Inverse Kinematics of a Manipulator for Minimally Invasive Surgery

In this report we describe the inverse kinematics of our robotic system for minimally invasive surgery. Special respect is given to an intuitive operability of the user interface. Therefore we apply the concept of so-called trocar kinematics. Meaning that the manipulator (in our case an instrument for minimally invasive surgery) has to pass a fixed opening through the surface of the patient's body. It is the principle idea of minimally invasive surgery to perform all surgical tasks through small keyhole-openings (so-called ports) in order to avoid traumatic invasions. Evidently, this procedure restricts the degrees of freedom of the instrument. Feed and rotation axes always have to intersect with the fixed port. With respect to kinematics this point is often called trocar point. Given the position and rotation of the end effector, as a result of the instrument's trocar kinematics, we get the position and rotation of the robot flange that bears the instrument. Therefore we have full cartesian control of the instruments. Since no direct cartesian control of the robot is possible within our interface, we also have to determine the inverse kinematics of our robots. As a final result we will get three joint angles for the minimally invasive instrument, while we get six angles for directly controlling the robot's joints.     «

In this report we describe the inverse kinematics of our robotic system for minimally invasive surgery. Special respect is given to an intuitive operability of the user interface. Therefore we apply the concept of so-called trocar kinematics. Meaning that the manipulator (in our case an instrument for minimally invasive surgery) has to pass a fixed opening through the surface of the patient's body. It is the principle idea of minimally invasive surgery to perform all surgical tasks through small...     »