An active cannula is a surgical device capable of dynamically changing its curved shape in response to rotation and translation of the several precurved, concentric, superelastic tubes from which it is made. As the tubes move with respect to one another in response to input motion at their bases (outside the patient), they elastically interact, causing one another to bend. This bending can be harnessed to direct the cannula through winding trajectories within the human body. An active cannula has the potential to perform a wide range of surgical tasks, and it is especially well suited for guiding and aiming an optical fiber (e.g. BeamPath from OmniGuide, Inc.) for laser ablation. Controlling the trajectory of the laser requires control of the shape of the active cannula, and in particular the position and orientation of its tip. Prior work has shown that beam mechanics can be used to describe the shape of the cannula, given the translations and axial angles of each tube base. Here, in order to aim the laser, we invert this relationship (obtaining the “inverse kinematic”), solving for the translations and axial angles of each tube, given a desired position and orientation of the cannula tip. Experimental evaluation of inverse kinematics was carried out using a prototype consisting of three tubes. The outermost tube is straight and rigid (stainless steel), with an outer diameter (OD) of 2.4 mm. The 1.8 mm OD middle tube is superelastic Nitinol, with a preshaped circular tip. The 1.4 mm OD innermost tube is Nitinol and is not precurved, representing the straight trajectory of a laser emanating from the tip of the cannula. We assessed the accuracy of the inverse kinematics by computing the necessary tube translations and rotations needed to direct the beam of the “laser” to sequential locations along a desired trajectory consisting of two line segments that meet at a corner. These inputs were then applied at tube bases to direct the laser to thirty points along the trajectory on a flat surface 100 mm away the cannula base. The position of the tip of the simulated laser was measured using an optical tracker (Micron Tracker H3-60, Claron, Inc.). Mean error between desired and actual positions was 3.1 mm (maximum 5.5 mm). This experiment demonstrates proof of concept for laser guidance, and establishes the accuracy of the inverse kinematic model. We note that these results are applicable to guidance of a wide range of medical devices in addition to lasers. Relevant references, as well as images of our prototype and experimental data described here can be found in an online version of this abstract at http://research.vuse.vanderbilt.edu/MEDLab/. This work was supported by NSF grant #0651803, and NIH grant #1R44CA134169-01A1.
Static Kinematics for an Antagonistically Actuated Robot Based on a Beam-Mechanics-Based Model
