Fig. 2.

Conceptual illustration of the SCADE algorithm for position estimation of a CM/FI working in an obstructed environment. In the SCADE, using an EIU providing intermittent external position feedback and an ESU (e.g., FBG or magnetic sensors) with continuous feedback, a priori model-independent sensor fusion algorithm is used to simultaneously recalibrate the ESU and estimate the deformation behavior of the CM/FI. In this figure, ${\mathbf{r}}^{\text{act}},{\mathbf{r}}^{\text{ESU}},{\mathbf{r}}^{\text{EIU}}\in {ℝ}^M$ represent the position of the CM/FI’s tip position with respect to a Cartesian space {act}, embedded sensing unit {ESU}, and external imaging unit {EIU} frames, respectively. Also, $\mathit{\theta }\in {ℝ}^N$ denotes the vector of actuation inputs of the CM/FI.