Large Language Model Assisted Human-AI Collaborative Development of Analytical Inverse Kinematics Solvers for Robot Manipulators

Department of Mechanical and Aerospace Engineering, The Ohio State University, Columbus, OH 43210, USA

Mechanism and Machine Theory, Vol. 222, 106392, 2026

Flowchart of the AI Agent-assisted IK solver development process — **Figure 1:** Flowchart describing the AI Agent-assisted development process for IK solvers. The human expert supplies DH parameters, validation strategy, and a solution strategy; the LLM coding agent generates the symbolic FK, decouples the problem, calls a library of helper solvers, and iterates until the numerical validation passes.

Flowchart for AI-assisted helper function development — **Figure 2:** AI Agent-assisted helper function development flowchart. A refined user prompt plus a system prompt drive code generation and testing; the agent iteratively refines code until every test case passes or a maximum iteration count is reached.

**Figure 3:** A general 6R robot with spherical wrist architecture (a₄=a₅=d₅=0). The last three joint axes intersect at the wrist center *p_w*, enabling kinematic decoupling of position and orientation.

**Figure 4:** Illustration of a 6R robot with parallel joint architecture (α₂=α₃=0). Joints 2, 3, 4 have parallel axes, which reduces the IK to a bilinear system for joints 1 and 6 followed by a planar 3R subproblem.

Abstract

This paper presents a large language model (LLM) assisted process for developing analytical closed-form inverse kinematics (IK) solvers for robot manipulators. The collaborative workflow enables human experts to supervise AI agents through carefully designed prompts, while AI handles all coding, symbolic manipulation, and testing. This division of labor leverages each party’s strengths: human intuition for problem decomposition and strategic guidance versus AI capability for systematic execution of labor-intensive tasks. The methodology comprises two key components: (1) a library of robust helper functions for common trigonometric equation systems, and (2) structured prompts that direct AI agents through derivation, code generation, and validation. Refined prompts significantly reduce iterative exchanges. We demonstrate the methodology on two major 6R robot architectures—spherical wrists and parallel joints—representing over 90% of industrial manipulators. The resulting solvers achieve 100% success rates across 842 industrial robots and 1000 random configurations, with working code produced in minutes rather than weeks. This work establishes a new paradigm where human expertise guides AI execution, significantly reducing development time while maintaining mathematical rigor.

Presentation Video

Results

Two kinds of tests were conducted to validate the solvers: (1) real-robot validation using industrial robot models from the RobotKinematicsCatalogue database, and (2) stress testing with selected degenerate/edge cases of DHM parameters as well as randomly generated DHM parameters. All solvers and test codes were implemented in Python and executed on a desktop with an Intel i7-10700KF CPU @ 3.80 GHz and 32 GB RAM.

Table 3 — 6R Spherical Wrist Solver Validation Results
Test Type	# Robots	Tests / Robot	Success Rate	Avg. Time	Max Error
Real Robots	723	10	100%	1.22 ms	2.19×10⁻⁹
Random Robots	1000	20	100%	1.17 ms	2.68×10⁻¹¹

Table 4 — 6R Parallel Joint Solver Validation Results
Test Type	# Robots	Tests / Robot	Success Rate	Avg. Time	Max Error
Real Robots	119	10	100%	1.79 ms	3.45×10⁻⁹
Random Robots	100	10	100%	1.12 ms	1.82×10⁻⁹

Across 842 industrial robots and 1000 randomly generated configurations, both solvers achieve a 100% success rate with average solve times in the 1.1–1.8 ms range and maximum position errors on the order of 10⁻⁹ m or lower—close to the limits of double-precision floating-point arithmetic. No iterative refinement or convergence criteria are needed, confirming the analytical nature and numerical stability of the derived solvers.

Generated Scripts & Data

Helper trigonometric equation solvers (CAS-derived, stress-tested): haijunsu-osu/kinematics_eq_solvers
Spherical wrist 6R solver, prompts, and benchmark scripts: haijunsu-osu/llm_ik_6r_wrist
Parallel-joint 6R solver, prompts, and benchmark scripts: haijunsu-osu/ik_6r_parallel
Robot kinematic data used for validation: SaltworkerMLU/RobotKinematicsCatalogue

BibTeX

@article{Su2026-LLM-IK,
  title   = {Large language model assisted human-AI collaborative development of analytical inverse kinematics solvers for robot manipulators},
  author  = {Su, Hai-Jun},
  journal = {Mechanism and Machine Theory},
  volume  = {222},
  pages   = {106392},
  year    = {2026},
  issn    = {0094-114X},
  doi     = {10.1016/j.mechmachtheory.2026.106392},
  url     = {https://doi.org/10.1016/j.mechmachtheory.2026.106392}
}