Active cannulas are remotely actuated thin continuum robots with the potential to traverse narrow and winding environments without relying on "guiding" environmental reaction forces. These features seem ideal for procedures requiring passage through narrow openings to access air-filled cavities (e.g. surgery in the throat and lung). Composed of telescoping concentric pre-curved elastic tubes, an active cannula is actuated at its base by translation and axial rotation of component tubes. Using minimum energy principles and Lie Group theory, we present a framework for the kinematics of multi-link active cannulas. This framework permits testing of the hypothesis that overall cannula shape locally minimizes stored elastic energy. We evaluate in particular whether the torsional energy in the long, straight transmission between actuators and the curved sections is important. Including torsion in the kinematic model enables us to analytically predict experimentally observed bifurcation in the energy landscape. Independent calibration procedures based on bifurcation and tip and feature positions enable model parameter identification, producing results near ranges expected from tube material properties and geometry. Experimental results validate the kinematic framework and demonstrate the importance of modeling torsional effects in order to describe bifurcation and accurately predict active cannula shape.
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