Constrained Visual Predictive Control of a Robotic Flexible Endoscope With Visibility and Joint Limits Constraints

In this letter, a constrained visual predictive control strategy (C-VPC) is developed for a robotic flexible endoscope to precisely track target features in narrow environments while adhering to visibility and joint limit constraints. The visibility constraint, crucial for keeping the target feature within the camera's field of view, is explicitly designed using zeroing control barrier functions to uphold the forward invariance of a visible set. To automate the robotic endoscope, kinematic modeling for image-based visual servoing is conducted, resulting in a state-space model that facilitates the prediction of the future evolution of the endoscopic state. The C-VPC method calculates the optimal control input by optimizing the model-based predictions of the future state under visibility and joint limit constraints. Both simulation and experimental results demonstrate the effectiveness of the proposed method in achieving autonomous target tracking and addressing the visibility constraint simultaneously. The proposed method achieved a reduction of 12.3% in Mean Absolute Error (MAE) and 56.0% in variance (VA) compared to classic IBVS.