1

2

Rally Car Frames

3

4

End Effector: Two-Fingered Hand

q1

q2

5

TerminatorBot Crawling

6

7

Rotation Matrices

• Around a unit axis is simple:

• Around an arbitrary axis is more complex:

R(q,u) =

u must be a unit vector!!! (If not magnitude of 1, then normalize)

8

Rotation Quaternions

• Quaternions are multi-dimensional

complex numbers

q = a + bi + cj + dk

• Used all the time in computer graphics and

video games

• Rotation Quaternions are special:

q = cos(q/2) + sin(q/2) (uxi + uyj + uzk)

u must be a unit vector!!!

Rotation Quaternions are unit Quaternions!

9

10

Camera Calibration

11

Finding Extrinsic and Intrinsic

Parameters

12

Use a “Grid” to Find Transform