
许多连续体和软机器人设计的动力学方程可以简洁地表示为一组基于经典Cosserat杆理论的偏微分方程（PDE），其中包括弯曲，扭转，剪切和延伸。在这项工作中，我们提出了一种数值方法的前向动力学仿真Cosserat为基础的机器人模型在真实的时间。该方法隐式离散偏微分方程中的时间导数，然后解决由此产生的常微分方程（ODE）边值问题（BVP）的弧长在每个时间步。我们表明，这种策略可以包括各种各样的机器人模型和数值方案在时间和空间上，所需的符号操作最少。由于隐式方法在大时间步长的稳定性，计算效率得到了提高，并且实现相对简单，我们通过提供一个简短的MATLAB编码的例子来证明这一点。我们调查和量化的权衡与几个数值子程序，我们验证的准确性与动态棒数据收集的高速摄像机系统相比。为了证明该方法的应用程序的连续体和软机器人，我们推导出几个基于Cosserat的动态模型的机器人使用各种驱动方案（可伸缩杆，肌腱，和流体室），并应用我们的方法来实现实时仿真在每种情况下，与肌腱机器人的额外的实验验证。结果表明，这些模型捕捉几个重要的现象，如稳定性转变和可压缩工作流体的影响。
The dynamic equations of many continuum and soft robot designs can be succinctly formulated as a set of partial differential equations (PDEs) based on classical Cosserat rod theory, which includes bending, torsion, shear, and extension. In this work we present a numerical approach for forward dynamics simulation of Cosserat-based robot models in real time. The approach implicitly discretizes the time derivatives in the PDEs and then solves the resulting ordinary differential equation (ODE) boundary value problem (BVP) in arc length at each timestep. We show that this strategy can encompass a wide variety of robot models and numerical schemes in both time and space, with minimal symbolic manipulation required. Computational efficiency is gained owing to the stability of implicit methods at large timesteps, and implementation is relatively simple, which we demonstrate by providing a short MATLAB-coded example. We investigate and quantify the tradeoffs associated with several numerical subroutines, and we validate accuracy compared with dynamic rod data gathered with a high-speed camera system. To demonstrate the method's application to continuum and soft robots, we derive several Cosserat-based dynamic models for robots using various actuation schemes (extensible rods, tendons, and fluidic chambers) and apply our approach to achieve real-time simulation in each case, with additional experimental validation on a tendon robot. Results show that these models capture several important phenomena, such as stability transitions and the effect of a compressible working fluid.