On constrained manipulation in robotics-assisted minimally invasive surgery

Results of a study on the restricted motion of manipulators in robotics-assisted minimally invasive surgery are presented in this paper. The governing equations of trocar kinematics are derived and the constrained manipulation is generically formulated in terms of the trocar geometry as well as the kinematics of the manipulator. The results are validated through a numerical simulation with a Mitsubishi PA10-7C arm. Following this analysis, by utilizing the constrained manipulation formulation, a modified measure of manipulability, specifically applicable to surgical tasks, is proposed. The measure is proven to be frame-invariant and dimensionally homogeneous for manipulators with similar joints (revolute or prismatic). Furthermore, the measure is shown to be capable of quantifying the impact of trocar constraints on surgical task performance when the remote center of motion is maintained through active compliant motion control.