Planar Inverse Statics and Path Planning for a Tendon-Driven Discrete Continuum Robot

Abstract

This study addresses the clinical requirements of a transoral surgery-assisting continuum robot. This application requires both high bendability and stiffness in order to ensure precise positioning and stable fixation of surgical tools. To meet these needs, we developed a tendon-driven discrete continuum robot unit featuring a ball–socket joint and superelastic Nitinol rods. One to three serially connected robot units were tested by applying proximal tendon tension (Tl) in the range of 100–1000 g while distal tension (Ts) was continuously increased to induce bending. During bending, the curves were interpolated using third-order to fifth-order polynomials at discrete Tl levels. The interpolated inverse statics were validated experimentally and compared with finite element simulations using ANSYS. Furthermore, we propose a planar path planning algorithm and numerically evaluate it for a three-unit robot following an arc-shaped trajectory. The inverse statics successfully captured the nonlinear bending behavior of the tendon-driven robot. Validation experiments showed average angular errors of 2.7%, 6.6%, and 5.3% for one, two, and three connected units, respectively. The proposed path planning method achieved an average positional deviation from the reference trajectory ranging from 0.95 mm to 19.77 mm. This work presents a practical and generalizable experimental mapping framework for the inverse statics of tendon-driven discrete continuum robots, avoiding the need for complex analytical models.