Potential Function Based Inverse Kinematics of Robotic Manipulators

The inverse kinematics (IK) of redundant robotic manipulators can be particularly challenging to solve algebraically, especially when dealing with uncertain information about the manipulator link lengths or target location. Potential functions offer a method to obtain numerical solutions for various problems by leveraging well-known optimization algorithms. However, their construction requires careful attention to avoid the creation of parasitic local minima. In this seminar, we will introduce potential functions designed specifically to solve the inverse kinematics problem for planar redundant manipulators. Additionally, we will present a novel proof of convergence for the method, which has significant implications for other IK algorithms, particularly Jacobian or gradient-based methods. We will highlight several important properties of these potential functions, which enable their application even when given uncertain data.