When they appear on stage, Heather Knight, a robotics graduate student, and Data, her stand-up-comedy-performing robot, seem like a futuristic Odd Couple. Ms. Knight is tall, blond and human while Data—sheathed in a white plastic shell and about a third her size—resembles a RoboCop action figure.

Data plays the feisty star; Ms. Knight takes on the role of the "straight man." At a performance last year, Data, perched on a stool, waved to the crowd. "I would say it's a pleasure...