linearSubproblemSltns 1.0.3

This is a new tool for multi-joint robotic arm calculations developed at RPI.

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

Subproblem	Time With Inputs	Time Without Inputs
Sp1	78716.896 ns	73754.058 ns
Sp2	325238.43 ns	318135.293 ns
Sp2E	409206.773 ns	400298.479 ns
Sp3	127781.537 ns	122444.399 ns
Sp4	104747.862 ns	99615.851 ns
Sp5	1353110.805 ns	1341531.159 ns
Sp6	614233.523 ns	596708.225 ns