INVERSE KINEMATICS SOLUTIONS OF ROBOTIC MANIPULATORS USING PADEN-KAHAN SUBPROBLEMS AND SCREW THEORY

In this paper, we used the Paden-Kahan subproblems and their extensions in the context of screw theory to solve the inverse kinematics of common robot manipulators: RR, RRR, RPR planar, and RPP spatial robot models. The inverse kinematics problem of a robot is fundamental to determining a robot’s mechanics, and among the different ways to solving it, we chose the Paden- Kahan subproblems approach for its effectiveness and simplicity. The canonical subproblems have been significantly extended and of particular interest to us are the inclusion of solutions to paral- lel screw axes for the second subproblem and prismatic joints instead of only revolute joints, also known as Pardos-Gotor subproblems, After solving the inverse kinematics of each robot model and representing the solutions via graphs, we then proceeded to demonstrate the correctness of our solutions against the desired configuration and found that the orientational and positional errors between the desired configuration and our solution were in the range of floating-point arithmetic errors. Taking into account the simplicity during solving the inverse kinematics and the number of operations performed, we concluded that, at least where applicable, the Paden-Kahan subproblems and their extensions provide significant advantages to other methods.