A Noniterative Neural Algorithm Involving Dini Derivatives for Visual Servoing of Joint-Constrained Robotic Endoscope

In minimally invasive surgery (MIS), surgical endoscope can be automated using visual servoing by incorporating motion constraints into a time-variant quadratic programming (TVQP). Zeroing neural network (ZNN) is a superior recurrent neural network (RNN) for solving TVQP in real time. However, ZNNs cannot handle bound constraints in a TVQP directly and require differentiable elements, meaning that visual servoing requires the accelerations of feature points. Unfortunately, accelerations usually cannot be accurately retrieved. Motivated by the expected low accelerations in MIS, this article proposes a novel noniterative algorithm termed Dini-RNN to solve TVQP by introducing a Dini derivative operator. Unlike the existing ZNNs, the Dini-RNN can handle bound constraints directly and allows partial elements to be continuous but not differentiable everywhere. The convergence of the Dini-RNN is theoretically analyzed and proved. Subsequently, simulative and experimental results show that the Dini-RNN solution is effective to achieve visual servoing with superior performance.