Spatial probability distribution for port planning in minimal invasive robotic surgery (MIRS)

Abstract

In minimal invasive robotic surgery (MIRS) port placement has a particular status accounted for joint limits of the robots. The port depicts a pivot point so that the robots movement is constraint by reducing its degrees of freedom (DOF). Additionally the workspace of reachable points is limited by the instrument length and the robots' flexibility. Our approach for optimizing the port position and evaluate the robots' performance uses a knowledge base, represented by trajectories, to generate a master trajectory of a specific operation type. Therefor a cluster algorithm is applied to establish a Markov model. To handle loops a second order Markov model is created as well. With the help of the each trajectory a transition matrix is build. By combining the most likely transitions of the clusters the chain is generated, giving a rough approximation of a master trajectory. A spatial probability distribution can be calculated for each point by discretization. Therefor, only the relevant clusters, respectively their points, are taken in account. This reflects the probability of a predicted direction by a specific point, which allows a more precise preparation of a master trajectory. After a workspace analysis of the robot it is possible to combine the knowledge of the robot's workspace and the trajectory of interest. By means of selected evaluation factors the robot's performance with a given pivot point is analyzed.