This paper describes a state estimation model for a multi-segment continuum robot that utilizes the displacement of passive cables embedded along the robot's length to estimate its overall shape. As continuum robots are used in activities outside a laboratory environment, methods of measuring their shape configuration in real-time will be necessary to ensure robust closed-loop control. However, because these robots deform along their entire length and lack discrete joints at which primary

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... cements take place, conventional approaches to sensing joint displacement (e.g., encoders) are inappropriate. Furthermore, elasticity plays a key role in determining the resulting shape of the continuum robot, instead of the mechanicsindependent kinematic configuration frequently seen in rigid-link robotics. In order to enable accurate estimates of a continuum robot's shape, the measured displacements of passive cables are utilized to detect the change in shape of the continuum robot. An optimization is used with a static model based on the principle of virtual power to map these cable displacements into the resulting continuum robot configuration. This state estimation model was implemented numerically in MATLAB and validated on an experimental test platform.