Robotics 501: Mathematics for Robotics

ROB 501: Mathematics for Robotics, is a graduate-level course at the University of Michigan that introduces applied mathematics for robotics engineers.

Topics include vector spaces, orthogonal bases, projection theorem, least squares, matrix factorizations, Kalman filter and underlying probabilistic concepts, norms, convergent sequences, contraction mappings, Newton Raphson algorithm, local vs global convergence in nonlinear optimization, convexity, linear and quadratic programs.

This offering of the course is from Fall 2018.

Prerequisites

It is assumed that students know basic matrix algebra, such as how to multiply and invert matrices, what is the rank of a matrix, and how to compute eigenvectors; know how to compute means and variances given a density of a continuous random variable, and conditional probability and how to compute it; know vector calculus and will review how to compute gradients of functions and what is the method of Lagrange multipliers; simple properties of complex numbers; and how to use MATLAB, including plotting, various types of multiplication, such as * vs .* (star vs dot star), writing a for loop, or finding help.

Lecture Videos, Textbook & Notes

All lecture videos are available on YouTube:
ROB 501 Fall 2018 videos

Also, the textbook, lecture notes and handouts are available.

Recitatioins

Recitation questions and answers are both available.

Course Plan

Lecture	Topic	YouTube	Assignments Due
1	Intro & Proofs	Video
2	Induction, Fundamental Theorem, & Contradiction	Video
3	Abstract Linear Algebra	Video
4	Subspaces & Linear Independence	Video	Homework 1
5	Basis Vectors & Dimension	Video
6	Linear Operators & Eigenvalues	Video	Homework 2
7	Similar Matrices & Norms	Video
8	Inner Product Spaces	Video	Homework 3
9	Projection Theorem & Gram-Schmidt	Video
10	Normal Equations & Least Squares	Video	Homework 4
11	Symmetric & Orthogonal Matrices	Video
12	Positive Semi-Definite Matrices & Schur Complement Theorem	Video	Homework 5
13	Recursive Least Squares & Kalman Filter	Video
14	Least Squares & Probability	Video
15	Best Linear Unbiased Estimator	Video	Homework 6
16	QR Factorization	Video	Exam 1
17	Modified Gram-Schmidt & Minimum Variance Estimator	Video
18	Probability Space & Random Variables	Video
19	Gaussian Random Vectors	Video	Homework 7
20	Real Analysis & Normed Spaces	Video
21	Real Analysis & Interior of a Set	Video	Homework 8
22	Newton-Raphson Algorithm	Video
23	Cauchy Sequences	Video	Homework 9
24	Continuous Functions	Video
25	Weierstrass Theorem	Video
26	Final Class & Linear Programming	Video	Homework 10 & Exam 2

A more detailed course plan is available.

Credits

• Jessy Grizzle, Director, Michigan Robotics
• Nils Smit-Anseeuw

License

All code is licensed under the GNU General Public License v3.0.

All other content, including textbooks, homeworks, and video, is licensed under the Creative Commons Attribution-NonCommericial 4.0 (CC BY-NC 4.0).

For more

• University of Michigan Robotics
• Michigan Robotics Twitter
• Michigan Robotics Instagram