GA_MultiRobot

Calibrate Multi-Robot with Geometric Algebra (GA) and Geometric Calculus (GC). More specifically the $\mathbf{AXB=YCZ}$ problem.

Problem Formulation

As an updated version of hand-eye calibration, $\mathbf{AXB=YCZ}$ aims at solving the hand-eye $\mathbf{X}$, base-base $\mathbf{Y}$, and hand-tool $\mathbf{Z}$ given two forward kinematics $\mathbf{A}$ and $\mathbf{C}$, and one measurement $\mathbf{B}$

Folder Structure

• utils: fundamental functions such as basic GA calculation, robot kinematics, and GA robot kinematics.
• project_utils: the DualRobotCalibrator solver, which includes all the solver functions from the article and the reproduced version of other researchers' algorithms.
• Benchmark: the benchmark code for the proposed method and other algorithms.
• Experiments: scripts related to experimental pose generation, raw data (point cloud) processing, and final benchmarking.
• images: This folder contains all the saved results.
• test: some test scripts.

Each folder has its own README.md for detailed illustration.

Installation:

You need to install Julia and Matlab ahead to run this package. We recommend julia>1.9.2 and MATLAB>2022b for best performance and visualization.

1. You need to enter the folder in your terminal by cd GA_MultiRobot (or whatever you name the folder)
2. dir (windows) or ls (linux), and you should see all folder names and Project.toml, Manifest.toml
3. Activate and setup the project environment for julia

julia> ]
(@v1.8) pkg> activate .
(GA_MultiRobot) pkg> instantiate      # This may take long depending on your network condition

Demo

Run the demo with the following command:

julia --project=. -O3 demo.jl

It may take a while for plotting, which is a known issue for Julia and will be fixed in v1.9.x.

The result will be saved at ./Assets/demo.svg. Noted that the result marked by "GA" is the unpublished version of the proposed method, which is based on Projective Geometric Algebra (PGA). The published version is based on $\mathbb{G}^3$, which is (definitely) more efficient and (probably) more accurate.

Highlights

High accuracy

Result in a measurement experiment. The proposed GA-based method reached identical optimal accuracy as Wang's (SOTA) and Wu's method, and higher accuracy than Fu's and Ma's method.

High Efficiency

Execution Time	Flops

The proposed method solves the problem ~4.5x faster with ~3.5x less computational load than SOTA.

Benchmark

Read Benchmark.md for detailed benchmark.

Related Methods

• Wang's method (previous SOTA): Simultaneous calibration of multicoordinates for a dual-robot system by solving the AXB = YCZ problem
• Wu's method (previous SOTA): Simultaneous Hand-Eye, Tool-Flange, and Robot-Robot Calibration for Comanipulation by Solving the AXB = YCZ Problem
• Fu's Method (A method based on Dual-quaternion): A Dual Quaternion-Based Approach for Coordinate Calibration of Dual Robots in Collaborative Motion
• Ma's Method (temporal info free): Probabilistic approaches to the AXB= YCZ calibration problem in multi-robot systems
• Bayro's AX=XB Method: Motor algebra for 3D kinematics: the case of the hand-eye calibration

Cite this work

@ARTICLE{10215071,
  author={Sui, Sizhe and Ding, Ye},
  journal={IEEE Transactions on Automation Science and Engineering}, 
  title={Solving the AXB=YCZ Problem for a Dual-Robot System With Geometric Calculus}, 
  year={2023},
  volume={},
  number={},
  pages={1-19},
  doi={10.1109/TASE.2023.3299969}}

An open-sourced version of this article can be found on the Author's Researchgate.