Virtual Joints to Solve the Inverse Kinematics Problem

Abstract:
If off-line programming systems (OLP) enable the user to define robot arms with any number of joints and various degrees of freedom in operational space an iterative numerical solution to solve the inverse kinematics is necessary. This paper presents a new approach to solve the inverse kinematics for redundant and non-redundant serial-chain manipulators with any number of joints in a general way. The manipulator arm is equipped with additional virtual prismatic joints to manipulate the length of the links and all joint limitations are initially neglected. For this virtual redundant manipulator the inverse kinematics is solved by a nonlinear optimization approach on the base of inverse differential kinematics. If a solution exist for a goal pose specified in Cartesian terms, the performance criteria enforces a solution inside the workspace of the original manipulator and the values of the virtual prismatic joints are converging to the original length of the links.