Robots consisting of several concentric, preshaped, elastic tubes can work dexterously in narrow, constrained, and/or winding spaces, as are commonly found in minimally invasive surgery. Previous models of these “active cannulas” assume piecewise constant precurvature of component tubes and neglect torsion in curved sections of the device. In this paper we develop a new coordinate-free energy formulation that accounts for general preshaping of an arbitrary number of component tubes, and which explicitly includes both bending and torsion throughout the device. We show that previously reported models are special cases of our formulation, and then explore in detail the implications of torsional flexibility for the special case of two tubes. Experiments demonstrate that this framework is more descriptive of physical prototype behavior than previous models1 it reduces model prediction error by 82% over the calibrated bending-only model, and 17% over the calibrated transmissional torsion model in a set of experiments.

中文翻译：

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同心管连续体机器人的平衡构象

由几个同心、预成型、弹性管组成的机器人可以在狭窄、受限和/或缠绕的空间中灵巧地工作，这在微创手术中很常见。这些“主动插管”的先前模型假设组件管的分段恒定预弯曲并忽略设备弯曲部分的扭转。在本文中，我们开发了一种新的无坐标能量公式，它考虑了任意数量的组件管的一般预成形，并且明确地包括整个设备的弯曲和扭转。我们展示了先前报告的模型是我们公式的特例，然后详细探讨了扭转柔韧性对两个管的特殊情况的影响。