Generalized Trajectory Planning for Nonlinear Interventions

Minimally invasive procedures with flexible instruments suchas endoscopes, needles or drilling units are becoming more and more common.Their automated insertion will be standard across several applicationsin operation rooms of the future. In such scenarios regular replanningfor feasible nonlinear trajectories is a mandatory step towardautomation. However, state of the art methods focus on isolated solutionsonly. In this paper we introduce a generalized motion planningformulation in SE(3), regarding both position and orientation, that issuitable for these approaches. To emphasize the generalization of this formulationwe evaluate the performance of proposed Bidirectional RapidlyexploringRandom Trees (Bi-RRT) on four different clinical applications:Drilling in temporal bone surgery, trajectory planning for cardiopulmonaryendoscopy, automatic needle insertion for spine biopsy and livertumor removal. Experiments show that for all four scenarios the formulationis suitable and feasible trajectories can be planned successfully.