Enhancing Gradient-Based Inverse Kinematics with Dynamic Step Sizes

Inverse kinematics (IK) plays an essential role in the field of robotics, enabling robots to determine the joint configurations required to achieve desired end-effector poses. Gradient-based numerical methods are commonly used for IK problem-solving, where the step size influences the convergence success and solving time. In this work, we propose a novel approach that employs dynamic step sizes based on the relative gradient norm at each iteration, aiming to improve solve rates and overall performance. We evaluated the proposed method on six different kinematic chains of robotic manipulators and compared it with conventional fixed step size approaches. Experimental results demonstrate that the use of dynamic step sizes, specifically the Gradient Scaling method, achieves significant improvements in solve rates, surpassing 150% improvement in various kinematic chains. Moreover, we enhance the solve rate further by incorporating a random restart approach to escape local minima. The proposed approach presents a viable alternative to conventional gradient-based IK methods, automating the step size selection and offering improved efficiency and robustness in solving complex robotic tasks.