Solving Inverse Kinematics with Large Language Models

This repository is for generating and testing the inverse kinematics solutions generated by large language models (LLMs) for kinematic chains with a single "end effector".

For viewing results, the key areas are under the Interactions, Solutions, and Results folders.

• Each of these folders contains information related to each LLM for every chain and mode attempted in the form of LOWER-UPPER-SOLVING-MODE.
  • LOWER - The lower joint of the chain being solved which is zero-indexed.
  • UPPER - The upper joint of the chain being solved which is zero-indexed.
  • SOLVING - Either Position or Transform indicating what the solution was being tasked with solving for.
  • MODE - Either Normal, Extend, Dyanmic, Cumulative, or Transfer indicating what the solving mode was.
• Interactions - Contains the raw messages to and from the LLMs.
• Solutions - Contains final extracted Python code IK solutions.
• Results - The results as tested against the testing data.

Quick Access

Here are some helpful quick-access links to view key findings from the results.

• Google Gemini 2.5 Pro Six Degrees-of-Freedom Position and Orientation Results achieved with the Extending Approach
  • Initial prompt given to Google Gemini 2.5 Pro.
    • Note that the existing solution provided in the prompt does not have in-line comments. This is due to how code is extracted and loaded dynamically in this implementation, and thus added into extending, dynamic, cumulative, and transfer prompts.
    • However, it can be easily seen that this solution itself, achieved via OpenAI's o3-mini using the direct approach, contains full comments.
  • Final response with the complete solution received by Google Gemini 2.5 Pro.

Features

• Can load URDF files.
• Supports both Chat-based and API-based LLMs.
• Can solve in five modes.
  • Normal: Directly attempts to solve the chain.
  • Extend: Tries to extend an existing solution for a chain one link smaller than the current.
  • Dynamic: Tries to base the solution off of already solved sub-chains.
  • Cumulative: Like dynamic but passes all possible solved-sub-chains.
  • Transfer: Tries to base the solution for a position and orientation solver off of a position only solver.
• Model-inheriting where more expensive models can extend or dynamically build from the solutions of cheaper models.

Setup

1. Recommended: Create a virtual environment python3 -m venv .venv.
   • Activate the virtual environment.
     • Windows: .venv\Scripts\activate.bat.
     • Linux: .venv\Scripts\activate.ps1.
     • Mac: source .venv/bin/activate.
2. Install all requirements with pip install -r requirements.txt.
3. If doing your own experiments, it is recommended to delete all folders in this project, except for the Robots or Models, and Providers folders if you wish to use some of the same robots or LLMs as we have.
4. In the root directory, ensure there is a folder named Robots, and place the URDF files of the robots you wish to use inside.
5. In the root directory, ensure there is a folder named Models, and place all your LLM specification files you wish to use inside as detailed in the Models section.
6. Optional: These steps only apply if you wish to use OpenAI API compatible APIs.
   • In the root directory, ensure there is a folder named Providers, and place your OpenAI API compatible specification files you wish to use inside as detailed in the Providers section.
   • In the root directory, ensure there is a folder named Keys, and make .txt files named the same as the OpenAI API compatible specification files in the Providers folder and paste the appropriate API keys into each.
7. Run llm_ik with the parameters outlined in the Usage section.
8. View the results in the Results folder in the root directory.

Models

• Models are specified in .txt files in the Models folder in the root directory.
• The name of the file is what will appear in results.
• Each line of the file represents information about the file, with only the first line being needed for non-API models.

Format

1. If the model is a reasoning model or not, specified by either True or False and defaulting to False. If not a reasoning model, the prompts will include a statement to "think step by step and show all your work" to elicit some benefits from chain-of-thought thinking. Otherwise, this is omitted, as reasoning already do a process like this internally.
2. The name of the "provider" of the model being the name of the OpenAI API compatible specification file (without the .txt extension) to use from the Providers folder. See the Providers section for how to configure these files themselves.
3. The input cost per token of this model. If unspecified, this model cannot be inherited by other API models.
4. The output cost per token of this model. If unspecified, this model cannot be inherited by other API models.
5. If this model supports function calling via the OpenAI API, specified by either True or False and defaulting to whether its provider supports functions. This is useful as some providers, such as OpenRouter, supports function calling, but, not all models they provide do as well, thus giving you an option to perform a per-model override. However, if the provider does not support function calls and this is set to True, the provider's configuration will override this to False, so this can only be used to disable function calling and not enable it. If this is False, additional details are added to the prompt so models can still call methods, just not through the OpenAI API functions and instead the regular message response is parsed.
6. The API name to use for this model. If omitted, the file name (without the .txt extension) will be used.

Providers

• OpenAI API compatible providers are specified in .txt files in the Providers folder in the root directory.

Format

1. The API endpoint of the provider.
2. If this model supports function calling via the OpenAI API, specified by either True or False and defaulting to False. If the provider supports methods but a model does not as explained in the Models section, this will be overwritten to False for that model only.

Usage

Arguments

• -r or --robots - The names of the robots. Defaults to None which will load all robot URDF files in the Robots folder.
• -m or --max - The maximum chain length to run. Defaults to 0 which means there is no limit.
• -o or --orientation - If we want to solve for orientation in addition to position. Defaults to True.
• -t or --types - The highest solving type to run. Defaults to Transfer, meaning all are run.
• -f or --feedbacks - The max number of times to give feedback. Defaults to 5.
• -e or --examples - The number of examples to give with feedbacks. Defaults to 10.
• -a or --training - The number of training samples. Defaults to 1000.
• -v or --evaluating - The number of evaluating samples. Defaults to 1000.
• -s or --seed - The samples generation seed. Defaults to 42.
• -d or --distance - The acceptable distance error. Defaults to 0.01 m.
• -n or --angle - The acceptable angle error. Defaults to 1 degree.
• -c or --cwd - The working directory. Defaults to None which gets the current working directory.
• -l or --logging - The logging level. Defaults to INFO.
• -w or --wait - How long to wait between API calls. Defaults to 1 second.
• -u or --run - Flag - Enable API running .
• -b or --bypass - Flag - Bypass the confirmation for API running.

Manual Chat

• If manually chatting with an LLM, after running, look in the Interactions folder until you find the robot, model, and solving you are looking for.
• Copy the last X-Prompt.txt, X-Feedback.txt, X-Forward.txt, or X-Test.txt into your chat interface and wait for a response where X is a number.
  • Copy the entire response, not just the code. The program will look for a Python code block to extract from the response, so if you manually extract this code, the program will not recognize it.
• Once a response was received, make a text file named X-Response.txt where X is the next number for the chat history and run the program again. Repeat the previous step and this until a file named X-Done.txt appears where X is a number.

Additional Comparison Tests

For running the additional comparisons tests from additional.py, you will need to install ur_ikfast and pytracik onto your systems. ur_ikfast is only officially supported on Linux while pytracik can run on both Linux and Windows.

1. Run sudo apt install libblas-dev liblapack-dev libboost-all-dev libeigen3-dev liborocos-kdl-dev libnlopt-dev libnlopt-cxx-dev to install required dependencies for both ur_ikfast and pytracik.
2. Clone each repository into your current directory for this project:
   • git clone https://github.com/cambel/ur_ikfast.git
   • git clone https://github.com/chenhaox/pytracik.git
3. Run the required setup for each. The below commands assume you are executing them from the root directory of this project. Note that the core requirements.txt of this project already contains all Python dependencies for each.
   • pip install -e ur_ikfast
   • cd pytracik followed by python3 pytracik/setup_linux.py install