A gradient-based neural network accelerated for vision-based control of an RCM-constrained surgical endoscope robot

This paper presents an accelerated gradient-based neural network (GNN) to achieve visual servoing of a surgical endoscope robot. A KUKA LWR 4+ robot with seven joints is used to serve as an endoscope holder. Kinematic mapping is established between the joint space of the robot and the image space of the camera. For surgical applications, the motions of the KUKA robot are constrained with respect to a remote-center-of-motion (RCM) point. Meanwhile, each joint of the KUKA robot has its own physical limits (e.g., joint-angle and joint velocity limits) that cannot be violated. By taking into account the kinematic equation, RCM constraints and physical limits, a control scheme possessing a quadratic programming (QP) formulation is constructed. To solve the QP problem, an inverse-free GNN model is accelerated to be finite-time convergent using a powerful activation function. Mathematical derivations of the accelerated GNN model and theoretical proofs relevant to the finite-time convergence are detailed. Comparative validations are conducted with the superior convergence performance of the accelerated GNN model substantiated. The effectiveness of the proposed GNN solution for vision-based control of the surgical endoscope is verified with RCM constraints and physical limits respected simultaneously.