I don't have much info about them. These animatronics were created for a premier event for the 2001 film, and Dexter Liu is one of the people who worked on them.
Here is some info taken directly from an archived version of a geocities.ws site:
"DreamWorks launched 'Shrek', a CG animated feature, in the Spring of 2001. Using the smart-motor control technology being developed for Real Friend E.T., we created robotic Shrek and Donkey to assist with the premier event. They stole the spot light and the campaign was a great success."
"Dexter Liu's concept of 'smart motor control' utilizes standard micro processors to control mass market toy-spec electric motors but with custom software. This allows the inexpensive motors to function essentially like high grade servos. This platform coupled with quality animation programming delivers unprecedented life-like magic at low cost mass marketable prices."
Here's another photo of them from designii.com, which shows the electronics.