## 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.