Python ( robot module): conversion hom. transformation (rotation) matrix and Euler or RPY angles

I'm using in the robotics toolbox (c.q. robot module) in Python http://code.google.com/p/robotics-toolbox-python/) and I'm utterly confused how to interpret the following conversion results (I've done things like this in the p开发者_Python百科ast could always work them out...).

A simple phi=PI/10 rotation about the x-axes produces the following (3x3) rotation matrix:

R = 
 [ 1.          0.          0.        ]
 [ 0.          0.99609879 -0.08824514]   
 [-0.          0.08824514  0.99609879]]

( where 0.996..=cos(phi) and 0.0882..=sin(phi) )

with corresponding (4x4) homogeneous transformation matrix:

T = | R 0 | =
    | 0 1 |

[[ 1.          0.          0.          0.        ]
 [ 0.          0.99609879 -0.08824514  0.        ]
 [-0.          0.08824514  0.99609879  0.        ]
 [ 0.          0.          0.          1.        ]]

Conversion of T into angle representation produces the following:

RPY (Roll, pitch, yaw) angles (around z, y and x axes, respectively, ... I presume):

print robot.tr2rpy(T)

[[ 0.          0.          0.08836007]]

Problem: How can the x-rotation be the last element (rather than the first)....?

Further:

Euler angles (around x, y and z axes, respectively, ... I presume):

print robot.tr2eul(T)

[[-1.57079633  0.08836007  1.57079633]]

( = [[ -PI/4, sin(phi), PI/4 ]] ))

Problem: My interpretation (sequential rotation around x,y,z axes) tells me the result is dead wrong...?

What am I missing? Thanks.

-- Henk

---

Solved:

With successive angles, a[0],a[1],a[2],

1) For Euler angles these are successive rotations around Z-Y-Z axes;

2) For RPY angles these are successive Y(aw)-P(itch)-R(roll) rotations (i.e around Z-Y-X axes).