In this article, we present a novel stochastic algorithm called simultaneous sensor calibration and deformation estimation (SCADE) to address the problem of modeling deformation behavior of a generic continuum manipulator (CM) in free and obstructed environments. In SCADE, using a novel mathematical formulation, we introduce a priori model-independent filtering algorithm to fuse the continuous and inaccurate measurements of an embedded sensor (e.g., magnetic or piezoelectric sensors) with an intermittent but accurate data of an external imaging system (e.g., optical trackers or cameras). The main motivation of this article is the crucial need of obtaining an accurate shape/position estimation of a CM utilized in a surgical intervention. In these robotic procedures, the CM is typically equipped with an embedded sensing unit (ESU) while an external imaging modality (e.g., ultrasound or a fluoroscopy machine) is also available in the surgical site. The results of two different set of prior experiments in free and obstructed environments were used to evaluate the efficacy of SCADE algorithm. The experiments were performed with a CM specifically designed for orthopaedic interventions equipped with an inaccurate Fiber Bragg Grating (FBG) ESU and overhead camera. The results demonstrated the successful performance of the SCADE algorithm in simultaneous estimation of unknown deformation behavior of the utilized unmodeled CM together with realizing the time-varying drift of the poor-calibrated FBG sensing unit. Moreover, the results showed the phenomenal out-performance of the SCADE algorithm in estimation of the CM's tip position as compared to FBG-based position estimations.

中文翻译：

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SCADE：配备 FBG 的未建模连续体机械手的同步传感器校准和变形估计

在本文中，我们提出了一种称为同时传感器校准和变形估计（SCADE）的新型随机算法，以解决在自由和障碍环境中对通用连续机械臂（CM）的变形行为进行建模的问题。在 SCADE 中，我们使用一种新颖的数学公式，引入了一种先验模型无关的滤波算法，将嵌入式传感器（例如磁性或压电传感器）的连续且不准确的测量与外部成像系统（例如、光学跟踪器或相机）。本文的主要动机是获得外科手术中使用的 CM 的准确形状/位置估计的迫切需要。在这些机器人手术中，CM 通常配备嵌入式传感单元 (ESU)，同时手术部位也可使用外部成像设备（例如超声波或透视机）。使用在自由和障碍环境中两组不同的先前实验的结果来评估 SCADE 算法的有效性。这些实验是使用专门为骨科干预设计的 CM 进行的，该 CM 配备了不精确的光纤布拉格光栅 (FBG) ESU 和高架摄像机。结果证明了 SCADE 算法在同时估计所使用的未建模 CM 的未知变形行为以及实现不良校准 FBG 传感单元的时变漂移方面的成功性能。此外，结果表明，与基于 FBG 的位置估计相比，SCADE 算法在估计 CM 尖端位置方面具有显着的性能优势。