Model-Free and Uncalibrated Eye-in-Hand Visual Servoing Approach for Concentric-Tube Robots

This article proposes a model-free and uncalibrated eye-in-hand visual servoing (EiH-VS) approach for controlling concentric-tube robots (CTRs) in minimally invasive surgery (MIS). Traditionally, a closed-loop EiH-VS controller requires an accurate robot kinematic model and hand-eye calibration. However, it is difficult to model CTR accurately when considering torsion, shear, friction, interactive force, and nonlinear constitutive behavior. In this article, we map image deviations to robot actuation variables with numerically calculated image Jacobian. The estimation of dynamic image Jacobian is based on a modified adaptive square-root unscented Kalman filter (MASR-UKF). A customized measurement matrix is constructed to describe the transformation between state and observation vectors. Moreover, an adaptive gain controller is designed to accelerate convergence. As a result, no prior knowledge of the CTR kinematic model and hand-eye calibration is needed in visual servoing tasks. Simulations and experiments have been conducted. The results validated the efficacy and efficiency of the proposed methods.