Adaptive gradient descent algorithm for inverse kinematics of a 3-DOF robotic arm

Source abstract

The mounting demand for automation in manufacturing and critical infrastructure underscores the necessity for efficient algorithms capable of accurately determining end-effector pose in robotic systems. This study focuses on the implementation and evaluation of a computationally lightweight gradient descent method for inverse kinematics. Analysis established that the algorithm’s stability and efficiency are critically dependent on the total link length, which is an inherent limitation of the standard method. To overcome this issue, a geometry-aware adaptive procedure for selecting the optimal step size was formulated based on this total length, ensuring stable convergence without per-iteration computational overhead. Numerical experiments across over 48,000 target points confirmed that the resulting adaptive strategy achieves robust success rates (up to 93.6% of reachable target points) and minimal iteration counts while maintaining a high positional accuracy (errors below 10^-4 m) for all tested geometries. These findings substantiate the robustness and efficiency of the proposed adaptive method, establishing its value as an essential hardware-friendly enhancement for real-time robotic control systems design and analysis.