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The equilibrium shape of a continuum robot is resulted from both its internalactuation and the external physical interaction with a surrounding environment.A fast and accurate shape estimation method (i) can be used as a feedback tocompensate for more accurate motion; and (ii) can reveal rich information aboutphysical interactions (e.g. instrument-anatomy contacts / forces during asurgery). From a prior work that demonstrated an offline calibration ofcontinuum robots, we adopt its shape modal representation and error propagationmodels that include identification Jacobians. In this work, we present aniterative observer approach to enable online shape estimation. We develop adual Extended Kalman Filter (EKF) to estimate both the robot state and theshape modal parameters. The dual EKF provides robust estimation on (i) theconfiguration space variables that are controllable and driven by internalactuation; and (ii) the modal coefficients representing homotopies of shapefamilies that are governed by the physical interactions with the environment.We report results from simulation studies in this work, and plan to investigatemethods in the future to use the proposed approach for predicting physicalinteractions.

Shape Estimation of Continuum Robots via Modal Parameterization and Dual Extended Kalman Filter