SCADE: Simultaneous Sensor Calibration and Deformation Estimation of FBG-Equipped Unmodeled Continuum Manipulators

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.