A High-Precision 3-D FBG-Based Force Sensor Utilizing Nested Orthoplanar Springs for Laparoscopic Palpation

Abstract

This paper introduces a compact and high-precision three-dimensional fiber Bragg grating-based force sensor for palpation in robotic laparoscopic surgery. An innovative force-sensitive flexure is developed by incorporating two radial-type orthoplanar spring leaves (ROPSLs) nested within a side-type orthoplanar spring structure (SOPSS), resulting in a compact sensor design with a length of 12 mm. Two ROPSLs with a thickness of 0.2 mm are designed to achieve high axial force sensitivity and are connected in series via a coupling shaft to improve bending stiffness. The SOPSS, designated for radial force sensing, incorporates an increased thickness to enhance its axial stiffness. The distinct stiffness characteristic between ROPSLs and SOPSS results in a balanced 3-D force sensitivity and minimized crosstalk, facilitating improved accuracy. The performance evaluation and optimization were conducted employing finite element analysis. Calibration experiments demonstrated excellent resolutions of 1.2 mN, 1.1 mN, and 2.5 mN for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F_x</i>, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F_y</i>, and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F_z</i>, respectively, as well as superior linearity with the maximum error of 1.35%. Dynamic loading experiments validated the sensor’s high measurement precision, with average root mean square error (RMSE) values of 15 mN (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F_x</i>), 16 mN (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F_y</i>), and 72 mN (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F_z</i>). Finally, palpation experiments on silicone phantoms and ex vivo porcine tissues successfully confirmed the sensor’s efficacy in differentiating tumor tissue from normal tissue.