# EE/BIOE C125 Introduction to Robotics

## Homework and Lab Assignments

Problem Set 1

Lab 1

Problem Set 2

Problem Set 3

Problem Set 4

Problem Set 5

Problem Set 6

Problem Set 7

Lab 2

Lab 3

Problem Set 8 (complete)
## Sample Final Exam Problems

Sample Problems

Sample Problem Solutions
## Matlab Code for Lab 3

corio.m

coriotd.m

mass.m

potfor.m

robotsim.m

simurobot.m
## Solutions

Problem Set 1 Solution (corrected -- there was a small sign error in the last question in previous posting)

Problem Set 2 Solution

Problem Set 3 Solution

Midterm 1 Solution

Problem Set 4 Solution

Problem Set 5 Solution

Problem Set 6 Solution

Problem Set 7 Solution

Problem Set 8 Solution
## Some Fun Robot Links

Here are just a few links to interesting robots. If you find more, especially pages with links to many robots rather than just one project, please let me know. -FT

Cool Robot of the Week. This site is old (last updated 2003), but a lot of the robot links are still relevant and still cool.

Some links to dancing Sony QRIO ("queue-ree-oh") robots, provided by Cole Ratias:

http://www.sony.net/SonyInfo/QRIO

http://weblogs.asp.net/christoc/archive/2004/02/04/67627.aspx

http://www.plyojump.com/qrio.html

Some links to bipedal walking robots, provided by Bobby Gregg:

http://www.eecs.umich.edu/~grizzle/papers/RABBITExperiments.html

http://www-personal.engin.umich.edu/~shc/robots.html

## Muddy Card Answers

There was a question about the second part of the proof that the
exponential map e^(omega_hat*theta) is a member of SO(3) (beginning of
9/6 lecture; top of p. 29 in MLS). In this part we prove that the
resulting matrix R has determinant +1. Don't worry if you don't
understand all the details of the proof or aren't familiar with the
continuity of e^X etc. Some of the details are beyond the scope of
this class, and you won't be called upon to do any similar proofs.
But here's a little more detail anyway.

A linear algebraic identity says that the determinant of the product
is equal to the product of determinants. Since we know that
transpose(R)*R = I, the square of the determinant of R must equal the
determinant of I, which is 1. So det(R) must = +/-1. Now, both the
exponential map e^X and the determinant of a matrix are continuous
functions (take the book's word for it). Consequently, if det(R) is
+1 for one value of omega*theta, it must be +1 for all values because
there's no way a continuous function could jump from +1 to -1, and we
know those are the only possible values of det(R). But when theta=0,
we know that e^(0) = I, so det(e^(0)) = +1. So det(R) must be +1 for
any omega and theta.