Fundamentals of Mathematics for Robotics (CMU 16-811)

July 2020

Abstract: 

To brush up on the mathematics involved in Robotics I completed CMU's 16-811 course. This covered a vast range of topics and had homework assignments which ranged from handwritten problems sets to proofs to programming assignments in MATLAB and Python. The course covered the following topics:

1. Matrix Decomposition (LDU, SVD)

2. Interpolation Methods 

3. Root Finding Methods (Newton, Muller)

4. Differential Equations 

5. Gradient Descent 

6. Calculus of Variations and Lagrangian Mechanics

7. Convex Hull Algorithms 

8. Shortest Path in an Environment of 2-D Polynomials (Dijkstra's Algorithm)

Results: 

Most of the solutions for problem sets did not have a visual component to them, but the solutions can be found on my GITHUB. However, I'll include photos of a convex hull algorithm at work using the 'Gift Wrapping' Algorithm as well as a 1D robot finding the best path in a world of polynomial obstacles.