In this paper, we present a new forward kinematic model for a novel class of long and thin continuum robots for operation in spatial workspace. Such robots are well suited for navigation through unstructured environments with superior reach using their flexible and thin profile, especially for inspection applications. This cable-like continuum robot design [1] has a concentric backbone arrangement but is spring-loaded and tendon-actuated, has improved compliance with a light and compact motor-encoder actuation mechanism. To account for the spring-loading, a compression factor is introduced on top of the established constant curvature continuum kinematics. The resulting continuum or shape variables are then estimated as a function of the measurable encoder variables. The effectiveness of the model is validated by performing experiments with the robot prototype.
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