Inverse Kinematics Control Methods for Redundant Snakelike Robot Teleoperation During Minimally Invasive Surgery

Pierre Berthet-Rayne| Konrad Leibrandt| Gauthier Gras| Philippe Fraisse| André Crosnier| Guang-Zhong Yang
IEEE Robotics and Automation Letters (Volume: 3, Issue: 3, July 2018)

This paper investigated and compared existing inverse kinematics control methods for a redundant snakelike robot that was designed for Ear Nose Throat Surgery(ENT). The authors evaluated these inverse kinematics control methods regarding their intrusiveness, processing speed and the ability to avoid collision in an ENT simulator. In the simulator, a virtual robot was used and its model is based on the Intuitive Imaging Sensing Navigated and Kinematically Enhanced robot, as known as i2Snake. The i2Snake is a soft robot arm design consisting of a series of rolling joints. For the virtual robot in the simulator, there are 8 independent degrees of freedom(DOFs), and for its human-machine interface, there is one master manipulator which can specify the desired position and orientation in the 3D space.

In total, six inverse kinematics control methods were discussed in the paper: Pseudo-inverse jacobian, Joint limit based jacobian modification, Sparse pseudo L0 norm, Sparse iterative, Sparse linear programming and Sparse hierarchical linear programming. Mainly, the principal idea of all the methods is to find a solution, which is the time derivative of the vector of joint variables, for the time derivative of tracking error. The input of tracking error comes from the difference of the movement of the master manipulator and the current position which are derived from the forward kinematics model. The six methods use different optimization algorithms, for example, linear programming and local search, and different constraints to provide different inverse kinematics solutions. Afterward, these methods are used for controlling the virtual robot when the participants are steering the master manipulator.

Evaluation metrics were calculated from the information recorded at 50 Hz in the ENT simulator, which includes transformation matrices, joint variables and usage of clutch and so on. As mentioned, the performance is judged by the intrusiveness, speed and ability to avoid collisions. In general, all the methods have similar performance in intuitiveness. The participants could all complete the required tasks. The authors selected the Sparse pseudo L0 norm and the Joint limit based jacobian modification method to be the better solutions based on the metrics. The two methods both provide less travel volume voxels in the space and less traveling distance of the control joints. Also, among the two methods, when increasing the frequency of input information, Joint limit based jacobian modification showed less accumulated error makes it suitable for real-time application.