Robotics

Helper page for the Peter Corke: Introduction to robotics MOOC.

L3.10 2-axis representation

Check understanding: The rotation matrix

 0.9363 −0.2896  0.1987
 0.3130  0.9447 −0.0978
−0.1593  0.1538  0.9752

is equivalent to the 2-vector representation:

• A=(−1.8833,6.1427,1.0000),O=(1.0000,−0.4925,4.9085)
• A=(1.0000,−0.4925,4.9085),O=(2.9914,1.0000,−0.5091)
• A=(1.0000,−0.4925,4.9085),O=(−1.8833,6.1427,1.0000) (CORRECT)
• A=(−1.8833,6.1427,1.0000),O=(2.9914,1.0000,−0.5091)

Solution:

o=[-1.8833, 6.1427, 1.0000];     %Orientation vector
a=[1.0000, -0.4925, 4.9085];     %Approach vector
R=oa2r(o,a)    %To create rotation matrix R from o and a vectors

R =

 0.9363         -0.2896         0.1987
 0.3130          0.9447        -0.0978
-0.1593         0.1538         0.9752
 
n=cross(o,a)     %To calculate normal vector n
n =
30.6439       10.2442       -5.2152

r=[n' o' a']     %To create rotation matrix r with columns of n, o, a vectors

# Wrong, n, o and a are unit vectors: 

r=[unit(n') unit(o') unit(a')]     %To create rotation matrix r with columns of n, o, a vectors

tr2rpy(R)     %To calculate roll, pitch and yaw angles from rotation matrix R
tr2rpy(r)     %To calculate roll, pitch and yaw angles from rotation matrix r

Can you please explain:

1. How can matrices R=oa2r(o,a) and r=[n' o' a'] proved to be equivalent? 2. Why is a difference appearing in the yaw angle calculated from matrix R and from matrix r?