Collection of ROB 501 Lecture Notes
J.W. Grizzle
Fall 2015
1
Page = 2
Rob 501 Fall 2014
Lecture 01
Typeset by: Jimmy Amin
Proofread by: Ross Hartley
Introduction to Mathematical Arguments
Notation:
N = cfw_1, 2, 3, Natural numbers or counting numbers
Z =

Rob 501 - Mathematics for Robotics
HW #9
Prof. Grizzle
Due Dec. 1, 2016
3PM via Gradescope
Remarks:
If you have been hearing about quadratic programs (QPs), well, Problem 2 is a simple case of a QP.
You also solved one in HW 7 and in HW 1 (go back and loo

HW # 01 Solutions
Problem 1: Good notation is everything. We let aij = [AB]ij . By the definition of matrix multiplication,
[AB]ij =
m
X
aik bkj , 1 i n, 1 j p
k=1
(a) To show: [AB]ij = Ab1 |Ab2 | . . . |Abp ij for 1 i n, 1 j p.
For a column vector, we le

HW # 05 Solutions
Problem 1:
(a) < x, y >= x> y =
n
X
xi yi .
i=1
=
(i) < y, x > = y > x
n
X
yi x
i =
i=1
n
X
yi xi
i=1
=< x, y > .
(ii) < 1 x1 + 2 x2 , y > = (1 x1 + 2 x2 )> y
= 1 x>
+ 2 x>
1y
2y
= 1 < x1 , y > +2 < x2 , y > .
(iii) < x, x >=
n
X
xi x
i

Rob 501 - Mathematics for Robotics
HW #8
Prof. Grizzle
Due Nov. 17, 2016
3PM via Gradescope
Remarks: Start Problem 4 early enough that you can seek MATLAB help in time! Problems 1 through 3
use the minimum variance estimator (MVE); do all the calculations

Rob 501 - Mathematics for Robotics
HW #5
Prof. Grizzle
Due Oct. 13, 2016
3PM via Gradescope
Remarks: Problems 1 through 4 are really quick. Problems 5 and 6 involve numerical computations. We
are getting to a point in the course where we know enough to so

Rob 501 - Mathematics for Robotics
HW #7
Prof. Grizzle
Due Nov. 10, 2016
3PM via Gradescope
Remarks: Problems 1 through 5 involve calculations. Problem 5 is very important. Please spend extra time
on it as it is very helpful for understanding the Kalman F

Rob 501 - Mathematics for Robotics
HW #1
Prof. Grizzle
Due 3 PM on Thur., Sept 15, 2016
Where to turn in will be announced later.
Remarks: The initial lectures in Rob 501 are not required for working this HW set. These problems should
be doable using stan

Rob 501 - Mathematics for Robotics
HW #10
Prof. Grizzle
Due Dec 8, 2016
3PM via Gradescope
Remarks:
Final Exam is an in-class exam, similar to your midterm. It will be held on the date and time of our
nal as set by the registrar of the university, that is

Rob 501 - Mathematics for Robotics
HW #2
Prof. Grizzle
Due Sept. 22, 2016
3PM via Gradescope
Preliminaries:
Review logic symbols here: http:/en.wikipedia.org/wiki/List_of_logic_symbols
Read about truth tables here:
http:/sites.millersville.edu/bikenaga/ma

Rob 501 - Mathematics for Robotics
HW #3
Prof. Grizzle
Due Sept. 29, 2016
3PM via Gradescope
Preliminaries: Read Chapter 4 of Nagy.
1. Nagy, Page 117, Prob. 4.1.5 (denote the eld by
2. Nagy, Page 121, Prob. 4.2.1 (the eld is
F ).
R)
3. Nagy, Page 121, Pro