Here's enough links on the subject to make your head explode:
http://mathworld.wolfram.com/EulerAngles.html
http://mathworld.wolfram.com/EulerParameters.html
http://www.euclideanspace.com/maths/geometry/rotations/euler/
http://mathworld.wolfram.com/RotationMatrix.html
And if you are REALLY sick & twisted, you can try to understand ABB's method of using Quaternions
Don't want this topic to die out... c'mon, people, reveal your deep dark KUKA secrets! 
Well, here's some more from me. It's not UNdocumented, entirely, but it is kind of obscure.
The KRC1 and KRC2 series controllers are kind of split-brained -- they run Windows (95 or XP) for the user interface, but at the same time run VxWorks in parallel to handle the actual robot operations. These two operating systems *think* they are running on separate machines, communicating via a TCP/IP link. What this means for us is that you can Telnet from the Windows side into the VxWorks side. It turns out there are some low-level diagnostic tools available for networked I/O, like Devicenet and Profibus.
In W95 and WXP, the commands to start Telnet are somewhat different.
95: START,RUN, "Telnet 192.0.1.1"
XP: START,RUN, "Telnet95 192.0.1.1"
Once you've Telnetted in, the command prompt looks like this: ->
Remember that, in VxWorks, capitalization matters. So you must capitalize the commands as shown.
For DeviceNet on MFC1 cards, type: dnLookIO or dnShow will show all the nodes currently slaved to the robot, and their I/O size and state. dnWho will scan the DeviceNet network, and any slave device that is correctly wired to the network and has the correct baud rate set will be discovered and displayed.
For later MFC cards, that use the dn2drv driver (check your IOSYS.INI), the same commands work, but have to be typed in differently: exec "dnShow" or exec "dnLookIO" or exec "dnWho". Typing in the quotes is important.
For LPDN cards (2 channels per card), a different driver and a different set of commands is used.
dnsc?Show displays the state of the DN channel. Replace the ? with the number (1-6) of the channel you're trying to check.
dnsc?ShowDevice ?? bout a specific device on the network. Replace ?? with the MAC ID you are looking for.
dnsc?GetNodeInfo ?? retrieves the network specs of the slave at the ?? MAC ID.
dnsc?SetConfig ? ?=1 turns Config Mode on, ?=0 turns Config Mode off. Never used this one myself.
dnsc?SetMacId ?? ?? is supposed to remotely set the MAC ID of devices that don't have hardware settings for it. Changes the device at the first MAC ID to the second MAC ID. I've never used it.
dnsc?SetbaudRate ?? xxx Sets the device at MAC ID ?? to baud rate xxx (125, 250, or 500 kbaud).
dnsc?NetWho will search out and display all slave modules attached to the network (if their baud rate is correct).
Aside from DeviceNet, using iosysShow or exec "iosysShow" will display all the active I/O drivers and their current states.
I don't know if this is documented or not, but I discovered it today.
In "Monitor-Variable-Single", when setting the variable to display - holding down shift while pressing enter to set the current variable sets a watch so that it's value is updated whenever it changes rather than having to constantly check the value yourself. The icon next to "Current value" changes to indicate this.
It is documented, but I'm sure that not everybody knows it...and it's always good as a reminder. So thanks for it!
Yes! I should have thought of that one myself. 
One indicator is that, under the NAME bar, there's a little icon of two curving arrows chasing each other in a circle. By default, this icon has a little slash through it, but if/when you use the Shift-Enter trick on the name, you should see the little slash vanish. That can help if you can't recall if you hit Shift-Enter or not.
Another trick in Monitor-Variable-Single, in the New Value bar you can type in a new variable value, or you can type in another variable of the same type (there's a bit of flexibility here: you can set an E6POS variable to a FRAME variable, for instance, but generally the two variables need to be of the same declaration type). For simple single-element variables, you can even type minor basic math equations into the New Value bar, like 2*4, or stuff like that.
Now, if you want to really play games with variable monitoring, Monitor>Variable>Overview>Setup is where it's at.
Because we're on it and to add another trick with the single variable window, if you type the ampersand symbol (&) followed by an integer representing an error code under the "Name" combobox, you will have a small description of it in the "current value" window. In fact, you will have the internal text string. For example, if you type:
&118
You will see:
Heat sink temperature %1.
$MOT_TEMP[] is an array variable that displays the current temperature of each motor (based on an internal sensor) in degrees Kelvin. $MOT_TEMP[1] is axis 1, $MOT_TEMP[7] is axis 7, etc, up to 12 axes for one controller. A disconnected motor may not read 0, though, and not all non-KUKA add-on servo motors have these temp sensors built in.
The sensors appear to have good *relative* accuracy, but their zeroing isn't very precise -- if the motor temp changes by 10deg, you'll see the value change by 10, but even on a robot that's been sitting still for hours I've seen the sensors report 10-20 deg different than ambient temperature.
Still, if you just want to see how much the motor temp changes over time, this is pretty handy.
Okay,
I don't know if it is documented as it is pretty new. It is from version 5.5. We now have error handling with the statement ON_ERROR_PROCEED and the 2 subprogram ERR_CLEAR(ERROR_T) and ERR_RAISE(ERROR_T). ERROR_T is a struct. It really *looks like* the "On Error Resume Next" from VB, together with both Err.Clear() and Err.Raise(int)
Here's an example:
DECL CHAR foo
foo = 32 ; Should be okay
ON_ERROR_PROCEED
foo = 1025 ; Error handling: Overflow!
; Here, we catch the error, but we don't know yet
; what kind of error it is:
IF($ERR.NUMBER > 0)THEN
; Check to be sure it is not an Overflow error
IF($ERR.NUMBER == 1423)THEN
; It is an Overflow error: raise it so that we
; stop the program here and show the proper message
; in the Kuka HMI.
ERR_RAISE($ERR)
ELSE
; It's another type of error. In this example, we want
; to step over and continue the program process.
ERR_CLEAR($ERR)
ENDIF
ENDIFWhat is important to know is that the line you want to check for should be the very next line after ON_ERROR_PROCEED. If there is a space in between or something else (even a comment), it will not work. Hope this helps.
$TRACE
This is a handy one if you use the KRC's built-in Oscilloscope feature (MONITOR>DIAGNOSTICS>OSCILLOSCOPE).
Normally, you have to switch to the O-Scope screen and hit the Start button, then switch back to your program and start running. Given how slowly the O-Scope screen comes up/goes down, this can get very tiresome.
Instead, in your program you can trigger the O-Scope to start using $TRACE.MODE=#T_START, monitor the trace status via $TRACE.STATE, and control the name of the trace using $TRACE.NAME[].
Disabling operating modes:
You can disable #T2, #AUT and #EXT on the robots, the function have moved around a bit and is placed in to different places on 8.2 and 8.3
In 8.3 it is placed in C:\KRC\ROBOTER\Config\System\Common\CabCtrl.xml
In 8.2 it is C:\KRC\Roboter\Config\User\Common\CabCtrl.xml
XML tag: <OpModes T2="on" AUT="on" EXT="on"/>
Just change to off to disable and reboot with reload files.
Asimo: Whoa. Okay, I can see just how powerful that could be -- I've wanted something like that more than once in the past. In fact, it could come in handy for something I'm working on right now.Bert: Leave it to you to recognize the exact matrix algebra function on sight.
I knew it had to be some kind of matrix math, but what exactly it was doing escaped me.
I am puzzled about one thing, though. A bit of quick Googling implies that matrix inversions only work on square matrices. An POS or FRAME variable in KRL only consists of 6 elements, though, which it's hard to make a square matrix from. It looks to me as if, in order to make a square matrix, we would need three additional elements (to produce a 3x3 matrix), which must be derived from the original six elements somehow. Or am I overlooking something obvious?
So, anyway, if I have a POS variable of {X,Y,Z,A,B,C}, how would it appear if formatted in matrix form?
did matrix stuff many years ago, may recalled wrong:
matrix=[N O A P](4x4)
which is
nx ox ax px
ny oy ay py
nz oz az pz
0 0 0 1
Euler angle of kuka seems like X-Y-Z
so, [N O A](3x3)= Rotx(A)*Roty(B)*Rotz(C)
http://www.mathworks.com/help/phased/ref/rotx.html
or
ON_ERROR_PROCEED
Ignore error and resume next command.
