A implicit function-based method for describing the obstacles in a robot-assisted celiac intervention surgery environment

In view of the fact that the surgery environment of robot-assisted celiac interventional therapy system is complex and the surgical planning needs the surface information of the obstacles in the environment, the obstacle description was deeply studied, aiming to uniformly describe the surface information of the varieties of obstacles in the surgery environment using the implicit functions method. According to the sample points of the target surfaces measured by an electromagnetic tracking device, the surfaces of a blood vessel, a rib, a patient abdominal epidermis and a puncture needle were obtained by the generalized eigenvector fitting method. Furthermore, the implicit functions of the target surface were obtained and the three-dimensional models were displayed with the Matlab toolbox. The experimental results demonstrate that the generalized eigenvector fitting method, which is fast, effective, accurate, widespread and insensitive to the starting value, is superior to the Levenberg-Marquardt method for the solution of nonlinear least squares question. The obstacles' implicit functions successfully established in the study can provide operative constraints for the medical robot surgical planning.