Exploring LLM-based approaches for wrist-center positioning of an anthropomorphic manipulator: a preliminary comparative study

This paper explores the feasibility of using Large Language Models (LLMs) to solve the wrist-center inverse positioning problem for a 3-degree-of-freedom (DOF) anthropomorphic manipulator sub-problem. The study investigates whether LLMs can perform meaningful spatial and trigonometric reasoning on kinematic equations. Three LLM-based approaches are proposed and evaluated on 50 target positions across the manipulator workspace: (1) zero-shot prompting (LLM-ZS), (2) few-shot in-context learning (LLM-FS) and (3) LLM-Guided Iterative Refinement (LGIR). All methods are benchmarked against four reimplemented traditional solvers—analytical closed-form, Damped Least Squares (DLS), Levenberg–Marquardt and Nelder–Mead—executed on the same hardware under identical conditions. The LGIR method achieves a median position error of 7.44e-05 cm across 50 targets, while traditional numerical solvers achieve near-zero errors (1.12e-15 cm for the analytical method). LLM-based methods incur computation times of several seconds per solution owing to API latency, rendering them unsuitable for real-time control. The results demonstrate that LLMs possess measurable trigonometric reasoning capability but cannot match the precision or speed of established solvers. This study provides the first multi-target comparison of multiple LLM prompting strategies against reimplemented traditional solvers for a robot positioning sub-problem, with all methods evaluated under identical experimental conditions. The findings contribute an empirical baseline for understanding the current limitations and potential of LLMs in kinematic computation tasks.