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Force sensing in compact concentric tube mechanism with optical fibers 329

               the bevel needles to be directed by their own steering forces. A compact 3-DOF cannula
               robot [7] utilized a screw-spline and two stepper motors, while the stylet was separately
               connected to its own screw-controlled stepper. The robot was good at target error correction,
               able to reach multiple points and navigate curved trajectories previously not possible.
               Motor actuated systems also have the advantage of handling uncertainty during actuation,
               employing highly accurate kinematic models to minimize the probability of collision with
               sensitive tissue [10]. Moreover, automated tubular robots can have path generation and
               navigation through complex, critical tissue structures, such as through the bronchi of the
               lung [11].
               14.2.1.2 Tube design considerations

               Curved tubes are fitted with each other from largest to smallest, with a common axis
               creating a mutual-resultant curvature. Through actuation, the tubes can be rotated and
               translated, varying the length and curvature of the needle.

               Using the primary form of a two-tube pair, there are two instances where interactions between
               tubes can be generalized and illustrated: a dominating stiffness pair and a balanced stiffness
               pair where the bending stiffnesses of the tubes in the pair are equal [1]. Segregation of these
               two tube designs is useful when extending to an arbitrary number of tubes.

               In the dominating stiffness tube pair, the tubes are characterized with a polarity in bending
               stiffness. This characteristic causes the curvature of the precurved inner tube to conform to
               the outer tube when retracted, but upon translation and extension outward of the outer tube,
               the inner tube regains its original curvature.


               14.2.2 Fiber Bragg gratings for tactile feedback

               Studies have investigated using various methods to provide force feedback. Strain gauges
               have been utilized in minimally invasive surgery (MIS) [16], but as electrically driven
               systems, they face limited application when introduced to the human body. This is also true
               for the capacitative-based sensors introduced by Gray and Fearing [17] and other piezo-
               based materials [18]. Sensors that do not utilize electricity, such as fiber-based sensors [18],
               exhibit superior compatibility, mainly due to the fibers experiencing lower degrees of loss
               compared to other sensors. However, they are limited by their sensitivity to changes in total
               light intensity.

               FBGs are well suited to biomedical applications due to their inherent properties. Their
               weight, coupled with their small diameter and flexibility, makes them ideal to be integrated
               along the shaft of a concentric tube. Their ability to withstand high pressure and
               temperature, along with their electromagnetic inertness [12], lend them a degree of
               resilience to adverse environments and allow them to be used in conjunction with a wide
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