Forward and inverse solution of a 9-DOF hybrid robot for minimally invasive surgery

Focusing on the recently developed "5R+4T" 9-DOF(degree-of-freedom) hybrid robot for thoracoabdominal percutaneous cryosurgery by the robotics institute of Beijing University of Aeronautics and Astronautics, an original single-constraint-condition algorithm was put forward to obtain analytic solutions to the forward and inverse kinematics of the robot, based on the product of exponentials (POE) formula using inverse transformation method and characteristics of inverse matrix. The mutual derivation between the forward and the inverse solution, namely, the effectiveness of the algorithm, was demonstrated by several sets of numeric data. A modification for the algorithm was also advanced by discussing the demonstration results, so as to expand the range of its applicability. This algorithm overcomes the difficulties in performing the forward and inverse kinematic calculations which result from the DOF redundancy and the structure complexity of the hybrid robot, bringing a new idea about solving kinematic problems of multi-DOF hybrid robots.