Summary:

• This is a research project led by Alexander Elias and Dr. John Wen at RPI.
• Summation of research: https://arxiv.org/pdf/2211.05737.pdf
• Included here is the Python version of the MATLAB-based canonical subproblems for inverse kinematics on robots.
• Additional MATLAB, C++, Rust, and Python files are located at https://github.com/rpiRobotics/linear-subproblem-solutions/.
• See the project on PyPi: https://pypi.org/project/linearsubproblemsltns/

Python Branch Guide:

Dependencies:

• NumPy: https://numpy.org/install/
• SciPy: https://scipy.org/install/
• Python (version compatible w/ installed NumPy)

To Use Example Code:

• Clone the above repo
• To see timing information and a simple demo, run each sp#.py file
• Otherwise, just include the pip module in your applications as needed using pip install linearSubproblemSltns

Advice:

• NumPy vs MATLAB can be confusing at first, see this article for some clarity.
• See the below note on precision/formatting.
• NumPy makes it extremely easy to export/import entire matrices as csv/excel files. Make use of this if you can.

Precision and Formatting

• If comparing values in Python to MATLAB output, be careful with how inputs are entered.
• Also, note that values printed in the test files are not the exact values used in the calculations.
• Vectors in NumPy are of form [n n n] (0 row, 3 col). You cannot have a vector of 3 col, 0 row.
  • Note, the MATLAB version of this code uses vectors of 3 col, 0 row, which is why some calculations look slightly different.

In Python:

p1 = [0.85421456 0.9145417 0.28164908]
p2 = [0.71384302 0.84785577 0.40390217]
k1 = [0.53432959 0.73260445 0.42164275]
k2 = [0.89871158 0.33336884 0.2849258 ]

In MATLAB:

p1 = [0.85421456; 0.9145417; 0.28164908]
p2 = [0.71384302; 0.84785577; 0.40390217]
k1 = [0.53432959; 0.73260445; 0.42164275]
k2 = [0.89871158; 0.33336884; 0.2849258 ]

Timing