Algorithm for the Inverse Kinematics Calculation of 6-DOF Robots Based on Screw Theory and Paden-Kahan Sub-problems

Denavit-Hartenberg(D-H) notation method and screw theory method are usually used to set up the kinematics model of a robot when its inverse kinematics calculation is to be carried out.D-H method is relatively mature and wildly used in kinematics analysis of robots.Screw method is relatively less in practical application,but with this method,the coordinate of each link of the robot is set up with reference to the base of the robot,so the coordinate has definite geometric meaning.For the kinematics model set up by screw method,the inverse kinematics calculation is usually realized by using Paden-Kahan sub-problem method.Pure Paden-Kahan sub-problems method can only be used for the inverse kinematics calculation of robot with low-DOF.The kinematics model of the robot with 6-DOF and with the last three joint axes intersecting to one point is set up by using screw method,and a new algorithm is proposed for the inverse kinematics calculation of this kind of robot,by using the combined method of algebraic elimination method and Paden-Kahan sub-problem method,and the result of explicit solution is given.The correctness of the algorithm is verified by KUKA KR-150 robot,whose kinematics mode is set up by using the proposed algorithm.