Optimal visual control of tendon-sheath-driven continuum robots with robust Jacobian estimation in confined environments

Accurate control of continuum robots in confined environments presents a significant challenge due to the need for a precise kinematic model, which is susceptible to external interference. This paper introduces a model- less optimal visual control (MLOVC) method that enables a tendon-sheath-driven continuum robot (TSDCR) to effectively track visual targets in a confined environment while ensuring stability. The method allows for intraluminal navigation of TSDCRs along narrow lumens. To account for the presence of external outliers, a robust Jacobian estimation method is proposed, wherein improved iterative reweighted least squares with sliding windows are used to online calculate the robot's Jacobian matrix from sensing data. The estimated Jacobian establishes the motion relationship between the visual feature and the actuation. Furthermore, an optimal visual control method based on quadratic programming (QP) is designed for visual target tracking, while considering the robot's physical constraint and control constraints. The MLOVC method for visual tracking provides a reliable alternative that does not rely on the precise kinematics of TSDCRs and takes into consideration the impact of outliers. The control stability of the proposed approach is demonstrated through Lyapunov analysis. Simulations and experiments are conducted to evaluate the effectiveness of the MLOVC method, and the results demonstrate that it enhances tracking performance in terms of accuracy and stability.