Continuum robots navigate narrow, winding passageways while safely and compliantly interacting with their environments. Sensing the robot's shape under these conditions is often done indirectly, using a few coarsely distributed (e.g., strain or position) sensors combined with the robot's mechanics-based model. More recently, given high-fidelity shape data, external interaction loads along the robot have been estimated by solving an inverse problem on the mechanics model of the robot. In this article, we argue that since shape and force are fundamentally coupled, they should be estimated simultaneously using a statistically principled approach. We accomplish this by applying continuous-time batch estimation directly to the arclength domain. A general continuum robot model serves as a statistical prior that is fused with discrete, noisy measurements taken along the robot's backbone. The result is a continuous posterior containing both shape and load functions of arclength, as well as their uncertainties. We first test the approach with a Cosserat rod, i.e., the underlying modeling framework that is the basis for a variety of continuum robots. We verify our approach numerically using distributed loads with various sensor combinations. Next, we experimentally validate shape and external load errors for highly concentrated force distributions (point loads). Finally, we apply the approach to a tendon-actuated continuum robot demonstrating applicability to more complex actuated robots.

中文翻译：

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连续体机器人的统一形状和外部负载状态估计

Continuum 机器人在狭窄、蜿蜒的通道中航行，同时安全、顺从地与环境交互。在这些条件下感知机器人的形状通常是间接完成的，使用一些粗略分布的（例如应变或位置）传感器与机器人的基于力学的模型相结合。最近，在给定高保真形状数据的情况下，通过解决机器人力学模型的反演问题来估计沿着机器人的外部相互作用载荷。在本文中，我们认为，由于形状和力从根本上是耦合的，因此应该使用统计原则方法同时估计它们。我们通过将连续时间批量估计直接应用于弧长域来实现这一点。通用连续体机器人模型充当统计先验，与沿机器人主干进行的离散、噪声测量相融合。结果是包含弧长的形状和载荷函数及其不确定性的连续后验。我们首先使用 Cosserat 杆测试该方法，即底层建模框架，它是各种连续体机器人的基础。我们使用分布式负载和各种传感器组合对我们的方法进行数值验证。接下来，我们通过实验验证高度集中的力分布（点载荷）的形状和外部载荷误差。最后，我们将该方法应用于肌腱驱动的连续体机器人，证明其适用于更复杂的驱动机器人。