Feedback control system design for force-sensing concentric tube-based surgical robot: Kinematics using Bernstein polynomials

A novel force sensing module integrated into a concentric tube robot (CTR) was proposed for vitreoretinal surgery in our previous work, and this robot was able to provide tip force information to the operating surgeon. However, when the force-sensing module was integrated, the property of the tube changed, and the conventional modeling-based control algorithm proved to be unsuitable for the force-sensing concentric tube robot (FSCTR). In this work, we have proposed a shape optimization algorithm for the FSCTR to prevent snapping issue while providing an adequate workspace. A corollary actuation system was used to control the FSCTR. The forward kinematics of the FSCTR consisted of rigid body motion and shape variation, where the shape variation was determined using Bernstein polynomials. Inverse kinematics was derived using the Newton-Raphson method. A feedback controller was designed to compensate for the error caused by rigid body motion. Several experiments were conducted to evaluate the performance of the proposed control system. The experimental accuracy of the proposed forward kinematics was 0.15 +/- 0.16 mm, and this result was superior to that of the torsionally compliant model. The accuracy of the inverse kinematics was 0.55 +/- 0.24 mm, and the accuracy of point tar-geting under feedback control was 0.12 +/- 0.05 mm. Overall, the results of this study indicate that the proposed motion control system satisfies the standards required for vitreoretinal surgery.