Lingua Mechanica

Lingua Mechanica solves the inverse kinematics problem by training a Reinforcement Learning model from a URDF description of a robotic arm. It is able to solve thousands of Inverse Kinematics in parallel or create swarms of thousands of initial poses to solve a single inverse kinematics problem.

Specifically, the inverse kinematics solver has the following features:

• It translates the robot URDF into its exponential form, as a differentiable network that outputs forward kinematics.
• The robot arm kinematic chain is part of the model. An advantage is that the optimizer has access to the robot's jacobian through backpropagation.
• The SE(3) representation are Implicit Dual Quaternions (Neil T. Dantam), a fast and singularity-free compact Dual-Quaternion representation.
• The Reinforcement Learning reward is the cumulative geodesic on SE(3). The geodesic can be weighted if desired ( note that for most collaborative arms the T(3) geodesic, in meters, is not far from π ). The geodesic loss is formally defined as the (weighted) sum of the vee se(3) target pose with respect to the current pose. The all computations (forward kinematics, exponentiations, logarithms, etc) are differentiable and integrated into PyTorch's autograd.
• The actor training is two-folded:
  • The geodesic loss is used directly to train the actor.
  • There is a Q-Learning pair network.

User's Manual

Setup

Currently only Ubuntu is supported, but PRs to support other Linux distributions are welcomed but active efforts will be put on dockerizing the solution.

There are dependencies such as pyenv and several other Ubuntu dependencies that are required. This script installs them:

source ./bin/install-deps.sh

The next step is to set up the environment by running run:

poetry install
poetry shell

And finally, with the activated poetry shell, install torch and other torch-related dependencies running:

source ./bin/install-torch.sh

To run unit tests:

make test

Usage

To train inverse kinematics use:

python -m linguamechanica.train --urdf URDF_PATH

To train inverse kinematics from checkpoint use:

python -m linguamechanica.train --urdf URDF_PATH --checkpoint CHECKPOINT_ID

To run inference use:

python -m linguamechanica.inference --checkpoint 927000 --target_thetas 0.4,-0.6,0.3,-0.5,0.5,0.2 --iterations 100 --samples 10000

To visually test inverse kinematics from checkpoint use:

python -m linguamechanica.test --urdf URDF_PATH --checkpoint CHECKPOINT_ID

Example to visually test inverse kinematics using target pose:

python -m linguamechanica.test --checkpoint 927000 --target_pose 1.13,-0.935,-0.0869,0.466,-2.67,2.2

Example to visually test inverse kinematics using target thetas:

python -m linguamechanica.test --checkpoint 927000 --target_thetas 0.5,-0.8,0.3,-0.5,0.5,0.6 

Checkpoints

You can find checkpoints in Google Drive, currently only for CR5 robot arm. You need to download the checkpoints and leave them into the checkpoints folder. Then launch any of the command line programs such as:

python -m linguamechanica.test --checkpoint 927000 --target_thetas 0.4,-0.6,0.3,-0.5,0.5,0.2 --iterations 100 --samples 10000

Docker

See the docker documentation to setup a docker. Note that the way Docker is approached for Linugua Mechanica is to set up a docker image with a mapped local home folder. Dockerization of the project is Work In Progress.

ROS

First step is installing dependencies using the ROS Python by running:

source ros/bin/install-python-deps.sh

Then add the following projects in your ROS workspace while adding linguamechanica root folder in PYTHONPATH :

https://github.com/paucarre/lingua_mechanica_kinematics_server
https://github.com/paucarre/lingua_mechanica_kinematics_msgs
https://github.com/paucarre/lingua_mechanica_kinematics_plugin

The next step is to launch the IK server by launching:

rosrun lingua_mechanica_kinematics_server lingua_mechanica_kinematics_server.py

Finally, add lingua mechanica as kinematics solver by updating your IK node configuration:

YOUR_ROBOT_ARM:
  kinematics_solver: lingua_mechanica_kinematics_plugin/LinguaMechanicaKinematicsPlugin

References

• Robust and efficient forward, differential, and inverse kinematics using dual quaternions. Neil T. Dantam
• A micro Lie theory for state estimation in robotics
• Modern Robotics: Mechanics, Planning, and Control