Uncalibrated Model-Free Visual Servo Control for Robotic Endoscopic with RCM Constraint Using Neural Networks

With the advancement of robotic-assisted minimally invasive surgery, visual servo control has become a crucial technique for improving surgical outcomes. However, traditional visual servo methods often rely on precise kinematic models and camera calibration, limiting their generalizability. Considering these, this article proposes a novel uncalibrated model-free visual servo control scheme. Specifically, we introduce a Jacobian matrix and interaction matrix estimation method based on a gradient neural network (GNN), which enables online estimation by utilizing control signals and sensor outputs. Then, the estimated results are incorporated into a visual servo control framework that considers remote center of motion (RCM) constraint, joint-drift problem, and physical constraint, formulated as a quadratic programming (QP) problem. Subsequently, focusing on the joint limits and endoscope insertion depth constraint, we develop a nonpiecewise differentiable multilevel constraint handling technique. For the formulated QP problem, a predefined-time convergent error-regulating zeroing neural network (PTCER-ZNN) solver is designed, and we can derive the optimal control signals. Detailed theoretical analyses of the developed GNN estimation method and the PTCER-ZNN solver are provided. Simulation results demonstrate the effectiveness of the proposed scheme in image feature regulation and tracking tasks, exhibiting its advantages over existing approaches.