Variable Step Sizes for Iterative Jacobian-Based Inverse Kinematics of Robotic Manipulators

Abstract

This study evaluates the impact of step size selection on Jacobian-based inverse kinematics (IK) for robotic manipulators. Although traditional constant step size approaches offer simplicity, they often exhibit limitations in convergence speed and performance. To address these challenges, we propose and evaluate novel variable step size strategies. Our work explores three approaches: gradient-based dynamic selection, cyclic alternation, and random sampling techniques. We conducted extensive experiments on various manipulator kinematic chains and IK algorithms to demonstrate the benefits of these approaches. In particular, variable step sizes randomly derived from a normal distribution consistently improve solve rates across all evaluated cases compared to constant step sizes. Incorporating random restarts further enhances performance, effectively mitigating the effect of local minima. Our results suggest that variable step size strategies can improve the performance of Jacobian-based IK methods for robotic manipulators and have potential applications in other nonlinear optimization problems.

Keywords

• Robotic manipulators
• inverse kinematics
• variable step size
• random sampling
• nonlinear optimization
• iterative methods