Incorporating Trocar Clearance in the Kinematics of Multi-Backbone Continuum Robots for Single-Port Surgery

Yue Ding, Xiang Wang, Haomin Kuang, Kai Xu

Abstract: The intrinsic characteristics of structural compliance and compactness of continuum robots make them suitable for minimally invasive surgical procedures. The current paradigm of single-port laparoscopy (SPL) and natural orifice transluminal surgery (NOTES) concerns extensive uses of trocars/sheaths for instrument delivery. Most existing kinematics models for continuum robots neglect the clearance between the trocar and the internal instrument, which might result in significant modeling errors. In this paper, the effects of clearance between a multi-backbone continuum robot and its outer trocar for surgical site delivery are investigated via mechanical approaches. Based on the mechanics of the multi-backbone continuum segments and a constant curvature kinematics framework, the robot's equilibrium shape in contact with the trocar is found by minimizing the elastic potential energy. It was then found that a 0.25-mm trocar clearance in diameter accounted for 38.11% positional error. The constant curvature kinematics model that incorporates a clearance-compensation scheme also allows the real-time implementation for control. Comparative experiments were carried out, showing that the mean tip positional error was reduced to 2.42 mm from 3.91 mm by incorporating the clearance in the model.